PHYSICAL PROPERTIES OF ROCK EXPERIMENT REPORT
Author:
Febrian Sukma W.
3714100027
2014
TEKNIK GEOFISIKA INSTITUT TEKNOLOGI SEPULUH NOPEMBER SURABAYA 2016
CHAPTER I CHAPTER I PRELIMINARY 1.1 BACKGROUND Geophysics is an interdisciplinary physical science concerned with the nature of the earth and its environment and as such seeks to apply the knowledge and techniques of physics, mathematics and chemistry to understand the structure and dynamic behavior of the earth and its environment. The physical properties of earth materials (rocks, air, and water masses) such as density, elasticity, magnetization, and electrical conductivity all allow inference about those materials to be made from measurements of the corresponding physical fields - gravity, seismic waves, magnetic fields, and various kinds of electrical fields. Because Geophysics incorporates the sciences of Physics, Mathematics, Geology (and therefor Chemistry) it is a truly multidisciplinary physical science. One of the important things on Geophysic study is wave. It is being so important because Geophysicist activity can’t be separated separ ated from the waves phenomena. For example, in seismic methode, we used a wave called seismic waves to measure the properties of rock inside the Earth. We know that A seismic wave is an elastic wave generated by an impulse such as an earthquake or an explosion. Seismic waves may travel either along or near the earth's surface (Rayleigh and Love waves) or through the earth's interior (P and S waves).. To measure the wave properties, we used a tool called Oscilloscope. An oscilloscope is a laboratory instrument commonly used to display and analyze the waveform of electronic signals. In effect, the device draws a graph of the instantaneous signal voltage as a function of time. A typical oscilloscope can display alternating current (AC) or pulsating direct current (DC) waveforms having a frequency as low as approximately 1 hertz (Hz) or as high as several megahertz (MHz). High-end oscilloscopes can display signals having frequencies up to several hundred gigahertz (GHz). The display is broken up into so-called horizontal divisions (hor div) and vertical divisions (vert div). Time is displayed from left to right on the horizontal scale. Instantaneous voltage appears on the vertical scale, with positive values going upward and negative values going downward. Other signals (such as sound or vibration) can be converted to voltages and displayed. Oscilloscopes are used to observe the change of an electrical signal over time, such that voltage and time describe a shape which is continuously graphed against a calibrated scale. The observed waveform can be analyzed for such properties as amplitude, frequency, rise time, time interval, distortion and others. Modern digital instruments may calculate and display these properties directly. Originally, calculation of these values required manually measuring meas uring the waveform against the scales built into the screen of the instrument. That’s why we have to know how to use oscilloscop e. From this tool, we can know about the properties of the wave. By knowing all that stuff, we are expected to know the type of rocks that we observed before and easier us later in determining the rock formation that appropriate with the physical characteristic of rocks that have potential to store the natural resources. Because of all that stuff, we do the experiment of physical properties of rocks.
1.2 PROBLEMS FORMULATIONS This experiment have some problem to explore : 1. How to use oscilloscope? 2. How to measure the wave properties (Vp&Vs) using oscilloscope? 3. How the relation between Vp with density and porosity? 4. How to measure young’s modulus? 5. How to measure shear modulus? 6. How to measure poisson’s ratio? 7. How to know the type of the rock sample?
1.3 OBJECTIVES This experiment had two main objective as output : 1. Use oscilloscope to measure wave properties using parameter of time and sample dimension 2. Measure anisotropy of velocity using few model of calculation 3. Determine the relation between Vp with density and porosity 4. Measure the bulk modulus, shear modulus, and poisson ratio from the rock sample 5. Determine the type of rock sample base on the experiment
1.4 BENEFITS From this experiment, the student get some benefits such as : 1. Students know how to use oscilloscope 2. Students can measure the wave properties using oscilloscope 3. Students can analyze few model of calculation to determine anisotropy of wave properties 4. Student know the relation between Vp with density and porosity 5. Student know how to measure bulk modulus, shear modulus, and poisson’s ratio 6. Student can identify the type of rock base on their physical properties
CHAPTER II LITERATURE REVIEW 2.1 WAVE One of the simplest ways to demonstrate wave motion is to take the loose end of a long rope which is fixed at the other end and to move the loose end quickly up and down. Crests and troughs of the waves move down the rope, and if the rope were infinitely long such waves would be called progressive waves – these are waves travelling in an unbounded medium free from possible reflection.
