A priori model building building Inversion parameterization and QC of results
Ad A d v anc an c ed i n v ers er s i o n t ech ec hn i q u es
Geostatistical inversion
Joint PP/PS inversion
4D inversion
Geostatistical inversion
Geostatistical inversion concept Generate impedance models that satisfy the statistics of the input data: mean, variance, variogram
Impedance models are geologically constrained:
• stratigraphic framework • 3D a priori information • variograms Wavelet
Vertical covariance on Well lo g
Amplitud e
0 0
time
Horizontal variogram on seismic (h)
1
Statistical L F a prio ri mod el AI
1
20ms 0
800 m h
time Mean Mean +/- 2*s.d.
Variogram analysis Variogram: Mean squared difference between pairs of points as a function of distance
Horizontal variogram (seismic amplitude)
Semi-variogram Model Data varianc e
Lag Distance (feet)
Horizontal variograms (2D) are calculated parallel to stratigraphy
Vertical variogram (AI well log s)
Vertical (1D) variograms along the vertical direction (Courtesy O. Dubrule)
Lag Distance (feet)
Semi-variogram Data variance Combined Model Model Structure 1 Model Structure 2
Geostatistical inversion algorithm For each global realization Define a random path through all nodes (x,y) to be sim ulated
Trace loc ation to be simulated
For each node (x,y) perform a local optimization
(x,y)
generation of a large number of local realization s o f acoust ic impedance traces, such that inpu t data statisti cs are honoured
convol utio n with t he wavelet
comparison w ith t he actual seismic
retain the best t race which b ecomes conditioning data
Go to next node
Actual seismic trace
Local realizations
Dozens of realizations… Real. 7
Real. 27
All honour the well and seismic data Real. 13
Real. 31
Main features of geostatistical inversions One realisation
Impedance realizations honour - seismic data - well data
4
AI (km/s . g/cc)
9
Great number of AI realisations =>
Mean
uncertainty on impedance results High vertical frequency of impedance realizations controlled by vertical variogram model
SD
Impedance results are at high resolution related to the stratigraphic grid definition (~ 2 - 8m ; ~ 0.5 - 2ms) 0
AI
(km/s . g/cc)
0.7
Frequency bandwidth in a geostatistical inversion Statistical layer constraints control low frequencies Seismic amplitudes control medium frequencies Variogram model controls high frequencies
Seismic bandwidth
(Courtesy E. Robein & L. Barens)
How to summarise geostatistical inversion results? Threshold impedance probability without s eismic
1
P (AI > 6.6)
0
N
Threshold impedance probability with seismic
From impedance to petrophysical properties 50 Impedance realizations 50 Porosity realizations
Impedance vs. Porosit y
Collocated cokriging
Deterministic versus Stochastic inversion The mean of all stochastic realizations looks like the deterministic, but it is different in details Ra-10 w
Ra-7 w
Ra-1 w
Ra-10 w
Ra-1 w
Ra-7 w
0.25ms sampling rate
4ms sampli ng rate
Reservoir Top
Reservoir Top
s m 5 1 Reservoir Base
Reservoir Base
STOCHASTIC REALIZATION
DETERMINISTIC Red color indic ates low AI
& porosi ty development
Ra-10 w
Ra-1 w
Ra-7 w
Litho 3 > 15% Litho 2 10< < 15%
W -10
Reservoir Top
Litho 1 < 10%
W -1 W -7
Reservoir Base 4 km
CO-SIMULATED LITHOTYPE Depth Map
Joint PP/PS inversion
Joint PP/PS inversion Simultaneous inversion of PP and PS seismic volumes PS data need to be transformed into PP time and reflections need to be correlated Calibr ation of PS data with shear-wave logs is necessary Joint PP/PS inversion often constrains IS better than single PP inversion
