3_multicomponent_data_processing.pdf

Chapter 3

Multicomponent Data Processing Introduction Multico Multi comp mpon onent ent se seism ismic ic da data ta pr proc oces essin sing g is a co comp mplex lex su subje bject ct th that at wo woul uld d re requ quir iree a se sepparate book to cover all aspects of the topic in a thorou thorough gh manner. This chapter summarizes only basic principles and is not intended to be a complete treatise on multicomponent dataprocessing proces sing concepts and strategi strategies. es. When nine-component nine-component (9C) data are acquired, processing S-wave data propa propagating gating in isotropic isotro pic media is in concep conceptt no dif different ferent than proces processing sing conventional conventional singlesingle-compon component ent P-wave data because SH-SH and SV-SV modes satisfy the constraints of common-midpoint (CMP) data processing just as P data do. The fundamental requirement for CMP processing is that the velocity of the downgoing mode must be the same as the velocity of the upgo up goin ing g mo mode de.. Th That at as assu sump mpti tion on is va vali lid d fo forr SH SH-S -SH H an and d SV SV-S -SV V da data ta ju just st as it is fo forr PP-P P da data ta.. Becausee CMP data-processing Becaus data-processing software and expert expertise ise are widespread, processing processing 9C data to make SH-SH and SV-SV images is not a great challenge to a data processor skilled in processing proces sing conventional P-P data. Processing Proces sing three-component three-component (3C) and four-component four-component (4C) data is a dif different ferent matter. For those data, the velocity of the downgoing wavefield (P-wave) is not the same as the velocity of the upgoing wavefield (SV-wave), and CMP principles no longer apply. A different data-processing strategy based on common-conversion-point (CCP) principles has to be implemen implemented. ted. Some Some of the better better CCP CCP processing processing softwa software re is propri proprietary etary to seismic seismic concontractors and to a few research groups and service providers. The use of CCP software is beginning to be reasonably widespread, and CCP data-processing skills are expanding annually. However, it is accurate to say that in a worldwide context, CCP data processing is not as advance advanced d as CMP data processing. processing. For first-time users of 3C and 4C seismic technology, it is wise to use the services of data processors who can show evidence that they have developed CCP data processing to the level of CMP data processing. Onee da On data ta-p -pro roce cess ssin ing g st step ep th that at ha hass to be do done ne to pr prep epar aree 3D 9C da data ta fo forr CM CMP P pr proc oces essi sing ng of SH-SH and SV-SV modes is that sources and receivers be rotated mathematically from inline/cr cros ossl sline ine da datata-acq acqui uisit sition ion sp space ace,, wh wher eree SH an and d SV mo mode dess ar aree mix mixed ed in va vari riab able le pr prooportions, to radial/transve transverse rse data space where, in isotropic media, SV data are segregated as a radial-component response and SH data are isolated as a transverse-component respon sp onse. se. Th This is so sour urcece-re recei ceiver ver ro rotat tatio ion n do does es no nott ha have ve to be do done ne wh when en ap apply plying ing CM CMP P pr proc ocess ess-ing concepts to P-P data. Calculation of static corrections across marine prospects is another unique aspect of marine multicomponent seismic data. It is not necessary to apply source and receiver

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78

Multicomponent Seismic Technology

static corrections to marine data acquired with towed-cable technology because sources and receivers are surrounded by a homogeneous, constant-velocity medium — seawater. However, when 4C sensors are deployed on the seafloor so that multicomponent data can be acq acqui uire red, d, re recei ceive verr sta static tic co corr rrect ectio ions ns ha have ve to be cal calcu culat lated ed an and d ap appli plied ed to ach achie ieve ve op optim timalalquality P-SV and P-P data, just as is done with land-based data.

Common-midpoint (CMP) processing The bas The basic ic re requ quire iremen mentt fo forr CM CMP P ima imagi ging ng is tha thatt th thee pr prop opag agati ation on ve velo locit city y of the re refle flecte cted d upgoing wavefield be the same as the propagation velocity of the downgoing illuminating wavefield. In the P-P seismic imaging that the oil and gas industry has done for approximately 50 years, downgoing and upgoing wavefields both travel with P-wave velocity V P. CMP software was developed originally to make only P-P images and has been used primarily for only that restricted, single-mode imaging. However, CMP imaging can be applied to any data for which downgoing and upgoing wavefields have equivalent propagation velociti velocities. es. Thus, when 9C data are acquired, SH-SH and SV-SV images, in addition to P-P images, can be made with CMP software. Downgoing and upgoing SH wavefields that travel with velocity V SH SH are segregated from the 9C wavefield and are used to make an SH-SH image. Downgoing and upgoing SV wavefields that travel with velocity V SV SV, which differs slightly from SH velocity V SH SH, also are extracted from the 9C data and are used to make an SV-SV image. Many versions of CMP software are available throughout the seismic data-processing community. Any of those software packages can be used to process 9C seismic data to create crea te SHSH-SH SH and SVSV-SV SV imag images. es. The raypaths involved in such CMP imaging are shown in Figure 1. This Source Receiver diag di agra ram m sh show owss th that at in a fla flatt-la layyXm ered, isotropic earth, CMP reflection points generated at different reflectorr de to depth pthss st stack ack ver vertic ticall ally y ab abov ovee eachotheratcoordinateXm,thecommon midpoint, located halfway beP tween the source station and the receiver station. The image-point trend P labeled CCP in Figure 1 is discussed in the following section. CMP stacking is a powerful imCMP CCP agin ag ing g ste step, p, bu butt it ha hass lim limita itatio tions ns.. Specifically, if significant structure, laterall late rally y var varyin ying g velo velocity city,, and/orazFigure 1. Distinction between subsurface locations of imuthal anisotropy is present in the 9C CMP image points (vertical dashed line) and 3C subsur sub surface face,, CMP stac stackin king g sho should uld CCP CC P im imag agee poi point ntss (c (cur urve ved d da dash shed ed li line ne). ). Ra Rayp ypat aths hs sh show ow be replaced with prestack migration. the propagation paths involved in CMP imaging.

Chapter 3: Multico Multicomponen mponentt Data Proces Processing sing

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Common-conversion-point (CCP) processing Common-midpoint imaging concepts cannot be used when the propagation velocity of the downgoing illuminating wavefield differs from the propagation velocity of the upgoing reflected wavefield. The most common situation in which this wave physics is encountered involves the P-SV mode, which is created when a downgoing P wavefield converts to an upgoing SV wavefield via P-to-SV mode conversion at a reflecting interface. The inverse mode, SV-P, which is created by a downgoing SV wavefield converting to an upgoing P wa wave vefiel field d via SV SV-t -too-P P mo mode de co conv nver ersio sion, n, is an anot othe herr si situ tuati ation on in wh which ich CM CMP P da datataprocessing concepts cannot be used. For each of those converted-S modes (P-SV and SV-P), the image point does not occur at common-midpoint coordinate Xm, as in CMP imaging. In 3C (or 4C) P-SV imaging, the down do wngo going ing wa wave vefiel field d ha hass a fa faste sterr ve velo locit city y (V P) th than an th thee up upgo goin ing g wa wave vefie field ld (V SV SV). As a consequence of Snell’s law, the image point is positioned closer to the receiver station than to the source station. This image coordinate coordinate is called the commoncommon-conver conversion sion point. The raypaths involved in CCP imaging of a P-SV mode are depicted in Figure 2. This diagram shows that in a flat-layered earth, CCP image points generated at different depths do not stack vertically above each other, as CMP image points do, but they move closer to the receiver station as reflecting interfaces are imaged closer to the earth surface. In SV SV-P -P ima imagin ging, g, th thee do down wngo goin ing g wa wave vefiel field d pr prop opag agate atess at a vel veloc ocity ity (V SV that at is sl slow ower er SV) th than that of the upgoing wavefield (V P). As a result of Snell’s law, the image point occurs closer to the source station than to the receiver station. This image point is still called a common-conversion point even though it is located at a subsurface coordinate different from the CCP coordinate associated with P-SV imaging. The raypath involved in CCP imaging of SV-P data is illustrated in Figure 3. Again, image points generated at different depths do not stack vertically above each other as they do in CMP imagSource Receiver ing. in g. In co cont ntra rast st to PP-SV SV ima imagi ging ng,, SV SV-Xm P image coordinates move closer to the source station, not to the receiver station stat ion,, as refle reflectin cting g inte interfa rfaces ces approach the earth’s surface. S

P

CMP and CCP velocity concepts Stacking Stackin g and mig migrati ration on velo veloccities iti es ne need eded ed fo forr CC CCP P SS-wav wavee da data ta processing proces sing have to be determined by analyti ana lyticc pro procedu cedures res dif differ ferent ent than those used in CMP processing. The fundamental reason why a different approach to velocity estimation has

CMP CCP

Figure 2. Distinction between 3C CCP image coordinates (curved dashed line) and 9C CMP image point coordinates (vertical dashed line). Raypaths illustrate propagation paths involved in CCP imaging.

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Source station

Receiver station

SV

SV

Facies 1

Facies 2 P

B A = CCP coordinate coordinate for for P-SV mode mode

P

CMP A B = CCP coordinate coordinate for for SV-P SV-P mode

Figure 3. Distinction between an SV-P CCP raypath (dashed line) and a P-SV CCP raypath (solid line). Positive offset Negative offset

A

B

Facies 1

Facies 2

CMP

Figure 4. Traveltimes for positive offsets are the same as traveltimes for negative offsets in CMP imaging because the lengths of the travel paths in facies 1 and 2 are the same for both offset options. Positive offset Negative offset

A

B

SV

SV

Facies 1

Facies 2 P

CCPB

P

CMP

CCPA

Figure 5. Traveltimes for positive offsets are not the same as traveltimes for negative offsets in CCP imaging because the leng le ngth thss of the P an and d SV ra rayp ypat aths hs in fa faci cies es 1 an and d 2 ch chan ange ge whe hen n th thee offset direction changes.

to be done for CCP data than for CMP data can be explain exp lained ed by ref referr erring ing to thee si th simp mple le ea eart rth h mo mode dell show sh own n as Fi Figu gure ress 4 an and d 5. In this model, there is a ch chan ange ge in ro rock ck fa faci cies es alon al ong g th thee im imag agin ing g ra rayypaths. P-wave velocity V P and SV velocity V SV SV in facies 1 are assumed to be differ dif ferent ent fro from m the val values ues of V and nd V SV V P a SV in facies 2. To emphasize the distinctio tinc tion n betw between een velo velocity city analy ana lyses ses do done ne wit with h CM CMP P and CC CCP P da data, ta, the of offs fset et betw be twee een n so sour urce ce an and d receiv ce iver er st stat atio ions ns ne need edss to be defined in terms of the direction the raypath takes to propagate from the sour so urce ce to th thee re recei ceive ver. r. A receiver offset to the right of the source will be defined arbitrarily as a positive offset; receivers to the leftt of the so lef sour urce ce sta statio tion n then will be in the negative-offset direction. In CMP S-wave imaging in g (F (Fig igur uree 4) 4),, th thee sa same me raypath ray path vel velocit ocities ies and tra travveltimes occur in both negative ati ve an and d po posit sitiv ivee of offs fset et dire di rect ctio ion ns be beca caus usee th thee lengths of the travel paths in facies 1 and facies 2 are the sa sam me when B is th thee source station and A is the receiver rece iver stat station ion (ne (negati gative ve offs of fset et)) as wh when en A is th thee source station and B is the receiver rece iver stat station ion (po (positi sitive ve


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offset). The same stacking and migration velocities therefore are calculated in positiveoffset and negative-offset directions when SH-SH and SV-SV data are processed. A different conclusion is reached in CCP velocity analysis. The raypaths involved in CCP imaging of the P-SV mode are shown in Figure 5. If A is the source station and B is the receiver station (positive (positive offset), offset), the velocity of the downgoing downgoing P mode is contro controlled lled by facies 1, and the upgoing SV velocity is determined by facies 2. The image coordinate is CCPA. When B is the source station and A is the receiver station (negative offset), much of the P-wave velocity is controlled by facies 2, and all of the upgoing SV raypath is in facies 1. The image coordinate is now CCPB. Assuming that velocities V P and V SV SV in facies 1 differ from those of V velocities V P and V SV SV in facies 2, CCP stacking and migration velocities calculated for positive offsets and negative offsets are not the same. The fact that different velocity behaviors are observed in opposite offset directions for P-SV and SV-P imaging is a fundamental distinction between the wave physics of CMP and CCP seismic data. This model is simplified by using straight raypaths. Curved raypaths and prestack migration can vary the positions of the labeled image points. The purpose of the model is only to introduce the importance and distinction of positive and negative offsets in P-SV data processing.