If the medium is limited in extent; for example, if the rope were reduced to a violin string, fixed at both ends, the progressive waves travelling on the string would be reflected at both ends; the vibration of the string would then be the combination of such waves moving to and fro along the string and standing waves would be formed. Waves on strings are transverse waves where the displacements or oscillations in the medium are transverse to the direction of wave propagation.When the oscillations are parallel to the direction of wave propagation the waves are longitudinal. Sound waves are longitudinal waves; a gas can sustain only longitudinal waves because transverse waves require a shear force to maintain them. Both transverse and longitudinal waves can travel in a solid. (H.J. Pain, 2005, 108-109)
2.1.1 WAVE PHASE The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic motion. The same concept applies to wave motion, viewed either at a point in space over an interval of time or across an interval of space at a moment in time. Simple harmonic motion is a displacement that varies cyclically, and described by the formula :
2.1.2 R EFLECTION If a linear object attached to an oscillator bobs back and forth within the water, it becomes a source of straight waves. These straight waves have alternating crests and troughs. As viewed on the sheet of paper below the tank, the crests are the dark lines stretching across the paper and the troughs are the bright lines. These waves will travel through the water until
they encounter an obstacle - such as the wall of the tank or an object placed within the water. The diagram at the right depicts a series of straight waves approaching a long barrier extending at an angle across the tank of water. The direction that these wavefronts (straightline crests) are traveling through the water is represented by the blue arrow. The blue arrow is called a ray and is drawn perpendicular to the wavefronts. Upon reaching the barrier placed within the water, these waves bounce off the water and head in a different direction. The diagram below shows the reflected wavefronts and the reflected ray. Regardless of the angle at which the wavefronts approach the barrier, one general law of reflection holds true: the waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier. This is known as the law of reflection.
2.1.3 R EFRACTION Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves. In Lesson 2, it was mentioned that the speed of a wave is dependent upon the properties of the medium through which the waves travel. So if the medium (and its properties) is changed, the speed of the waves is changed. The most significant property of water that would affect the speed of waves traveling on its surface is the depth of the water. Water waves travel fastest when the medium is the deepest. Thus, if water waves are passing from deep water into shallow water, they will slow down.
2.1.4 DIFFRACTION Reflection involves a change in direction of waves when they bounce off a barrier; refraction of waves involves a change in the direction of waves as they pass from one medium to another; and diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path. Water waves have the ability to travel around corners, around obstacles and through openings. This ability is most obvious for water waves with longer wavelengths. Diffraction can be demonstrated by placing small barriers and obstacles in a ripple tank and observing the path of the water waves as they encounter the obstacles. The waves are seen to pass around the barrier into the regions behind it; subsequently the water behind the barrier is disturbed. The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength. In fact, when the wavelength of the waves is smaller than the obstacle, no noticeable diffraction occurs.
(HTTP://WWW.PHYSICSCLASSROOM.COM/CLASS/WAVES/LESSON-3/R EFLECTION,R EFRACTION,-AND-DIFFRACTION, 2015)
2.2 ELASTIC PROPERTIES Hooke’s law describes the relationship between stress and strain of anelastic material. In ageneral formulation, the stress_strain relationship is atensorial equation:
where
σik is the stress tensor εik is the strain tensor Ciklm is the elastic modulus (or stiffness) tensor. If strain is expressed as a function of stress, the resulting strain_stressrelationship is
where
Diklm is the elastic compliance tensor. Besides the Lame parameters λ,μ, any pair of two of the following modulican be used for a descriptionof the elastic properties of an isotropicmaterial:
Young’s modulus E, defined as ratio of stress to strain in a uniaxial stressstate; Compressional wave modulus M, defined as ratio of stress to strain in auniaxial strain state; Bulk compressional modulus k, defined as ratio of hydrostatic stress tovolumetric strain ; Shear modulus μ, defined as ratio of shear stress to shear strain;
Poisson’s ratio v, defined as the (negative) ratio of lateral strain to axialstrain in a uniaxial stress state. Corresponding to the two moduli are two independent body waves:
Compressional, longitudinal, or P-wave with the velocity:
Shear, transversal, or S-wave with the velocity:
where ρ is the bulk density. (Schon,2011,149-150) However, if elastic wave velocities and bulk density are known frommeasurements, the elastic parameters can be calculated:
(Schon J. H., 2011)
2.3GEOMECHANICAL PROPERTIES Examples of geomechanical problems are:
Deformation and failure processes originated by tectonic stress, earthquakes,etc.;
Landslides and rockfall;
Deformation of the underground (settlement) and subsurface constructions(tunnel, cavern) caused by the pressure of construction in civilengineering;
Slope and dam stability (failure problems);
Wellbore stability and fracturing;
Reservoir compaction during production and subsidence. There are two different types of response on a stress field:
1. The geomechanical response (deformation and/or a failure). 2. The geophysical response as change of the magnitude of a measuredparameter (e.g., velocity or resistivity).
Figure 2.3.1 The physical problem of geomechanical properties evaluation in the term of geophysical parameters.
(Shon,2011,245-246)
2.3.1 FUDAMENTAL LABORATORY TECHNIQUES Rock mechanical properties in the laboratory are determined in most cases at cylindrical sampes by observing the rock deformation(strain) under the influence of a defined stress. The International Society of Rock Mechanics (IRSM) has defined standards for sample preparation : the length of the cylindrical sample must be two to three times the diameters. For granular material, the diameter should be at least 10 times the diameter of the largest grains (Fjaer et al., 1992). Two types of properties are determined: 1. Static elastic or deformation moduli, 2. Strength properties.
A laboratory system consists of a triaxiall cell with a load frame, pressure system, and sensors. The rock sample is placed between the loading pistons introducing the axial stress σv, and is covered by
a surrounding (rubber or plastic) sleeve. The sleeve separat es the rock sample and the fluid introducing the radial stress σ H . Deformation are measured with different type of direct and indirect sensors.
Figure 2.3.2Traxial cell with a rock sample covered by the sleeve; the cell has pressure s ystem for axial pressure and radial pressure and a corresponding system for measurement of strain.
Triaxial cell allows different test, for example :
Standard test starting with σv = σ H and then an increase of
σv at contantσ H until failure
occurs ;
Test under drained or undrained condition for porous rocks; Simplified versions without radial stress or unconfined (uniaxial) tests mainly for determination of uniaxial compression strength. (Schon J. H., 2015, 274-275)
2.3.2 DEFORMATION PROPERTIES Deformation properties are derived from a static compression test. Young’smodulus is defined as ratio of an axial stress and the resulting axial strain:
The stress-strain diagram in most cases shows a nonlinear shape.Therefore, in general, the modulus is stress-dependent and defined as:
In engineering applications, Young’s modulus (modulus of elasticity) isoften derived from the linear portion of the stress-strain curve. Poisson’s ratio is defined as the relative change of the radius divided bythe relative change of axial length in stress direction:
(Schon J. H., 2015)
2.4 PRINCIPLES OF LABORATORY MEASUREMENTS There are two main techniques for measuring elastic rock properties in the laboratory (Fig. 2.1) : 1. Transmission technique : An ultrasonic pulse from the transmitter passes through the sample. The receiver transform the arriving elastic wave into an electrical signal. An oscilloscope visualizes the received signal and the travel time can be picked ( note the dotted connection between generator and oscilloscope for triggering). This principle can be combined with static measurement. Sophisticated equipment allows waveform storage, measurement of compressional and shear wave, and simulations of external and pore pressures, as well as temperatures. 2. Resonance technique : A transmitter ( driven by a frequency generator) generates vibrations of a cylindrical sample. The receiver detects the vibrations as amplitude signal. An amplitude versus frequency plot delivers a resonance curve. Resonance frequency is controlled by sample geometry and Young’s modulus. Thus, Young’s modulus can be determined. Resonance measurement in a torsional mode yield the shear modulus. From the shape on the resonance curve, the Q – factor characterizing the wave attenuation can be derived. ( Schon, 2015 , 174 – 175)
FIGURE 2.4.1 Principles of measuring technique for seismic / clastic rock pr operties. (Schon J. H., 2015)
Result of the sonic – pulse measurement were used to compute – P and Swave velocities and elastic moduli by use of the following formulas ( Howell , 1959; Jaeger, 1962) :
Where ,
Vp Vs σ/v E G L Tp Ts
: longitudinal – wave velocity : shear – wave velocity : Poisson’s ratio : Young’s modulus : shear modulus : length : longitudinal – wave traveltime : shear – wave treaveltime
ρ
: density
G
: gravity