Positive-offset and negative-offset P-SV images As a consequence of this offset-direction dependence of velocity, P-SV data acquired as 3C and 4C data are processed as two separate data volumes — negative offset and positive offset. The two data volumes are processed using stacking/migration velocities calculated separately for each volume. The two distinct images then can be summed to make a total to tal-o -offfs fset et ima image. ge. Mo Most st int inter erpr prete eters rs pr pref efer er th that at a dat dataa pr proc ocess essor or pr prov ovid idee all th thre reee ima image gess — positive offset, negative offset, and sumb) Negative offsets Positive offsets med. me d. Al Alll th thre reee ne need ed to a) 6 be inte interpr rpreted eted.. Som Someetimes a critical piece of geologic informa7 B A B tion is better seen in A one of the images ) s ( than in the two com- e8 C C m i panion images. T Toillustratethose 9 D D concep con cepts, ts, mig migrate rated d PSV images along an 10 offshore 2D 4C profilee ar fil aree di disp splay layed ed in Figure 6. One image Figure 6. Comparison of P-SV images made separately from (a) negais created from only tive-offset data and (b) positive-offset data. Windows A, B, C, and D negativ neg ative-o e-off ffset set data emphasize features that differ between the two images. The horizontal and an d one fr from om on only ly scale is not defined.

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positive-offset data. The subsurface information provided by the two images is in general agreement, but some structural and stratigraphic details differ. Data windows A, B, C, and D are examples of image differences. Window C illustrates differences in stratigraphic detail, with positive-offset data showing discontinuous discont inuous beddin bedding g but negative negative-of -offset fset data showing continuous reflections. Window D shows differences enc es in str struc uctu ture re,, wit with h th thee po posit sitiv ivee-of offs fset et ima image ge ind indiicating cati ng stee steeper per dip tha than n the neg negativ ative-o e-off ffset set imag image. e. Windo Win dows ws A an and d B ill illus ustra trate te ot othe herr dif diffe fere rence ncess in str struc uc-ture and stratig stratigraphy raphy depicted by negativ negative-of e-offset fset and positive-offset data. Additional examples of differences between negative-offset and positive-offset imFigure 7. Sum of the two offsetdomain images exhibited in Figure 6. ages exist across the profiles. The sum of the two images from Figure 6 is disThis composite image is good quality, played in Figure 7. In some parts of the image space, but in certain parts of the profile, the negative-of negati ve-offset fset image or the positi positiveve- po posi sitiv tive-o e-offfs fset et dat dataa det deter ermin minee wh what at ap appea pears rs in th thee offset image might be a better detotal-offset image. In other parts, negative-offset data scription scrip tion of the geology. The horizo horizonn- dominate the total-offset image. When high-dip strata tal scale is not defined. are present, as in this example, ray tracing confirms thatt as a rec tha recor ordin ding g sp spre read ad mo moves ves to towar ward d hig highh-di dip p units, one takeoff direction for a downgoing P wave (say the positive-offset direction) provides a better target illumination than does the other takeoff direction (negative offset). Thus, there are valid reasons why positive-offset and negative-offset data differ when structural dip is present. A seco second nd exa example mple that comp compares ares pos positiv itive-o e-off ffset set and neg negativ ative-o e-off ffset set P-S P-SV V imag images es involving involv ing flat-dip strata is display displayed ed in Figure 8. These images were made from deepwater 4C data using a walkaway VSP data-processing strategy described later in Figures 35 through 38. The objective was to analyze near-seafloor geology and to estimate hydrate concentration near the seafloor. In this case, there is a significant difference between negative-offset and positive-offset images in the data window between 0.9 and 1.1s. Within this interval, negative-offset data show strata that are indicated only faintly with positive-offset data. A puzzling feature of those data is that the imaging difference is not caused by high-dip strata, as was the case for the data shown in Figure 6. In addition, the image differences are not constrained to small, local areas of the image space, as is usually the case. They persist along the entire 14-km length of the profile. Although no subsurface data were available for confirmation, interpreters terpre ters concluded that negativ negative-of e-offset fset data provid provided ed a more reliable picture of geologic conditions in this particular data window. The message is that regardless of the sophistication of the data-processing algorithms applied to P-SV data, it is best to examine and preserve preserve negative negative-of -offset, fset, positiv positive-of e-offset, fset, and and total to tal-o -offfs fset et ima image gess as se sepa para rate te da data ta fil files es an and d gi give ve eq equal ual wei weigh ghtt to the ge geol olog ogic ic in inter terpr preta etatio tion n


provided provid ed by each image unt until il add additio itional nal inform inf ormatio ation n ind indicat icates es tha thatt one par particu ticular lar image should be given greater weight and confidence. Forr si Fo simp mplic licity ity,, 2D pr profi ofiles les are us used ed here to illustrate differences between positive-offs tive-o ffset et and negativ negative-of e-offset fset CCP data. The distinctions in CCP data behavior in these two offset domains can and must be extended to 3D CCP data. In 3D applications, data space around each source station should be segregated into a positiveazimuth azim uth dom domain ain and a neg negativ ative-a e-azimu zimuth th domain. It is arbitrary which 1808 azimuth sector is defined as positive-azimuth space, but once a data processor makes that decision, the remaining 1808 azimuth sector is the negative-azimuth domain. These definitions of positive-azimuth and negativeazimuth data spaces then have to be consistent for all source-receiver pairs across a 3D data grid.

Source and receiver rotation

a)

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Positive-offset Positiveoffset data 0 0.2 0.4

) s 0.6 ( e m i t 0.8 V S - 1.0 P 1.2 1.4 6250 m

1.6 250

50 0

75 0

1000

Station number

b)

Negative-offset data 0 0.2 0.4

) s 0.6 ( e m i t 0.8 V S - 1.0 P 1.2 1.4

When mu When multi ltico comp mpon onen entt sei seism smic ic da data ta 6250 m 1.6 are acquired as 2D profiles, 3C receivers 250 5 00 7 50 1000 Station number can be deployed so that a consistent horizontal sensor is oriented parallel parallel to the verFigure 8. (a) P-SV image made from positiveticall pla tica plane ne pas passing sing thr throug ough h rece receiver iver sta- offset data along the full extent of a deepwater tions. Because of the orthogonal-sensor de- profile. (b) P-SV image made from negativesign of 3C geophones (Figure 16 in Chap- offset data. The negative-offset data image strata ter 2) 2),, th thee co comp mpan anion ion ho hori rizon zontal tal se sens nsor or between 0.9 and 1.1s that are not seen well with then will be oriented perpendicular to this positive-offset data. vertica ver ticall pla plane. ne. Like Likewise wise,, dipo dipole le sou sources rces can be positioned at source stations along a 2D profile so that they create horizontal force vectors parallel to and orthogonal to the vert ve rtica icall pla plane ne pa pass ssing ing th thro roug ugh h so sour urce ce and re recei ceive verr st stati ation ons. s. Tho Those se or orien ientat tation ionss of sources and receivers create 2D S-wave data that have displacement vectors constrained to be either within the vertical plane passing through each source and receiver station or to be orthogonal to that plane, as illustrated in Figure 3 of Chapter 1. The result is that SH-SH and SV-SV data can be acquired along 2D profiles simply by consistent orientation of orthogonal horizontal sensors and orthogonal source-generated displacement vectors.

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However, when multicomponent seismic data are acquired as 3D data, a mathematical rotation of source and receiver orientations must be done to define SH-SH and SVSV wavefields. The procedure is shown in Figure 9. The terms inline and crossline will be use used d to defi define ne data data-ac -acqui quisiti sition on coo coordin rdinates ates in this dis discuss cussion ion.. Som Somee inv investi estigato gators rs

a)

b)

Ri

N A

N Rx

A

q A

Ri Si

B

Rr

q A

d)

N

Rt

Sx

Ri

A

A

Rx

B

C

C

c)

q B

N Rx

q A

Rr

Sr

C

B

q B R r

Rx

q B

Sr

St

B Rt

C St

Figure 9. (a) 9C 3D data-acquisition data-acquisition grid. Receiver lines are oriented north-south; north-south; source lines are oriented east-west. (b) Orientations of inline ( R i) and crossline (R x) horizontal sensors at receiver stations A and B, inline ( S i) and crossline (S x) S-source vectors at source station C, and source-to-receiver directional azimuths u A and u B. (c) Rotati Rotation on of vector sensors sensors at receiv receiver er station A and source vectors at source station C to radial/transverse (R r, R t, S r, S t) data space. (d) Rotation of ve vect ctor or se sens nsor orss at re rece ceiv iver er st stat atio ion n B an and d so sour urce ce ve vect ctor orss at so sour urce ce st stat atio ion n C to ra radi dial al/transv transverse erse data space (R r, R t, S r, S t).


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prefer to use a more general terminology such as H1 azimuth for the coordinate axis of sensor deployment, deployment, with the second coordi coordinate nate axis, H2 azimuth, being orthogonal to H1. In 3D acquisition, sources and receivers must be oriented in consistent orthogonal orientations, as described in Chapter 2. As a result, when vertical planes are extended from a source station to an active receiver across a 3D acquisition template, source-displacement vectors and horizontal sensors are not oriented parallel to and orthogonal to the vertical planes. For example, vertical planes connecting source station C to receiver stations A and B are depicted in Figure 9b. The source-displacement vector and sensor orientation are skewed away from vertical plane AC by angle u A and away from vertical plane BC by a different angle, u B. Nine-c Nin e-comp ompone onent nt 3D data mus mustt be tra transf nsform ormed ed fro from m field field-acq -acquis uisitio ition n coo coordi rdinate natess (inline/cro crossl ssline) ine) to rad radial ial/tr tran ansv sver erse se da data ta sp space ace in wh which ich so sour urcece-dis displ place acemen mentt ve vecto ctors rs an and d sensor orientations are parallel to and orthogonal to the vertical plane that passes through each source-receiver pair across a 3D data-acquisition template. Two of those data-space transformations are illustrated in Figure 9c and 9d. If a 3D acquisition template involves 1000 receiver stations, then 1000 such rotations must be done for every pair of source and receiver stations. The mathematical rotation that converts 9C 3D data to a domain in which SH and SV modes are distinguished more easily is accomplished by using the model illustrated in Figure 10. The coordinate transformation involves trigonometric projection of data from inline/crossl crossline ine coord coordinates inates to radial/transverse coordinates. The following methodology is similar to that of Alford (1986) and DiSiena et al. (1984). Assu As sume me th that at fie field ld da data ta F cre create ated d by co comb mbin inin ing g tw two o ho horiz rizon ontal tal so sour urce ce ve vecto ctors rs S an and d tw two o horizontal horizo ntal receiver receiverss R (vertical source vectors and vertical receivers are ignored) can be described as F

=



Si Ri

Sx Ri

Si Rx

Sx Rx



,

(1)

where subscripts i and x refer to inline and crossline directions, respectively, or to whichever orthogonal H1 and H2 axes are used to define data-acquisition space. The desired output D in radial/transv transverse erse coordin coordinates ates is D

=



Sr Rr

St Rr

Sr Rt

St Rt



,

(2)

where subscripts r and t refer, respectively, to radial and transverse. Using the coordinateaxis rotation matrix M , M (u ) =



cos u sin u −sin u cos u



(3)

and assuming that the orientation angle u is is the same for inline sources and receivers, the forward model of data F acquired in field coordinates is represented by F

= [ M (u )] D[ M T (u )].

(4)

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This eq This equa uatio tion n sta states tes th that at th thee de desir sired ed natural modes D are projected into a fieldcoordinate system which is determined by source sou rce and rece receiver iver ori orienta entatio tions. ns. Ang Angle le u used in these equations is measured clockwise from north (a right-hand, z-down coordina di nate te sy syst stem em wi with th no nort rth h 08). Rec Receive eiverr lines are arbitrarily oriented north-south in Figure 9, which often will not be the inline azimuth. To calculate u , it is necessary to kno now w on only ly th thee ( x,y) co coor ordi dina nate tess of al alll so sour urce ce and receiver stations. This sou source rce/rece receiver iver rot rotatio ation n math mathemaematics is based on several assumptions: (1) Si and Sx source vectors are orthogonal, (2) horizontal sensors Ri and Rx are orthogonal, (3) Si and Ri are aligned and Sx and Rx are aligned, and (4) 3C geophones are a righthanded, orthogonal set of xyz sensors with the positive z-axis pointing downward. Taking advantage of the properties of rotation matrix M that ¼

Figure 10. Transformation from inline/ crossline data-acquisition coordinates to radial/transverse coordinates. SH and SV modes mod es are mixe mixed d in inlin inlinee/cro crossl ssline ine data spa space ce but tend to be segregated in radial/transverse data space unless subsurface subsurface interf interfaces aces have significant 3D structure that produces considerable out-of-plane reflections. D can

be recovered from

F using

M T (u ) = M −1 (u ) = M (−u ),

(5)

the equation

D

= [ M T (u )] F[ M (u )].

(6)

In this notation, M T (u ) rotates the receiver coordinate system (the columns of field data matrix F), and M(u ) rotates the source coordinate system (the rows of F F) to invert the pro jections of equation 4. Even though the terms of equation 5 are mathematically mat hematically equivalent, thee co th cont ntex extt an and d me mean anin ing g of ea each ch de depe pend nd on th thee co conv nven enti tion onss an and d no nota tati tion on us used ed by in indi divi vidu dual al geophysicists. It is possible to interchange the rows and columns of D D and F and the positions of M in these equations equations and arrive at the same result, but this outcome results M T and M in strictly from the assumptions of orthogonality of sources and receivers. MacBeth and Li (1996) describe a mathematical rotation methodology when Si and Sx or Ri and Rx are not orthogonal. Equations 4 and 6 are based on a model that assumes an orthogonal set of two source vectors at each source location. When 3C 3D data are acquired using a vertical-displacement source (shot-hole explosive, vertical vibrator, or vertical impactor), the downgoing P wavefield radiates uniformly in all azimuths (and so does its companion SV wavefiel wav efield). d). Thi Thiss sou sourcerce-rad radiati iation on sym symmetr metry y elim eliminat inates es the nee need d for sou source rce-co -coord ordina inate te rotation, and there is no need to describe a dipole source term. In this case, F simplifie simplifiess to F

=

  SRi

SRx

,

(7)


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where S represents either downgoing P or SV generated at a source station. Thus, for 3C data, the transformation from inline/crossline coordinates to radial/transverse coordinates requires only a rotation of receiver coordinates: D

= [ M T (u )] F.

(8)

This receiver-rotation step also applies to converted-wave data recorded in 4C oceanbottom data acquisition with an air-gun source, with the exception that only a downgoing P-wave propagates through the water column to the seafloor.

Data rotation and signal-to-noise ratio In is isot otro ropi picc me medi diaa or in me medi diaa th that at ha have ve mi mild ld az azim imut utha hall an anis isot otro ropy py,, ro rota tati ting ng 9C 3D da data ta from field-coordinate space to radial-transverse space usually improves signal-to-noise ratio. rat io. An imp impress ressive ive exam example ple illu illustr stratin ating g that principle principle is dis display played ed in Fig Figure ure 11. In some prospect areas, improvements in signal-to-noise character are less than that demonstrated by this example. In this case, the source used to generate S-wave data across this

crossline-oriented ed source and crossl crossline-or ine-oriented iented receiver data Figure 11. (a) Superbin gather of crossline-orient (field-coordi (fieldcoordinate nate data space) and (b) the associ associated ated frequency spectrum. (c) Transv Transverseerse-source source and transverse-receiver data (rotated SH-SH data space) for the same superbin and (d) the associated frequency spectrum. Vibrator sweep 5 to 55 Hz. Data rotation causes the signal in part (d) to be 30 dB above ambient noise, whereas signal in field-coordinate space (b) is only 10 dB above background noise. ¼

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prospect was a horizo prospect horizontal ntal vibrator sweeping sweeping from 5 to 55 Hz. Thus, the frequency range of the input illumination wavelet and the frequency spectrum expected to be exhibited by reflection events are known. There are numero numerous us ways to define and calculate signal-to-noise signal-to-noise ratio. Usually Usually,, signal is de defin fined ed as da data ta th that at ar aree de desi sira rabl blee re refle flect ctio ion n ev even ents ts,, an and d noise is de defin fined ed as dat ataa th that at ar aree no nott reflecti refl ection on events. events. A simp simpler ler concept concept is used used in this exa example mple by defini defining ng signal a ass th thee am ampl pliitude level of data in the 20- to 50-Hz range and ambient background noise as the amplitude level of frequency components above 60 Hz. This simple definition of signal signal does not distingu tin guish ish be betwe tween en ev even ents ts th that at ar aree re reflec flectio tions ns fr from om de deep ep int inter erfac faces es an and d ev even ents ts th that at ar aree unwante unw anted d sha shallow llow-in -interf terface ace wav waves, es, cri critica ticall ref refrac raction tions, s, and inte interbe rbed d mult multiple iples. s. This meth method od of quantifying signal to noise simply indicates the magnitude by which organized events of any kind rise above background ambient noise. The data used in this example are a highfold trace gather across a 3D superbin before applying any moveout to flatten reflections. Using this definition of signal signal to noise, the signal portion of these field-coordinate data is only 10 dB above the noise floor (Figure 11b). After rotation from field-coordinate space to radial-transverse space, the signal portion of the data is 30 dB above ambient noise (Figure 11d). The improvement in the continuity of events caused by coordinate rotation, whether the events are reflection signals, interface waves, or multiples, can be seen by visual inspection of the data displayed in Figure 11a and 11c. Data rotation also causes amplitudes amplitu des of correla correlation tion noise preceding first arrival arrivalss to reduce relative to the amplitu amplitudes des of reflection events. Collectively, those data behaviors demonstrate that the improvement in signal-to-noise character of 9C data produced by rotation from field-coordinate space to radial-transverse space often can be significant.

Effect of 3D geometry on radial/transverse data The geometric shape of a 3D data-acquisition template plays an important role in controlling the degree to which coordinate transformations change the character of S-wave data. Two 3D data-acquisition grids will be used to illustrate that principle. The first survey involves a rather narrow, rectangular template. Data acquired across the template are displayed in Figure 12. Visual inspection of the figure shows little difference between the inline/crossline data and the radial/transverse data. Specifically, the radial SV-SV data (left panel of Figure 12b) look no different than the inline Si Ri data (left panel of Figure 12a), and the transverse SH-SH data (right panel of Figure 12b) do not seem to differ from the crossline Sx Rx data (ri (right ght pan panel el of Figu Figure re 12a 12a). ). How However ever,, dif differ ference encess exist, as demonstrated by the display in Figure 13. To illustrate how inline/crossline data differ from radial/transverse data, the SV-SV and SH-SH data (Figure 12b) are subtracted, respectively, from the Si Ri and Sx Rx data (Figure 12a). As shown in Figure 13, significant differences exist between those data when ther th eree is a sh shor ortt of offs fset et be betw tween een so sour urces ces an and d re recei ceive vers rs,, bu butt dif diffe fere renc nces es ar aree ne negli gligi gible ble for long-offset distances. Referring to the sketch of the narrow, rectangular data-acquisition template that acquired the data (Figure 13), far-offset data occur in area B of the


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transverse verse and inline/crossl crossline ine gathers for the rectan rectangular gular Figure 13. Difference between radial/trans data da ta-a -acqu cquis isit itio ion n tem templ plat atee sh show own n bel below ow th thee dat data. a. Re Recei ceive verr li lines nes ar aree la laid id ou outt al alon ong g th thee lo long ng di dimen mensi sion on of the template. Circle A represents the near-offset domain, and area B represents the far-offset domain. C is a source station. After Simmons and Backus, 1999, Figure 3.

acquisition template where the geometry between source and receiver stations is quasi-two dimensional. All vertical planes that pass through any source-receiver pair within template area B are approximately parallel to the inline direction in which receiver lines are deployed. Thus, there is little difference between inline/crossli crossline ne orient orientations ations and radial/ transverse orientations for source-receiver offsets occurring within data domain B. In contrast, across short-offset area A, receiver stations exist in all azimuth directions around each source station. The acquisition geometry within A is truly three dimensional, and an d th there ere ar aree sig signi nific ficant ant di difffer ferenc ences es be betwe tween en in inlin linee/cro crossli ssline ne ori orienta entation tionss and rad radial ial/transverse orientations. Thus, the geometric properties of a narrow, rectangular data-acquisition template dictate that the long-o long-off ffset set domain will have minor mixing of SH-SH and SV-SV modes, but the short-offset domain will have significant mixing of SH-SH and SV-SV wavefields. The second survey to consider was acquired with a square template. The inline/crossline data and radial/transverse data acquired with this source-receiver geometry are shown in Figure 14. For a square source-receiver patch, there are receiver stations in every

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Figure 14. (a) Superbin gathers in inline/crossline data space for a square data-acquisition template. Note that SV-P converted waves appear in each gather, in contrast to data acquired with a rectangular template (Figure 12). (b) Trace gathers in radial/transverse data space for the same square template. SV-P converted modes are strong on the SV-SV data panel (left), are absent on the SH-SH data (right), and are weak on the two-cross-term panels (two center panels). From Simmons and Backus, 1999, Figures 4 and 5.

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azimuth direction around most source stations, and there is no particular offset range in which the source-receiver geometry degrades to quasi-2D conditions as it does for a rectang ta ngul ular ar te temp mpla late te.. As a re resu sult lt,, th ther eree is se seve vere re mi mixi xing ng of SH SH-S -SH H an and d SS-SV SV mo mode des, s, as de demo monnstrated by the fact that SV-P converted modes appear in all four of the inline/crossline data panels. After the data are transformed to radial/transverse data space (Figure 14b), SV-P converted modes appear only on the SV-SV data panel, which is the correct wave physics. These square-template data can be used to demonstrate the severity of SH and SV mixing in inline/crossline data space. The right two data panels of Figure 15 are the SV and SH data from Figure 14b. The center panel of Figure 15 is an equal-weight sum of the SV and SH data. The two data displays on the left are inline/crossline data from Figu Fi gure re 14 14a. a. Vis Visua uall co comp mpari ariso son n sh show owss th that at th thes esee lat latter ter two tra trace ce ga gath ther erss ar aree ess essen entia tially lly id idenentica ti call to th thee 500-50 50 mi mix x of SV an and d SH dat ataa di disp spla laye yed d in th thee ce cent nter er pan anel el of Fi Figu gure re 15 15.. Be Beca caus usee of this mode mixing, optimal SH-SH and SV-SV images cannot be constructed from inline/crossline data. It is mandatory to first do the source-receiver rotation described in Figure 9 to segregate SV and SH modes into radial/transverse data space. Data processing

Figure 15. Demonstration that SH and SV modes are mixed in 3D field-coordinate (inline/ crossline) data space. The SV and SH data on the right are the radial/transv transverse erse data from Figure 14b. The center panel is the weighted sum of these SV and SH data. The two data panels on the left are the inline/crossline data from Figure 14a. Note the strong similarity between the inline/ crossline data and the 50-50 mix of SV and SH data. From Simmons and Backus, 2001, Figure 5.


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then can proceed by processin processing g the radial data to create an SV-SV SV-SV image and by processing processing the transverse data to create an SH-SH image.