(Holmes, 1978) Although these rock properties have a long list (e.g., Poisson’s ratio, Young’s modulus, shear modulus, bulk modulus, etc.), in reality, there are only two impedances or wave velocities that we need to measure to calculate these parameters: compressional or primary wave velocity (Vp) and shear or secondary wave velocity (Vs). Probably, the simplest parameter derived from these velocities is the ratio of these velocities (Vp/Vs) that is usually considered as one of the most useful parameters for lithological classification of rocks. This parameter has a simple relation to one of the most important geomechanical properties, dynamic Poisson’s ratio (vd), as follows:
(http://geomechanicscorner.com/category/uncategorized/page/2/)
2.5 SEDIMENTARY R OCK 2.6 DENSITY AND POROSITY 2.6.1 POROSITY “Porosity is the fraction of rock bulk volume occupied by pore space”(Jorden & Campbell, 1984).Thus, porosity is defined as the summarized volume of all pores, fractures,cracks, etc., or generalized all fluid(e.g., gas, water, hydrocarbons) or “nonsolid”containing parts of a sample related to the total volume of thesample( Figure 2.1):
Porosity is given as a volume fraction (dimensionless) or as percentage.The definition above describes the “total porosity”. If the rock contains apart of nonconnected or separated pores (vugs, moldic pores, etc.), then thispart does not contribute to any fluid transport within the
rock and is “noneffective.”Thus, effective orinterconnected porosity is the ratio of the connectedpore volume and the total rock volume. For reservoirdescription it is important to distinguish between:
Total porosity, the fraction of bulk volume occupied by total pore space; Effective porosity, the fraction of bulk volume occupied by interconnected pore space.
The following are applied in order to determine porosity:
direct measurements (laboratory) based on determination of bulk andsolid volume, gas expansion, or displacement techniques; indirect measurements (logging methods, seismic methods) based on correlati on between porosity and properties like density, neutron response,and seismic wave velocity. Porosity can also be derived from NMR measurements
Figure 2.6.1 Definition of Porosity
2.6.2 DENSITY A material's density is defined as its mass per unit volume. It is, essentially, a measuremement of how tightly matter is crammed together. The principle of density was discovered by the Greek scientist Archimedes. To calculate the density (usually represented by the Greek letter "ρ") of an object, take the mass (m) and divide by the volume (v):
Due to the heterogeneity of rocks, it is necessary to distinguish between different densities that are related todifferent rock components:
ρ — bulk
density: the mean density of the considered rock volume (includingpores,
etc.); for example, density of sandstone.
ρ i— density of any individual mineral rock component i; for example,density of
quartz.
ρma — mean density of the solid matrix material (mineral or mixture ofminerals), also called grain density; for example, density of a carbonatematrix (without pore fluid).
ρfl — mean density of the pore (or fracture) fluid; for example, density ofwater ρw.
Bulk density of a composite material (rock) consisting of n components is
where ρi is the density and V i is the volume fraction of component i.
Bulk density of rocks follows exactly equation aboveand depends on:
the mineral composition (mineral densities and volume fractions); porosity (pores, fractures) and density of pore fluids.
This explains the general rule of density variation:
Igneous rocks show an increase of density from felsic (acid) to mafic(basic) types; Porous rocks show a density decrease with increasing porosity anddecreasing water saturation.
If density of rock (ρb) is also known (either from wireline logs or lab measurements), it is also possible to find several of other dynamic properties of rock such as shear modulus (Gd), Young’s modulus (Ed) , and bulk modulus (Kd) usi ng the following simple equations:
BAB III EXPERIMENTAL METHODOLOGY 3.1 TIME AND PLACE The experiment for the elastic properties took time and place on Thursday 30 November 2015 at 13.00 WIB in Geophysics Laboratory.The experiment for the density of rock took time and place on Thursday 17 Desember 2015 at 13.00 WIB in Geophysical Laboratory. For other experiment such as geomechanical, and porosity there is no experiment.