Distinctions between SH-SH and SV-SV modes A fundamental thesis of multicomponent seismic technology and elastic wavefield seismic stratigraphy is that several S-wave modes can be extracted from multicomponent seismic data, and each of those modes can provide different geologic information about the earth than its companion modes can. A concept stressed in several places in this book is th that at th thee gr grea eate test st di difffe fere renc nces es be betw twee een n th thee wa wave ve ph phys ysic icss of SS-wa wave ve mo mode dess oc occu curr wh when en CC CCP P P-SV data are compared with CMP SH-SH and SV-SV data. However, even CMPSH-SH and SV-SV S-wave data differ in fundamental ways. Radial/transverse SV and SH data from Figure 12 are redisplayed in Figure 16. Two distinctions between SH-SH and SV-SV modes can be illustrated with these data. First, the downgoing SV mode converts to two upgoing modes, SV and P, but the downgoing SH mode converts to only one upgoing mode, SH. This wave physics is demonstrated by the presence of both SV-SV and SV-P refraction events on the SV-SV data display but only SH-SH refraction events in the SH-SH data. These refrac fr acti tion on ev even ents ts ar aree la labe bele led d on each data panel. We see in th this is SV SV-S -SV V fie field ld re reco cord rd (Figure 16a) the exact wavefield fie ld be beha havi vior or de descr scrib ibed ed by the SV dual-reflectivity equation ti onss li list sted ed in Fi Figu gure re 11 of Chapte terr 1. In the SH-SH field record (Figure 16b), we see the behavior indicated by the sing single-r le-reflec eflectivi tivity ty equ equaation illustrated in Figure 6 of Chapter 1. The fact th thaat a downgoing SH mode creates only a re refle flect cted ed-S -SH H mo mode de bu butt a downgoing SV mode creates bot oth h refl eflec ecte ted d SV an and d P is why the SH mode is sometimes tim es cal calle led d a “p “pur ure” e” sh shear ear mode. Sai aid d another way ay,, SH-SH field records tend to contain con tain onl only y she shearar-wav wavee in- Figure 16. 9C (a) SV-SV and (b) SH-SH supergathers shown form fo rmati ation on,, bu butt SV SV-S -SV V fiel field d in field-record format (Simmons and Backus, 1999).

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records contain both S-wave and P-wave information mixed together in a rather complicated way, as the SV reflectivity equations imply (Figure 11 of Chapter 1). This distinction between SH-SH and SV-SV data is fundamental. The events that curve across the data panels of Figure 16 between 2 and 3 s are SV-SV reflection events (Figure 16a) and SH-SH reflection events (Figure 16b). It is rare to see SV-P reflections in field-record data, and none is obvious in Figure 16a. However, SV-P reflections can contaminate SV-SV reflections in almost the same proportion that SV-P refractions refrac tions contami contaminate nate SV-SV refract refractions. ions. The second distinction to note between SV-SV and SH-SH data is that there is a significant difference in SV and SH shallow-refraction velocities. This fact is illustrated by marking the distances A and B that S-wave refraction events propagate after 1.5 and 2 s of traveltime. As shown in Figure 16, distances A and B for the SH-SH data are greater than distances A and B for the SV-SV data. SH velocity parallel to shallow bedding (the dire di rect ctio ion n of re refr frac acti tion on tr trav avel el)) is th ther eref efor oree gr grea eate terr th than an SV ve velo loci city ty (F (Fig igur uree 23 of Ch Chap apte terr 1) 1).. To further demonstrate differences between SH and SV propagation velocities, these supergathers were processed to emphasize primary reflection events in the time window between 2 and 2.5s. These processed data are shown in Figure 17. The normal-moveout corrections used to flatten reflection events in both the SH-SH and SV-SV data were done using SH-derived stacking velocities. The SV-SV events are overcorrected (Figure 17a), butt th bu thee SH SH-S -SH H ev even ents ts ar aree flattene flatt ened, d, as exp expecte ected d (Fi (Figgure 17b). In this case, a dif ifffer eren entt NMO velo loccity based on SV velocity analysis is required to flatten deep SV-SV reflections. This test is a compelling demon de monstr strati ation on th that at SH an and d SV sta stack ckin ing g vel veloc ociti ities es ar aree different. The difference between SV and SH velocities depends on the takeoff angle at which a raypath leaves a surface source station. Levin (1979, 1980) has shown that for a layered earth, SH velocity is greater than SV velocity at shallow takeoff angles (Fig (F igur uree 16 16); ); SV ve velo loci city ty is gr great eater er tha than n SH ve veloc locity ity Figure 17. 9C (a) SV-SV and (b) SH-SH trace gathers after over a range of steep takeoff processing to emphasize primary reflections between 2 and angl gles es (F (Fig igur uree 17 17); ); an and d at 2.5s. 2.5 s. Reflection events in both modes are corrected to horizontal an true-v tru e-vert ertica icall an and d on onee mi middevents with SH-derived velocities to demonstrate that SH and range takeoff angle, SH and SV stacking velocities differ (Simmons et al., 1999).


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SV velocities are equal. Part of Levin’s work is illustrated and discussed in Chapter 1 (Figure 23 of Chapter 1). In summary, two key concepts are described by these data: (1) SV-SV data are contaminated with SV-P data but SH-SH data are not, and (2) SH velocity is different from SV velocity. Those two fundamental distinctions sometimes cause one of the S-wave modes, either SH-SH or SV-SV, to react to geologic conditions in a manner different from that of the other mode. It is often not apparent which mode, SH-SH or SV-SV, will wi ll pr prov ovid idee mo more re val valua uabl blee inf infor ormat mation ion ab abou outt a par partic ticul ular ar ge geol olog ogic ic tar targe get. t. Th Thee be best st policy is to acquire data that allow both S-wave images to be created.

9C 3D CMP data processing Horizontal vibrators are a preferred source for generating 9C 3D data. Across some pros pr ospe pects cts,, SH SH-S -SH H an and d SV SV-S -SV V da data ta cre create ated d by ho horiz rizon ontal tal vi vibr brato ators rs of often ten ha have ve a lo low w signal-to-noise ratio, primarily because a horizontal vibrator operates with a drive force that is less than half the drive force of a vertical vibrator, even though both have the same vehicle weight. To overcome low signal-to-noise conditions, data first are analyzed as supergathers in which data are summed across many stacking bins to create excessive stacking fold. SH-SH and SV-SV supergathers from one 9C 3D survey are exhibited in Figure 18. The supergathers span an area of 15 × 15 normal bins. Even though there is a large amount of linear noise, particularly on the SH-SH data, signal emerges. Figure 19 shows the rich S-wave reflection information after subtracting linear noise. SH-SH velocity analyses performed at four of the numerous superbins distributed acro ac ross ss th thee su surv rvey ey ar area ea ar aree illustrated in Figure 20. Any comm co mmerc ercial ial alg algor orith ithm m tha thatt perf pe rfor orms ms ac acce cept ptab able le CM CMP P velocity analysis should produce stacking-velocity results similar to those exhibited in this th is di disp spla lay. y. In th this is st stud udy, y, stacks of 3D P-P and SH-SH data da ta vo volu lume mess we were re cr crea eate ted d usin us ing g a 3D ve velo loci city ty mo mode dell constructed from all superbin velocit vel ocity y fun functio ctions ns det determi ermined ned across the prospect area. This 3D da datata-st stack ackin ing g st step ep us used ed conven con vention tional al CMP con concept ceptss and pro proced cedure uress no dif differ ferent ent in principle from those used in data-processing shops that Figure 18. (a) SH-SH supergather supergather and (b) SV-SV supergather supergather special spe cialize ize in pro proces cessing sing P-P produced by Fairfield Industries across a 9C 3D survey. The source was a horizontal vibrator. CMP data.

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Application of interpreted stacking velocities to individual CMP gathers is illustrate tr ated d in Fi Figu gure re 21 21.. Re Refle flecti ction on ev even ents ts ar aree flatt acr fla acros osss of offs fset et sp space ace wi with th acc accep eptab table le acc accuuracy, and offset-dependent waveshapes are reaso re asona nably bly co cons nsis isten tentt fo forr eac each h re reflec flectio tion n event. These data are now ready for stacking across 9C image space. Optim Op timal al st stack ackss re requ quir iree ite itera ratio tions ns be be-tween velocity analyses and static calculations. Static calculations can be challenging, particularly particu larly for S-wave modes. Compar Comparison ison of inline and crossline P-P and SH-SH profiles through the 3D volumes used in this project are displayed in Figure 22 to demonstrat st ratee th thee in inter terpl play ay be betw tween een ve velo locit city y and statics. Usually,, S-wave data are adjusted to the Usually same timescale as P-wave data to define and interpr inte rpret et dep depthth-equ equiva ivalent lent geo geolog logic ic inte interrvals. In this instance, the opposite approach is taken, and P-wave data are adjusted to Swave data. The adjustment is approximate, nott pre no precis cise, e, bu butt it all allow owss val valuab uable le com compar pariso ison n of P-P and SH-SH data. Data equivalence is supergather after removal Figure 19. SH-SH supergather estab es tablis lishe hed d by filt filteri ering ng th thee PP-wav wavee dat dataa to of linear noise. Processing by Fairfield Indus4 to 25 Hz an and d th then en st strret etch chin ing g P-w -wav avee tries. time coordinates by a factor of 1.9, a factor determ det ermin ined ed in thi thiss ca case se by sei seism smicic-ba base sed d velocity ty ra ratio tios. s. Th Thee SH SH-S -SH H dat dataa th then en are de delay layed ed by 68 680 0 ms an and d dis displa played yed as V P/V S veloci inverse polarity. The result is a rather good registration of depth-equivalent P-P and SHSH reflections. Other options for depth-registering P and S data are discussed in Chapter 5. At the sequential step of data processing displayed here, P-P and SH-SH data have progressed through two cycles of static adjustments and velocity analysis. There is good agreement between P-P and SH-SH images in the inline direction (Figure 22a), but the images have opposing dips at the southwest end of the crossline profile (Figure 22b). The opposing dips correlate with a change in elevation of 70 to 80 ft (21 to 34 m) along this part of the profile. Additional static adjustments are required to bring the dips into alig al ignm nmen ent. t. In th this is re resp spec ect, t, CM CMP P pr proc oces essi sing ng of 9C da data ta is no di difffe fere rent nt th than an co conv nven enti tion onal al pr proocessing of single-component P-wave data.

CCP data polarities A key distinction between CMP and CCP S-wave data is that the polarity of the P-SV mode provided by CCP technology is fundamentally different from the polarity of the

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velocity analyse analysess performed at four superbin locations. locations. Analysis by Fairfield Figure 20. SH-SH velocity Industries. The source was a horizontal vibrator.

SH-SH SH-S H an and d SV SV-S -SV V mo mode dess pr proovide vi ded d by CM CMP P te tech chno nolo logy gy.. These distinctions are emphasized in the discussions of the SV-wave radiation patterns illustrated in Figures 24 through 27 of Chapter 1. Data from a 3C 3D seismic survey will be used us ed to fu furth rther er de demo mons nstr trate ate P-SV polari polarity ty behavio behavior. r. A source station near the cent ce nter er of th thee su surv rvey ey is us used ed to show the CCP response observed at each of the four corners of the survey grid. Data acquired at receiver station 50 in the southeast corner of the survey and at receiver station 488 48 8 in th thee no nort rthw hwes estt co corn rner er

Figure 21. Application of SH-SH stacking velocities to SHSH CMP gathers. The white line traversing each gather defines where an offset mute function will be applied to the data. Processing by Fairfield Industries.

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are displayed in Figure 23. Because the azimuths from the source station to these two receiver stations differ by approximately 1808, the polarity of the P-SV data at these two receiver coordinates should differ by 180 8. Positions of the source and receiver stations and the orientations of inline and crossline vector sensors, RIL and RXL, are shown in map views of the seismic grid accompanying each data display. These horizontal vector

Figure 23. Example 1 of polarities of 3C P-SV data measured in azimuth directions that differ by 1808 and the results of data-processing procedures that convert the data to dipole-source data. Data example from Fasken Oil and Ranch. The source was a vertical vibrator.

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sensors, RIL and RXL, are deployed with the same orientation at every receiver station, as emphasized in Chapter 2 (Figure 8 of Chapter 2). Directions of the sensor arrows in Figure 23 of this chapter indicate the earth-displacement directions that produce positive responses for each sensor. The data trace labeled V is the response of the vertical vector sensor. The long arrow extended away from the source station indicates the raypath of the illuminating P wavefield. Unprocessed 3C data are shown in Figure 23a and 23b. Comparing Figure 23a and 23b shows that data recorded by orthogonal horizontal sensors at receiver station 50 have algebraic signs opposite to those of the data recorded at receiver station 488. Thus, P-SV data exhibit a 1808 change in polarity for azimuth propagation directions that differ by 180 8, as Figure 27 of Chapter 1 indicates. Figure 23c and 23d shows the P-SV data after datapolarit pol arity y rev revers ersals als hav havee bee been n app applied lied to rec receive eivers rs RIL and RXL and rece receiver iver rota rotation tionss have been done to create radial data RR (equation 8). Except for traveltime, the resulting CCP S-wave data are equivalent to CMP data created by a dipole horizontal-displacement source. For a dipole source, there is no change in S-wave data polarity across the area illuminated by the source (Figure 17 of Chapter 1). That constan constant-polar t-polarity ity condition exists for the P-SV data shown in Figure 23c and 23d, and P-SV imaging can proceed only after that type of polarity correction has been made to all the 3C 3D data. Forr co Fo comp mple lete tene ness ss,, da data ta ac acqu quir ired ed at th thee ot othe herr tw two o co corn rner erss of th thee 3C 3D su surv rvey ey ar aree sh show own n in Figure 24. The principles illustrated here are the same as those that have been discussed for Figure 23. First, P-SV data acquired at receiver station 537 in the northeast corner have polarity opposite to the P-SV data acquired at receiver station 4 in the southwest corn co rner er (F (Fig igur uree 24 24aa an and d 24 24b) b).. Se Secon cond, d, the da data ta can be al alter tered ed to re repr prese esent nt con consta stantntpolarization S-wave data similar to what would have been produced by a dipole horizontal-displacement source (Figure 24c and 24d). The adjusted data illustrated in Figure 24c and 24d then can be used for image construction. P-SV-data polarity behavior involving a larger number of receiver stations is exhibited in Figure 25. These data are a 2D profile extracted from a 3D survey in which receiver stations are in line with the source station. The source station is between receiver stations 269 and 270 at the center of the profile. In this instance, the source was an explosive in a shot hole. Wave-physics polarity can be verified by comparing data polarities within data window A and between data windows B and C. Figure 25b shows the data after they have been bee n pol polari arity-a ty-adju djusted sted to sim simulat ulatee hor horizon izontaltal-dis displac placemen ementt data gen generat erated ed by a dip dipole ole source. These polarity-adjusted data then can be processed to create a P-SV image. Figu Fi gure re 25 do docu cume ments nts re resp spon onse sess of th thee inl inline ine ho horiz rizon onta tall ve vecto ctorr se sens nsor orss alo along ng th thee profile. Data shown in Figure 25a confirm that inline horizontal displacements measured to the right of the source station (positive offset) have polarities that are opposite to the polar po lariti ities es of th thee ho horiz rizon ontal tal di disp splac laceme ements nts mea measu sure red d to the le left ft of the so sour urce ce st stati ation on (negative offset).

CMP and CCP stacking During data processing, data traces are positioned across seismic image space by calculating bin locations where successive image points occur. In CMP (9C) imaging of


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Figure 24. Example 2 of polarities of 3C P-SV data measured in azimuth directions that differ by 1808 and the results of converting the data to represent dipole-source data. Data example provided by Fasken Oil and Ranch. The source was a vertical vibrator.

a flat-layered earth, image points occur at the midpoint between source and receiver, rega re gard rdle less ss of th thee de dept pth h of th thee re refle flect ctin ing g in inte terf rfac ace. e. A CM CMP P tr trac acee is sh shif ifte ted d in ti time me (source-static correction, receiver-static correction, other static corrections, and normalmoveout correction), and then the entire data trace is positioned at the common midpoint for the source-receiver pair that produced the trace. This type of imaging is indicated in Figure 26 by the vertical data trace in stacking-bin column A located at the common midpoint for the indicated source and receiver. The illuminating SV wavefield is created at the indicated source station, and the SV reflected wavefield is recorded at the labeled receiver station.

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Robust CMP stacking algorithms are widespread across the seismic industry, and most commercial commerc ial seismic data-processing data-processing shops have extensive experience in CMP processing. Numerous seismic data-processing companies therefore can create good-quality SH-SH and SV-SV images from 9C data because CMP concepts that they have applied countless times are all that are requir required ed to create those S-wave image options. The basic requir requirement ement is that a horizontal-displaceme horizontal-displacement nt vector source be positio positioned ned at the source station to create downgoing SH and SV illumination modes. The raypath notation in Figure 26 indicates Receiver station 250

260

a)

270

280

290

300

290

300

A

0.1 0.2

C

B 0.3 ) s ( e 0.4 m i T

0.5 0.6 0.7

Receiver station 250

260

b)

280

A

0.1

0.2

270

B

C

0.3 ) s 0.4 ( e m i T

0.5

0.6

0.7

Figure 25. 2D field record showing polarity behavior behavior of the inline-horizonta inline-horizontall component of P-SV data. (a) CommonCommon-sourc sourcee gather as record recorded. ed. Posit Positive-of ive-offset fset data and negative negative-of -offset fset data have opposite opposi te polarities. (b) When polarit polarity y of negativ negative-of e-offset fset data is revers reversed, ed, the data are equiva equivalent lent to data generated by an S-wave dipole source. A, B, and C are data-comparison windows.


103

Source

Receiver

SV SV

P

SV

CCP statics distribution over several bins

1

2

3

4

CMP statics affect only one bin

5

6

7

A

Figure 26. Comparison of 9C CMP image trace (vertical in stacking bin A) and 3C CCP image trace (curved across stacking bins 1 through 7).

only downgoing and upgoing SV modes because the objective here is to distinguish only between SV-SV and P-SV imaging. The curved wiggle trace in Figure 26 shows where the data trace would be distributed across the image space if a P-wave source occupied the source station, a 3C vector sensor occupied the receiver station, and the data were acquired according to 3C P-SV imaging constraints. In this case, the downgoing raypath is a P-wave, and the upgoing raypath is an SV mode. In contrast to CMP data processing, the static and normal-moveout time adjustments made to the image trace affect data across several columns of stacking bins. Segments from several CCP traces have to be patched together to create a stacked trace in eac each h co colu lumn mn of sta stacki cking ng bi bins ns.. Fo Forr ex examp ample le,, th thre reee 3C CC CCPP-pr proc oces essed sed da data ta tra traces ces that are offset from one another by one bin dimension in seismic image space are shown in Figure 27. That part of trace A between points 1 and 2 has to be combined with the data window extending from points 2 to 3 of trace B and with the data window extending between points 3 and 4 of trace C to create a vertical wiggle trace extending from point 1 to point 4 in the shaded stacking-bin column. CCP stacking is thus fundamentally different from CMP stacking. As a consequence of the more complex requirements of CCP stacking, some seismic data-processing shops do not have the software or experience needed to do 3C P-SV imaging. Even data-processing

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shops that hav shops havee esta establis blished hed them themselv selves es as repu re puta tabl blee CC CCP P da data ta im imag ager erss co cont ntin inue ue to develop software and to improve older algorithms.

Asymptotic binning Although construction of 3C P-SV imagess con age concen centrat trates es on det determi erminin ning g accu accurate rate values of V P/V S over the total image space, some so me da data ta pr proc ocess essor orss tak takee sh shor ortcu tcuts. ts. On Onee common shortcut is to do asymptotic binning. In asymptotic binning, the CCP coordinate for the deep part of the image space, where the CCP image trace is almost vertical (Figures 26 and 27), is calculated, and then the entire data trace is assumed to be aligned vertically at that coordinate. This approximation would cause all the curved trace in Figure 26 to be positioned in stacking bin 7, th thee as asym ympt ptot otic ic bi bin n fo forr th that at tr trac ace. e. Th Thee deep part of the image would be correct, but the upper part would be incorrect, with the imaging error error increas increasing ing as a reflectin reflecting g interface approaches the earth’s surface. For deep targets tar gets,, asym asympto ptotic tic bin binnin ning g is acce acceptab ptable. le. For shallow targets, it is not. Moree adv Mor advanc anced ed dat data-p a-proc rocessi essing ng sho shops ps usua uall lly y li limi mitt th thee us usee of as asym ympt ptot otic ic bi binn nnin ing g to vertical image trace in one us Figure 27. A single vertical stacking bin of CCP image space (shaded col- the calculation of surface-consistent paramumn) must be constructed by summing data eters such as statics, deconvolution testing, from different time windows of all CCP traces an and d amp amplit litud udee sca scalin ling. g. Th They ey the then n re repla place ce that traverse the bin. that shortcut technique with procedures that calculate time-dependent and space-dependent estimates of V P/V S over total CCP image space. In so doing, however, they still often take shortcuts, such as giving little attention to determining accurate values of V P/ V S in shallow data windows if there is no exploration interest in shallow targets. This imaging philosophy is a practical procedure in the low-profit-margin business of seismic data processing. There is no financial reward for work done to make the shallowest part of a P-SV image correct unless an interpreter is interested in shallow geology.

Gamma functions The pr The prin incip cipal al pa para ramet meter er th that at co contr ntrols ols th thee cur curvat vatur uree of a PP-SV SV tra trace ce in CC CCPP-ima image ge sp space ace is the V P/V S velocity ratio in the propagation medium. A model illustrating this for small

Chapterr 3: Multico Chapte Multicomponen mponentt Data Proces Processing sing

105

Source Receiver angles angl es of in incid ciden ence ce in a ho homo moge ge-XP XSV neou ne ouss ea eart rth h is pr pres esen ente ted d in Fi Figu gure re 28 28.. This simple, straigh straight-rayp t-raypath ath model shows that a P-SV image coordinate is de defin fined ed by of offs fset etss XP and XSV from fr om th thee so sour urce ce and re recei ceive verr sta sta-SV tions and that these offsets are proportional to the V P/V S velocity ratio in the propagation medium. The b a top equation listed in Figure 28 is P Snell’s law of reflection, the middle equation is a statement of the raypath geometry shown in the model, CCP and an d th thee bo bott ttom om eq equa uati tion on is va vali lid d sin (a ) V P = (Snell’s law) when the incident angles are small sin (b ) V SV enough eno ugh tha thatt sin(u ) is the same as tan(u ), ), which to some data procestan (a ) XP sors can be as large as 208. = tan (b ) XSV For larg larger er ang angles les of inci inciden dence ce and reflection in a layered earth, the relat re lation ionsh ship ip bet betwe ween en CC CCP P ima image ge XP V P ~ (for small angles) XSV coordinates and the V P/V S velocity V SV ratio is more complex than the simple rela relatio tionsh nship ip illu illustr strated ated in Fig Fig-- Figure 28. Simple, straight-raypath model showing that uree 28 ur 28.. Fo Forr ex exam ampl ple, e, Ch Chun ung g an and d the velocity ratio V P/V S in the propagation medium controls the position of a CCP image coordinate in P-SV Corrigan (1985) developed a P-SV image space. imag im agin ing g al algo gori rith thm m fo forr a la laye yere red d earth using the model displayed in Figure 29. The equation shown in this figure accounts for curved raypaths and allows stacked-earth layers to have variable thicknesses and P and S velocities. For a source-receive cei verr pa pair ir sep separ arate ated d by dis distan tance ce X, CC CCP P ima image ge po poin ints ts ar aree po posi sitio tione ned d acr acros osss PP-SV SV image space using only the V P/V S velocity-r velocity-ratio atio behavior along the P and SV propa propagation gation paths. Other forms of P-SV imaging algorithms algorithms have been develo developed, ped, but they all have the common feature that the V P/V S velocity ratio across a layered earth determines where CCP image coordinates are positioned in P-SV image space. When processing P-SV data, it is therefore necessary to determine V P/V S velocity ratios across seismic image space and to use those continuous velocity-ratio fields to position ti on CC CCP P im imag agee po poin ints ts.. Th Thee te term rm gamma function co comm mmon only ly is us used ed to de desi sign gnat atee th thee V P/V S velocity ratio used in CCP imaging. Because of the offset-direction dependence of velocities in CCP imaging (Figure 5), separate gamma functions need to be determined for positive-offset P-SV data and for negative-offset P-SV data when 2D data are analyzed and for reciprocal azimuth domains when 3D data are processed. An example of a gamma-function analysis for positive-offset data along a 3C profile is displayed in Figure 30. Figure 30a shows a starting estimate of the V P/V S velocity ratio. This initial gamma-function estimate can be determined by a variety of means — P and