3.2 TOOLS AND MATERIALS In elastic properties experiment, tools and materials were used, as follows: Tools: 1. 2. 3. 4. 5. 6.
Gel A set of oscilloscope Grinder and sandpaper A set of ultrasonic Ruler Coring tools In density experiment, tool were used, as follows :
1. 2. 3. 4.
Measuring Glass Digital Scale Water Ruler
Materials: 1. Sample of rock with diameter of 6 cm and thickness of 4,5 cm
3.3 EXPERIMENTAL PROCEDURE 3.3.1 ELASTIC PROPERTIES (VP&VS) In this experiment, carried out the experimental procedures that have been arranged. Prior to measuring, the rock sample which will be observed is performed smoothing by "coring" and grinding until the surface of rock is flat. After that, oscilloscope is prepared along with its supporting tools. Before the oscilloscope is used, calibration is done prior to the appliance. Then the rock that will be observed which on contact with the surface of the emitter and receiver instruments is given gel. After that, the wave emitter and receiver affixed to both of the flat surfaces of rock sample. Then gain and frequency on the oscilloscope is set
to acquire good waveforms. After the waveform obtained, paused and saved to a USB drive to get a screenshot of the oscilloscope screen. The obtained data is processed using the application "engauge digitizer" that converts images (.jpeg) into the coordinates of the curve (.xml).
3.3.2 DENSITY In this experiment, there are two data that we have to get. The first one is the weight of the rock sample and the second one is volume of the rock sample. To get the rock’s volume we can get from the measurement by the ruler and we find the volume, or we can find the volume by putting the rock sample to the water and see the delta of the volume. The first thing we do is measuring the mass of the rock. The weight measurement is important to get the rock density. After we get the rock mass, we get the measuring glass and fill it with water. After that record the first volume. Then we put in the rock sample to the measuring glass and then see the delta of volume. After we get all data we can get the density of the rock sample.
CHAPTER IV RESULT AND DISCUSSION 4.1DATA ANALYSIS 4.1.1 ELASTIC PROPERTIES EXPERIMENT In this experiment, we used the shell limestone to be measured. We have at least, two measurement in this experiment as figured on picture below. Those two pictures show that
Figure 1 Measurement result displayed on the oscilloscope monitor.
the waves that occured have nearly on same phase of sinusoidal form. In those pictures, we can also figure that the frequencies have a values on 3.048 KHz and 3.571 KHz. Oscilloscope is the tool that we used to captured the waves. After we measured the stone with oscilloscope, the waves or the results that show in oscilloscope are saved as an
Figure 2 Sinusoidal wave that have been d igitized by using engauge software.
image format to flashdisk. Next, those image format can be digitized by Engauge software. Engauge is a software that used to digitized the image format of the wave and transform it to Cartesian coordinates (x,y). So, we can get the information about wave position in Cartesian coordinates.
After the image format of the waves are digitized, the digitized data will be exported as a .xls file to be opened in Microsoft Excel. When the digitized data are opened in Microsoft Excel, we can observe where the data are changing drastically. In the first measurement, there are 9 points where the data are changing drastically. Then, in the second measurement, we get 8 points where the data are changing drastically. We can also observe in
Figure 3The first measurement have 162 data with 9 points drastically data changing (left) and the second measurement have 156 data with 8 points drastically data changing (right). Each points ar e displayed with different colors.