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S velocity logs, VSP data, data-processing data-processing experience, experience, or guesswork. guesswork. Figure 30b shows the qual qu alit ity y of PP-SV SV im imag ages es ac acro ross ss a sm smal alll se sect ctor or of th thee pr profi ofile le ce cent nter ered ed on CM CMP P co coor ordi dina nate te 200 200 when P-SV data are stacked with this assumed gamma function function adjusted by factors factors ranging from 0.7 to 1.2. The algorithm that created these particular P-SV image strips differs in detail from the equation listed in Figure 29, but it has a commonality with that equation because it uses the V P/V S velocity ratio to position CCP image points. The solid circles in Figure 30b show the choices of V V P/V S velocity ratio that this particular data processor thought created an optimal image in the local vicinity of CMP 200. Figure 30c shows an a) XP

XS

Source

Receiver

V P

j P

SV

Layer 1 2

ΔZ

j s Layer k

Layer k P N

P

N

SV

XS = ∑ ΔZ ktan j s,k

k=1

k=1

N k=1

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k

XP = ∑ ΔZ ktan j P,k

XP = ∑

ΔZ

N

ΔZ k V P,k p

N

XS = ∑

CCP

[1-(V P,k p)2]1/2

k=1

ΔZ k V S,k p

[1-(V S,k p)2]1/2

X

b) XP

Ts = vertical two-way SV traveltime Source

Receiver

TP = vertical two-wa two-way y P traveltime

Layer 1

V S =

SV velocity

V P =

P velocity

k P

SV

X

XP = 1+ N

2

TS

V S

TP

V P rms

X

= 1+

V P

V S 2

V S avg

V P rms

CCP

Figure 29. (a) P and SV propagation through a layered-earth system showing raypath behavior in one individual layer. p is horizontal slowness [sin(u )/V ], where u and and V relate to downgoing P or upgoing SV as needed for calculation. (b) Position of CCP image point for propagation in layered media. X is the source-to-receiver offset; XP is the position of the CCP image point relative relative to the source station. To calculate XP, it is necessary to know the V P/V s velocity ratio along the propagation propag ation path (Chun (Chung g and Corrigan, 1985).


a) 0

b)

107

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2 4 ) s ( e m i t 6 V S P

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70 80 90 100 110 120 Velocity multiplier (%)

100

200 CMP

300

Figure 30. (a) Starting estimate of the V P/V S velocity ratio (gamma function). (b) Stacks of positive-of posit ive-offset fset P-SV data across a small profile centered on CMP 200 when this gamma function is adjusted by factors ranging from 0.7 to 1.2. Solid circles show the choices of V V P/V S that the processor decided produced an optimal P-SV stack of positive-offset data. (c) Larger view of the P-SV profile centered on CMP 200. Data processing by WesternGeco.

expand expa nded ed vi view ew of th thee im imag agee th that at ad adds ds confi co nfide denc ncee to th thee se selec lectio tion n of th thee V P/V S velocity-ratio behavior chosen by the data processor. When this procedure is repeated along the full line of profile, the result is the continuous tinu ous gamm gamma-f a-func unction tion field acro across ss 600 CMPss of seis CMP seismic mic imag imagee spa space ce illu illustr strated ated in Figure 31. When this gamma-function field is combined with independently determined V P veloc velociti ities es an and d ap appl plied ied to bo both th negativ neg ative-o e-off ffset set and pos positiv itive-o e-off ffset set P-S P-SV V data, the results are the velocity fields displayed in Figure 32.

0 1.0 V P / V VS

2.0

1.60

) 3.0 s ( e m4.0 i t

1.85

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2.22

6.0 2.80

7.0 8.0

3.75 0

600

CMP

Smoothed d gammagamma-functio function n field Figure 31. Smoothe for positive-offset data along a 4C profile. Data processing by WesternGeco.

Marine 4C receiver statics Source, receiver, and elevation static corrections are essential data adjustments when processing onshore seismic data. Static corrections rarely are needed when processing

108 a)


0 V P

1.0

m/s 3400

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) s ( e 3.0 m i T 4.0

2950 2475 2000 1550

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) s ( 4.0 e m i T 5.0

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Figure 32. (a) P-wave velocity determined by CMP processing. processing. (b) SV velocit velocity y determ determined ined from positive-off positive-offset set CCP data by dividin dividing g CMP-based V P by the positive-offset positive-offset gammafunction (Figure 31). (c) SV velocity determined from negative-offset P-SV data by dividing CMP-based V P by the negative-offset gamma-function (not shown). Data processing by WesternGeco.

towed-cab towedcable le P-w P-wave ave mar marine ine data data.. Exce Excepptions tio ns oc occu curr on only ly acr acros osss of offs fsho hore re ar area eass wh wher eree there are significant changes in sea level betwee tw een n hi high gh an and d lo low w ti tide dess as se sequ quen enti tial al ca cabl blee tows traverse traverse a prosp prospect ect (for example, Cook Cook Inlet) or where seismic profiles traverse an abruptt contact between freshwater and saltabrup water (such as the mouth of the Amazon River Riv er). ). Ho Howev wever er,, wh when en 4C sen senso sors rs are pla placed ced on the the seafloor seafloor,, it is essen essential tial to calcul calculate ate and apply receiver-station static corrections to both P-P and P-SV data acquired at those sensor positions. A mo mode dell that ill illus ustr trate atess the maj major or iss issue uess involved in seafloor receiver static corrections tio ns is sh show own n in Fi Figu gure re 33 33.. Ac Acro ross ss so some me of offfshore areas, significant variations occur in seafloor topography, which introduces the requirement for elevation static corrections at receiver stations just as for processing onshor ons horee dat data. a. Like Likewise wise,, V P and V S velocities can vary laterally in the shallowest seafloor strata, just as they do across near-surface layers in onshore environments. Near-seafloor V P velo velociti cities es are som sometim etimes es reas reasona onably bly consis con sistent tent acro across ss rath rather er larg largee of offsh fshore ore area areas. s. In such cases, velocity-based velocity-based receiver static corrections might not need to be applied to P-P data acquired with 4C seafloor sensors. In other areas, V P velocity in near-seafloor strata can vary across a study area and thus require careful attention to velocity-based P-wave receiver statics. It appears that V S velocities tend to vary rapidly and significantly in many near-seafloor strata, and velocity-based S-wave receiver static corrections are essential for processing P-SV data acquired acquir ed with 4C seafloo seafloorr sensor sensors. s. Examples of P-SV data acquired along two profiles profiles with 4C seafloor seafloor sensor sensorss are displayed in Figure 34. Receiver-station static shifts of reflected P-SV events along these profiles create false indications of minorthrow faults that extend to the seafloor. A


single sing le pas passs of re recei ceive verr-sta statio tion n stati st aticc co corr rrect ectio ions ns re remo move vess th thee stati st aticc-in indu duce ced d fau fault lt th thro rows ws on line li ne 1 (F (Fig igur uree 34 34c) c).. A se seco cond nd pa pass ss of receiver static corrections appea earrs to be nee eed ded on li lin ne 2 (Figure 34d) to adjust a vertical anomaly in the image.

Sea level

109

}

+ h Tidal action +h

Seafloor sensor Elevation corrections

o o r f l o S e a

Static-correction layer

Imaging deepwater, near-seafloor geology using walkaway VSP concepts

Datum

receiver-station on static corA com common mon-re -receiv ceiver er gath gather er Figure 33. Factors that require receiver-stati rections when 4C sensors are deployed on the seafloor of 4C data acquired at a seafloor include adjustments for changes in seafloor topography recei re ceive verr sta statio tion n in insid sidee a de deep ep-(elevation) and lateral velocity variations in the shallowest water hydrate study area of the seafloor strata. Data need to be static-corrected to represent Gulf of Mexico is shown in data acquired at receiver stations positioned on a constantFigu Fi gure re 35 35.. Re Recei ceive verr sta statio tions ns we were re elevation datum plane. spaced spa ced at 2525-m m int interv ervals als alon along g ocean-bottom-cable (OBC) profiles that traversed the study area, and air-gun shots were taken at intervals of 50 m as a source boat traversed the 2D line of seafloor sensors. The key sensor-response equations involved in OBC data acquisition are illustrated and explained in Figure 36. Defining D as the downgoing compressional wavefield that reaches a seafloor station and U as the upgoing compressional wavefield at that same station, the responses of the hydrophone P, vertical geophone Z, and inline horizontal geophone X are

P = D + U,

(9)

Z = (D − U)cos(F ), X = (D + U)sin(F ) + SV waves.

(10)

(11)

The incident angle at which the downgoing compressional wave arrives at the seafloor is F. Thes Thesee equ equatio ations ns imp imply ly that aft after er app approp ropria riate te cali calibra bration tion,, a seafl seafloor oor hyd hydrop rophon honee response (P) and a seafloor vertical-geophone response (Z) can be combined to create the unknown downgoing (D) and upgoing (U) P-P wavefields at each receiver station using the follow following ing relation relationships: ships: D = P + Z/cos(F )

(12)

110 a)


0.0

Line 1

0.5

Line 2

0.5

) s ( e m i T

) s ( e m i T

1.0

1.0

1.5

1.5 241

c)

b) 0.0

321

401 481 Receiver station

0.0

561

241

321

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481

561

Receiver station Line 1

0.5

d) 0.0

Line 2

0.5

) s ( e m i T

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1.5 241

321

401

481

561

241

Receiver station

321

401

481

561

Receiver station

Figure 34. Examples of P-SV data acquired along (a) line 1 and (b) line 2 before receiver-station statics are applied. Arrows identify locations where images are distorted because of static shifts caused by lateral variations in near-seafloor V S velocity. (c) Line 1 data after receiver static corrections. (d) Line 2 data after receiver static corrections. The arrow in part (d) identifies a receiver-stati ceiver -station on interv interval al where additional static corrections might be needed.

and U = P − Z/cos(F ).

(13)

A mu multi ltiply plying ing fa facto ctorr of 0. 0.5 5 is omitte omitted d on th thee ri righ ghtt-ha hand nd si side de of th thes esee equatio equations ns bec becau ause se that that scaling factor is not important for wavefield separation. By having access to the downgoing (D) and upgoing (U) P-P wavefields, subseafloor P-P reflectivity R can be recovered by taking the ratio RPP = UP /DP

(14)

in the frequency domain, f . The inverse Fourier transform of RPP( f ) ) then creates a timebased reflectivity series that starts at the seafloor and extends to a depth below the base of the hydrate stability zone. This time-based reflectivity RPP(t ) is used to create high-resolution images of deepwater, near-seafloor geology.


a)

P

0

b)

0.5

) s ( e1.0 m i T

) s ( e 1.0 m i T

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111

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Figure 35. 4C OBC data collected at a single deepwater seafloor receiver station in the Gulf of Mexico. Source spacing is 50 m along the horizontal axis that defines the range of source-receiver offs of fset et.. At th this is lo locat catio ion, n, a se sea-b a-bot otto tom m mu mult ltip iple le app appea ears rs at a nor normal mal-i -inci nciden dence ce ti time me of 1. 1.75 75 s. Al Alth thoug ough h this multiple dominates the P-P section (a) when it arrives, it is ignored because its arrival time is below the targeted hydrate zone. However, the sea-bottom multiple also appears on the X (inline horizontal) component data (b) and interferes with P-SV reflections arriving later than 1.75 s. These P-SV events are in the range of hydrate interest. The polarity of the negative-offset data on the X sensorr has not yet been reversed to match positive-off senso positive-offset set data polari polarity. ty. The cross crossline line Y componen componentt (c) is low amplitude and can be ignored in the data-processing flow. (d) Z is the response of the vert ve rtic ical al geo geoph phone one.. P is th thee hy hydr drop opho hone ne re resp spon onse se.. Th Thee am ampl plit itude udess of Z and P dat dataa di difffe ferr by a fa fact ctor or of approximately 15 but are scaled to equal-amplitude displays.

The term (D + U) in equation 11 is the hydrophone response P. When the hydrophone response is calibrated to the horizontal geophone response X, weighted by sin(F ), ) , and subtracted from X, the difference is the upgoing SV mode, designated as U PS. A procedure similar to equation 14 then is used to determine the reflectivity of the P-SV wave. The extracted P-SV wave is divided by the downgoing P wavefield in the frequency domain to produce P-SV reflectivity, defined as RPS = UPS /DP .

An inverse Fourier transform produces time-based P-SV reflectivity.

(15)

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Ray tracing through a layZ = vertical geophone ered-velocity model of subsearesponse f floor flo or ge geol olog ogy y th then en is us used ed to X = radial horizontal U geophone response calculat calc ulatee cur curves ves of sou source rce-re -re-D Z = angle of incidence f = ceive cei verr of offs fset et ve vers rsus us tim timee tha thatt D = downgoing wavefield corres cor respon pond d to refle reflectio ction n dep depth th P X Seafloor U = upgoing wavefield poin po ints ts lo loca cate ted d a fix fixed ed-o -offfs fset et distanc dis tancee fro from m the rec receive eiverr loP=D+U cation. cati on. Exa Example mpless of ray ray-tr -trace ace Z = (D – U) cos( f ) X = (D + U) sin( f ) + SV waves curves calculated for one common-receiver gather are shown responses of 4C ocean-bottom ocean-bottom senso sensors. rs. Figure 36. Basic responses in Fi Figu gure re 37 37b b fo forr de depth pth-p -poi oint nt The three response equations listed here are the keys to this offsets starting at +10 m from unique imaging concept. The response of the Y (crossline) the receiver station and increashorizo hor izonta ntall geo geophon phonee is ignored. ignored. A key assumpti assumption on is tha thatt the ing in g at 25 25-m -m int inter erval valss to +160 m V P/V S velocity ratio is high, which positions the P-to-SV from fro m the rece receiver iver coo coordi rdinate nates. s. conversion point almost directly beneath the seafloor reImag Im agee-tra trace ce da data ta th then en can be re re-ceiver station. As a result, the upgoing SV raypath is almost covered by interpolation along vertical, and essentially all the SV response is on inline horizontal geophone X. The SV wavefield then can be the curves to produce P-P imseparated from the X response by calibrating and weighting agee tra ag traces ces at sp spec ecifie ified d de dept pthhthe P response and subtracting it from X. The wavefield that point offsets from the receiver is subtracted from X is calculated by a constrained crosslocation. equalization filter that changes P to X. Thee 4-k Th 4-km m PP-P P ima image ge in Fi Figguree 37 ur 37aa is a se serrie iess of sm smal alllscale, local P-P images constructed at each seafloor receiver station. Each local image is created by first calculating P-P reflectivity at each receiver station using equation 14. The P-P reflectivity at one arbitrary seafloor station A is shown in Figure 37b. A sequence of constant-depth-point offset traces then is calculated across these P-P reflectivity data, such as a data trace that would follow any of the curves that are shown overlaying overlaying this particular P-P reflectivity. It was decided arbitrarily to interpolate a P-P image trace at depthpoint offset intervals of 5 m. Five of the traces create a five-trace, 25-m-wide local image. This Th is ima imagi ging ng pr proc oced edur uree was do done ne at 16 160 0 co cons nsecu ecutiv tivee re recei ceive verr st stati ation onss sp space aced d at int inter erval valss of 25 m along the profile to make the 4-km P-P image that is displayed in Figure 37. The same scenario is repeated in Figure 38 for P-SV reflectivity. The principal difference between P-SV imaging and P-P imaging is that the low-magnitude V S velocities in deepwater, near-seafloor strata do not allow the P-to-SV conversion point to be farther than 1 or 2 m from each seafloor receiver station. As a result, a 25-m-wide P-SV image with 5-m trace spacing cannot be created local to each receiver station as with P-P data. Instead, a single zero-offset P-SV image trace is created at each receiver coordinate by summing all the traces between the 1-m depth-point offset curves shown in Figure 38. The result is a P-SV image along each OBC profile that has a trace spacing of 25 m, the same distance as the receiver-to-receiver interval. This data-processing strategy is equivalent to concepts that have been used for almost thre th reee de decad cades es to pr proc ocess ess wa walka lkawa way y ve verti rtical cal se seism ismic ic pr profi ofiles les.. Th Thee co conc ncep epts ts can be ap appli plied ed to P = hydrophone response


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Figure 37. (a) 4-km P-P near-seafloor image traversing a deepwater Gulf of Mexico hydrate prospect. (b) The imaging process that creates a local, five-trace, 25-m-wide P-P image at receiver station stati on A. This This commoncommon-receive receiverr P-P imaging proces processs was done at 160 consecutive consecutive receiv receiver er stations stations along this OBC profile to create the 4-km image shown in part (a). From Hardage et al., 2009.

deepwater 4C data acquisition because there is a large difference between the elevations of the source and receivers, just as there is when a surface source shoots into deep-well receivers. The deconvolution techniques used to define P-P and P-SV reflectivities (equations 14 and 15) cause the seafloor to begin at image time T 0 in P-P and P-SV image space. As a result, the seafloor is always flat in images created with this walkaway-VSP data-prodata-processing strategy. strategy. Seafloor topograp topography hy can be imposed on the images images if desired because because vertical P-wave traveltime to each seafloo seafloorr receiver can be measured from field data (Harda (Hardage ge et al., 2009). Each local image is made from a common-receiver gather. Thus, each of the 25-m imag im agee st stri rips ps us used ed to ma make ke th thee lo long ng-p -pro rofil filee im imag ages es in Fi Figu gure ress 37 an and d 38 in invo volv lves es no re rece ceiv iver er static corrections. Long-profile images constructed by abutting these local images thus can be compared with images made by other data-processing data-processing techniques techniques to determi determine ne whether correct receiver-static corrections have been applied using whatever alternative strategy was employed in the second data-processing effort. ¼

Wave-equation datuming Industry practice for processing deepwater 4C data typically involves wave-equation movementt of sources and receiver movemen receiverss to t o a common common-elevatio -elevation n datum. Standard data-processing data-processing

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Figure 38. (a) 4-km P-SV near-seafloor image traversing the same OBC profile as the P-P data shown in Figure 37. Depths below the seafloor are labeled along the right margin. (b) The imaging process that creates a local, one-trace, zero-offset P-SV image at receiver station A. This single image trace is the sum of all of the traces between the 1-m depth-point offset curves. This commonreceiver receiv er P-SV imaging imaging process was was done at 160 consecutive consecutive receiver receiver stations stations along this OBC profile profile to create the 4-km image shown in part (a). From Hardage et al., 2009.

algorithms based on the assumption of common-elevation coordinates for source and receiver stations then can be used to create P-P and P-SV images. When there is a large elevation elevatio n difference difference in the field positio positions ns of sources and receivers, as there is in deepwa deepwater ter 4C data acquisit acquisition, ion, wave-equation wave-equation datuming not only moves source and receiver stations vertically vertica lly but also laterally, sometimes by signific significant ant distances, as illustra illustrated ted in Figure 39. In this illustration, data generated at sea-level source station S are recorded at seafloor receiver station R. Wave-equation datuming adjusts the data to be equivalent to data acquired as if the source station and receiver station were on a common datum plane Zd. These new stations Sd and Rd are moved both vertically and laterally from the positions of stations S and R. Likewise, the original midpoint coordinate A between source S and receiver R is repositioned to coordinate B midway between stations Sd and Rd. P-P and PSV images then are made using algorithms that have been used for years to process data wher wh eree so sour urce ce an and d re rece ceiv iver er st stat atio ions ns ar aree on th thee sa same me da datu tum m pl plan ane. e. Af Afte terr im imag ages es ar aree co cons nstr truc ucte ted d


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in this adjusted adjusted station-c station-coor oordin dinate ate space, an inverse inverse datuming datuming pro process cess is appl applied ied to tran transfo sform rm the images to the original field-coordinate space in which the data were recorded. Wave-equation datuming is a powerful and useful data-processing step for deepwater 4C data. Several 4C P-P and P-SV images presented in this book were made using a waveequation datuming strategy. It is only when the data-processing objective is to study nearseafloor, deepwater geology that an alternate imaging strategy such as that described in Figuress 36 through 38 needs Figure needs to be considered. considered. Data comparisons comparisons in Figur Figures es 40 and 41 illustrate the differences between wave-equation-datuming and walkaway-VSP strategies for imaging near-seafloor, near-seafloor, deepwa deepwater ter geolog geology. y.

S

Offset (× 10 3 ft) 4 6

2

8

10

Sea level

2 Seafloor ) t f

3

4

0 1 × (

h t 6 p e D

Zd

Rd

Sd P

P P A

B

A

B

8

10

R

surfa face ce so sour urce ce P S = sur

Sd = datumed source R = OBS OBS st stat atio ion n Rd = datumed receiver A = CMP for original source and receiver B = CMP for datumed source and receiver Zd = datum plane

Wave-equation on datumFigure 39. Wave-equati ing of deepwater 4C source and receiver receiv er statio stations. ns. Raypat Raypaths hs are drawn to simulate P-P CMP imaging. The selected elevation datum Zd is arbitrary. A subseafloor position is indicated in this example. Wave-equation datuming adjusts data generated at sea-level source station S and recorded at seafloor receiver station R to data equivalent to those involving source and receiver stations Sd and Rd on the same datum plane. These new equal-elevation equal-el evation stations are displaced vertically and laterally from stations S and R.

Figure 40. Comparison of P-P images of deepwa deepwater, ter, near-seafloor geology made with (a) wave-equation datuming strategy and (b) walkaway VSP strategy. A walkaway VSP approach produces a superior image across a significant interval near the seafloor. The imaging advantage of a walkaway VSP approach weakens with increasing increasing depth below the seafloor,, and waveseafloor wave-equation equation datuming produces the superi superior or image at depths of most marine oil and gas targets.

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Calibrated-sensor versus uncalibratedsensor 4C data Whenseafloor-basedsensors are used to acquire multicomponent seismic data in marine mari ne env enviro ironmen nments, ts, dat dataaprocessing process ing strateg strategies ies involv involvee adding add ing an and d su subt btra racti cting ng hy hy-drophone and geophone data. Many data processors ignoree sen nor sensor sor cali calibra bratio tion n and simp si mply ly ad add d an and d su subt btra ract ct P (hyd (h ydro roph phon one) e),, Z (v (ver erti tica call Figure 41. Comparison of P-SV images of deepwater, neargeopho geo phone) ne),, and X (ho (horizo rizonta ntall seafloor geology made with (a) wave-equation datuming strategy geopho geophone) ne) wavefiel wavefields ds using and (b) walkaway VSP strategy. The improvement in image timetim e-in inva varia riant nt sca scalin ling g fa faccquality of geology is not as dramatic as it is for P-P data tors to rs to ba bala lanc ncee th thee am ampl plii(Figure 40). A walkaway VSP approach produces a superior tude tu dess of th thee re resp spon onse sess of ge geooimage across a narrow interval immediately below the seafloor, phone and hydrophone data. and then the two images have equivalent quality. At depths of It is important to determine most marine oil and gas targets, wave-equation datuming prowhether whe ther hyd hydrop rophon hone, e, ver vertitiduces the superior image of the two data-processing strategies. cal-geo calgeopho phone, ne, and hor horizo izonntal-geophone sensors should be ca cali libr brat ated ed bef efo ore P, Z, and X wav wavefie efield ldss ar aree co commbined bin ed to cr creat eatee do down wngo goin ing g and upgoing P-P and P-SV wavefields. OBC OB C dat dataa acq acqui uire red d alo along ng one marine profile were processed using both calibrate calibrateddsensor and uncalibrated-sensorr da so data ta to de dete term rmin inee th thee value of sensor calibration in imagee con imag constr structi uction. on. A typ typical ical trace gather of data acquired by a se seaflo afloor or-b -base ased d hy hydr drooCommon-hydroph hydrophone one trace gather constr constructed ucted at a Figure 42. Commonphone along this line is disreceiver station along the test line. played in Figure 42, with data adjusted to a reduced-time format in which the arrival time of the downgoing direct arrival is defined as T 0. Principal features of the data are labeled in the figure. Several air-gun bubbles are obvious ¼


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as fla flatt ev even ents ts pa para rall llel el to th thee dire di rect ct ar arri riva val, l, an and d nu nume mero rous us P-P reflection events appear as “smiles “sm iles.” .” Ear Earlyly-arr arrival ival even events ts appearing before the direct arrival riv al at larg largee of offse fsets ts rep repres resent ent isolated pure uptraveling events that th at ar aree us usef eful ul fo forr se sens nso or-r -reespons sp onsee cal calibr ibrati ation on.. Bec Becaus ausee equations 12 and 13 require that hydrophone and geophone data be adde ad ded d or su subt btra racte cted d to iso isolat latee thee do th down wngo going ing PP-P P wa wave vefiel field d from fr om up upgo goin ing g PP-P P an and d PP-SV SV wavefields, wavefiel ds, these estimatio estimations ns of upgoing and downgoing wavefields should be more accurate when wh en th thee ari arith thmet metica icall co comb mbiinations of hydrophone and geophon ph onee dat dataa in invo volv lvee cal calibr ibrat ated ed receiver responses using data such as these early-arrival early-arrival events. The common-receiver trace gather for the vertical geophone (Z geophone) positioned at the same sa me re rece ceiv iver er st stat atio ion n is di dissplayed in Figure 43. The four types of events — direct arrival, water-column multiples, primary P-P reflections, and early arriva ri vall — are sim simila ilarr to th thos osee se seen en Common mon-re -recei ceiver ver tra trace ce gat gather her for the ver vertic tical al in the hydrophone trace gather. Figure 43. (a) Com geophone. (b) Same data with P-SV reflections emphasized. However, important differences exist between hydrophone and vertical-geophone data: †

†

Air-gu Airgun n bu bubb bbles les ar aree we weake akerr on the ve vert rtica ical-g l-geop eopho hone ne da data ta (F (Fig igur uree 43 43)) th than an on th thee hy hydr droophone data (Figure 42) because direct and reflected waves interfere constructively in the hydrophone response but destructively in the vertical-geophone response (Figures 29 through 33 of Chapter 2). The vertical-geophone response contains P-SV reflections in addition to P-P P-P reflections. These P-SV reflection events appear as low-curvature (almost flat) events in a reducedtime display. Several of these reflections are highlighted Figure 43b to illustrate how they appear in common-receiver gathers.

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The comm commonon-rece receiver iver trac tracee gather of data recorded by the inline horizontal geophone (X geophone) is illustrated in Figure 44. Thee ra Th raw, w, un unpr proc oces esse sed d da data ta ar aree disp di spla laye yed d in Fi Figu gure re 44a 4a.. Fi Figgure 44b shows the data after the polarit pol arities ies of the neg negativ ative-o e-off ffset set trace tr acess ar aree re reve vers rsed ed.. If th thee ea earth rth consists of flat, horizontal layers, the polarity of negative-offset data acq acquir uired ed wit with h an inl inlin inee ho hori rizo zonntal geophone should be opposite to the pol polarit arity y of pos positiv itive-o e-off ffset set data. These data do not conform to tha thatt pri princip nciple. le. Pos Positiv itive-o e-off ffset set dataa and neg dat negativ ative-o e-off ffset set dat dataa do indeed have opposite polarity for refle re flecti ction onss th that at ex exten tend d to de dept pth h Z1 below the seafloor. This Th is no norm rmal al be beha havio viorr of Xgeophone data is seen best by the good phase alignment of the positive-offset and negative-offset data be betw twee een n Z1 and and th thee sea seaflo floor or that is exhibited in the “flippedpolari pol arity” ty” dis display play.. How Howeve ever, r, bel below ow depth Z1, the data have a phase shift that causes a simple polarity chan ch ange ge of a ne nega gativ tivee-of offs fset et re re-Figure 44. Common-receiver gather for the horizontal X- fle flect ctio ion n ev even entt to no nott al alig ign n wi with th geophone. (a) Data as recorded. (b) Data after reversing the its positiv positive-of e-offset fset equival equivalent. ent. The polarity polari ty of negati negative-of ve-offset fset traces. Reflect Reflections ions below depth anomalo ano malous us pha phase se beh behavio aviorr emb embededZ1 have a different phase shift than do reflections generated ded in the data below depth Z1 above Z1 because of local reflector dip. Rugose reflector interfaces at depth Z1 (and possibly deeper) cause polarity is caused by geology, not by the receive eiver. r. Othe Otherwi rwise, se, the sha shallow llow reversals to occur at offsets that are positioned either left or rec data da ta ab abov ovee de dept pth h Z1 would would not right of zero offset. Examples of some of these polarity exhibit the normal, expected bereversals are circled in part (a). havior of a horizontal inline geophon ph one. e. On Onee lik likely ely cau cause se fo forr th thee anomalous phase shift below coordinate Z1 is local reflector dip, not layer anisotropy. Local Lo cal di dip p wil willl cau cause se po polar larity ity re reve vers rsals als to oc occu curr at so sour urce ce-o -offfs fset et co coor ordin dinate atess th that at ar aree shifted away from the zero-offset coordinate, as occurs with these data. No subseafloor data are available local to this profile to define stratigraphic dip or to confirm anisotropic rock properties.


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The long-offset geometry involved in the data acquisition along this profile produced the early-arrival events noted in Figures 42 and 43. These events are upgoing wide-angle reflections, reflectio ns, head waves, and diving waves (Figure (Figure 45) that are ideal for calculating sensorto-sen tosensor sor cali calibra bration tion ope operato rators rs beca because use the they y are not con contami taminate nated d by any dow downgo ngoing ing events. Wide Wi de-a -ang ngle le da data ta wi winndows from the common-hydrop dr opho hone ne tr trac acee ga gath ther er ar aree shown in the left panels of Figu Fi gure re 46 46aa an and d 46 46b. b. Th Thee cente ce nterr pan panel el in Fi Figu gure re 46 46aa show sh owss th thee hy hydr drop opho hone ne re re-spon sp onse se est estima imated ted fr from om th thee early ea rly-a -arr rriva ivall wav wavefie efield ld re re-corded by the vertical geophone (Z). The center panel in Fig igu ure 46b shows the hydrophone response calculated late d fro from m the earl early-a y-arriv rrival al wave wa vefiel field d re reco cord rded ed by th thee inline inl ine hor horizon izontal tal geo geopho phone ne (X). The panels on the right Figure 45. The early-arrival events labeled in Figures 42 and of Figure 46a and 46b illus43 consist of upgoing (1) wide-angle reflections, (2) head trate the difference between waves, and (3) diving waves.

Figure 46. Early-arrival wavefields used to calculate sensor-to-sensor calibration operators. These data windows are the wavefields labeled “Early-arrival events” in Figures 42 and 43 that extend above the T 0 time datum; hence, the time coordinates are negative. These displays show that operators determined from these upgoing wavefields can convert either (a) vertical-geophone data or (b) inline horizontal-geophone data to hydrophone data. ¼

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Figure 47. Example Exampless of operat operators ors determined from early-arrival early-arrival events that allow hydroph hydrophone one (P), vertical-geophone (Z), and horizontal inline-geophone (X) data to be transformed from one sensor response to the other. (a) Operators are independent of offset. This offset range is the same as that displayed in Figure 46. (b) Expanded views of operators calculated at one specific offset.

the hydrophone data and each of the hydrophone responses estimated from the respective earl early-a y-arri rrival val wav wavefiel efield. d. The dif differ ference encess are app approx roximat imately ely zer zero, o, con confirm firming ing that sensor-to-sensor calibration operators calculated from full-wavefield early arrivals do a reasonable job of converting one sensor response to its companion-sensor response. Examples of sensor-to-sensor calibration operators calculated at different source-toreceiver offsets are plotted in Figure 47. An important finding illustrated in this figure is that these operators appear to be independent of offset, as demonstrated by the consistency of the op oper erato ators rs in th thee of offs fsetet-de depe pend nden entt pa panel nelss in Fig Figur uree 47 47a. a. Co Cons nseq eque uent ntly, ly, a si sing ngle le sen senso sorrcalibration operator can be used for the complete offset range of each common-receiver gather. Port Po rtio ions ns of th thee PP-P P im imag agee al alon ong g th this is pr profi ofile le ar aree il illu lust stra rate ted d in Fi Figu gure re 48 48.. Fi Figu gure re 48 48aa il illu lusstrates geology that extends to only 200 ms below the seafloor. Figure 48b focuses on the geology that exists between 200 and 500 ms below the seafloor. These images show that in this instance, sensor calibration improves image quality only for the shallowest geology that extends to 50 ms below the seafloor. Below 50 ms, calibrated-sensor data and uncalibrated-sensor data produce equivalent images. Simple frequency filters and timeinvariant scalar multipliers worked just as well as did more sophisticated transforms that adjusted the phase and amplitude responses of hydrophones and geophones. Although this same data behavior often is observed when comparing calibrated-sensor and uncalibrated-sensor 4C data, it is wise to repeat such tests when marine 4C data are acquired with any contractor’s technology or when the same data-acquisition technology is moved to a different type of seafloor environment. Simple frequency filtering and adjustments of amplitudes by scalar multipliers might not be adequate in all situations. Thiss data anal Thi analysis ysis establishe establishess tha thatt alth althoug ough h sen sensor sor-ca -calibr librated ated 4C data migh mightt not improve the imaging of deep-marine geology, such data do improve the resolution of


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near-seafloor geology. Sensor calibration appears to be quite important when studying seafloor geomechanical geomechanical properties. For example example,, amplitud amplitudee and phase spectra of hydro hydrophone phone and ver vertica tical-g l-geop eophon honee cro crossss-equ equaliz alizatio ation n filte filters rs calc calculat ulated ed at 400 suc success cessive ive rec receive eiverr stations along this profile (a distance of 5 km) are displayed in Figure 49. The corresponding spectra for the hydrophone and horizontal-geophone calibration operators are shown in Figure 50.

Figure 48. Comparisons of P-P images made without and with calibrated P and Z sensors. Calibrated data produce a superior image of the shallowest geology (top 50 ms, right panel of part [a]). There are no signifi significant cant dif difference ferencess betwe between en the calibr calibrated-se ated-sensor nsor and uncalib uncalibratedrated-sensor sensor imag im ages es at de deep eper er de dept pths hs (b (bot oth h pa pane nels ls of pa part rt [b [b]) ]).. Th Thee im impr prov oved ed PP-P P im imag agee in th thee fir first st 50 ms of im imag agee space is important for P-P to P-SV image registration when studying geology and geotechnical properties proper ties immediately below the seafloo seafloor. r.

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sensor-calibration on operators deterFigure 49. (a) Amplitude and (b) phase spectra of Z-to-P sensor-calibrati mined at 400 consecutive consecutive receive receiverr statio stations ns along the test profile profile.. An indivi individual dual operator was determined at receiver station intervals of 12.5 m.

Figure 50. (a) Amplitude and (b) phase spectra of the X-to-P cross-equalization filters determined at the same receiver stations analyzed in Figure 49. The color bars used in this display are more sensitive than those used for Figure 49.


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The properties of the spectra displayed in Figure 49 are reasonably consistent along the entire profile, and they show why a single, averaged Z-to-P calibration operator is almost as effective as station-dependent operators. However, there are local variations in the spectra, an example of which is the behavior between stations 550 and 600. For some near-seafloor studies, such as geomechanical evaluations of seafloor strata involved in seafloor installations and anchor sites, these types of local variations in sensor behavior define defi ne irr irregu egulari larities ties in sed sedimen imentt cou couplin pling g that mig might ht be valu valuable able ind indicat icators ors of elas elastic tic properties of seafloor strata. The X-to-P spectra (Figure 50) do not exhibit an anomalous behavior between stations 550 and 600 as do the Z-to-P spectra, but they do show anomalies at other locations along the profile, such as between stations 680 and 740. The physics of why these sensor-calibratio sensor-calibration n variati variations ons occur between these particular receiver stations and why Z-to-P and X-to-P spectral anomalies do not occur at the same locations needs further study by researchers in seafloor geomechanics.

3_multicomponent_data_processing.pdf

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