those data that each data have a difference between 2 or 3 fromy coordinate. As we know, oscilloscope plots the time in horizontal axis and voltage in vertical axis. From this axis, especially the horizontal axis, we can use it as the tool to find out the arrival time of P-Wave and S-Wave. Form the arrival time of those two types of wave, we can also find out the value of Vp and Vs. Supposed that the leftest part of the horizontal axis is 0 s. Then, we can measure the arrival time of P-Wave. From the two tables, we get that the value of the arrival time of P-Wave is 240 µs. The formula that used to calculate Vp and Vs are listed below : = = Where L is the length of the object (0.045 m), tp is arrival time of P-Wave, respectively. From the measurement, we get that t he value of Vp is 178,5 m/s. For the calibration we need to find T period, frequency, Vpp, Vp, and Vrms. The calculation are listed below
Figure 4 Calibration measurement for each data, left picture is calibration for the first measurement and right picture is calibration for the second measurement
4.1.2 DENSITY EXPERIMENT From the experiment of density we get the mass and the volume of the rock. The mass of the rock is 307 g and the volume of the rock is 120ml. After we get the data, then we can do the calculation such as the following :
The equation of the density is : ρ = m/v ρ =307/120 ρ = 2.55g/ml
so, from that equation we can get the value of density of rock is 2.55g/ml
4.1.3 GEOMECHANICAL EXPERIMENT For the geomechanical properties experiment, there are three data that we have to get. They are Young’s Modulus, Shear Modulus, and Poisson’s Ratio. But we did not do the experiment, so we find the equation from the literature. From the literature we get the equation such as the following :
The data for the calculation was got from the elastic properties above, so the calculation is : For the Poisson’s Ratio : )
0.5 ( =
(
−1
) −1
0.0049 ) 0.004 0.0049
0.5 ( = (
0.004
−1
) −1
= -0,4988 For the Young’s Modulus :
=
=
ρ ( 1 + )
72
2,55. 0.0049 ( 1 + ) 72 . 9,8
E=
For the Shear Modulus :
=
2(1 + )
4.2 DISCUSSION We do four kind of experiment in this rock physic experiment. There are some experiment about Elastic Properties, Geomechanical Properties, Density, and Porosity. From this experiment, we have an objective to know how to get the physical properties of rocks. In the first experiment, especially at elastic properties experiment, we have to find out the velocity of wave propagation. Then, the data that we get is P-wave velocity (Vp). There are three kind of physical properties for the geomechanical experiment that we have to get. The three kind of physical properties that we have to get are the Poisson’s Ration, Young’s Modulus, and Shear Modulus. Because of the limitation of the tools, we didn’t do the experiment of geomechanical properties. We get the characteristic of those physical properties from the literature. On the experiment before, we have known about the value of Vp. From the value of Vp, we can get the value of the Poisson’s Ration, Young’s Modulus, and Shear Modulus. Next, on the density experiment, we can get the value of density from the calculation of the mass and the volume of the rock sample. There are the Poisson’s Ration, Young’s Modulus, and Shear Modulus. But on this case we did not do the experiment because of the limitation of the tools. So we get the value of that physical properties from the literature. On the elastic properties we get the value of Vp and Vs. From that data, we can get the value of the poisson’s ratio, young’s modulus, and shear modulus. For the density we can get the value from the calculation of the mass and the volume of the rock sample. And the last experiment is porosity. We also cannot do the experiment because of the limitation of the tools. On this elastic properties experiment there are some tools and material that we need, such as rock sample, digital scale, ruler, water, oscilloscope, gel, scale glass, grinder, sandpaper, and a set of ultrasonic tools. For the elastic propertis, the tools that we need are the oscilloscope and a set of ultrasonic tools for the measurement of the velocity of P-wave and S-wave. A coring to get a rock sample, grind and sandpaper to subtilize the rock sample, a ruler to scale the length of the rock sample, and a gel to smooth the rock surface. The first thing we do is getting the sample rock by coring a rock, after that we subtilize the surface of the rock. After we subtilize the rock surface, we set up the oscilloscope and the ultrasonic tools, and then we apply the gel on the rock surface. The last thing to do is measure the velocity of wave and take a note the data. After we get the data, we process the data by a computer to get the velocity of wave. For the density experiment there are some tools and material that we need, such as a glass scale, digital weight scale, ruler, and water. The first thing to do is measuring the weight
of the rock sample. From the measurement we get the mass of the rock sample is 307g. After that we fill the scale glass by water. In our experiment we fill the scale glass until
CHAPTER V CLOSING REMARKS 5.1 CONCLUSION From this experiment, we have a conclusions listed as below : 1. We can find the value of Vp and Vs of an object by using oscilloscope. 2. The value of Vp and Vs on the first measurement is 0.0049 m/s and 0.0045 m/s 3. The value of Vp and Vs on the second measurement is 0.004 m/s and 0.004 m/s 4. The value of Poisson’s Ratio is 5. The value of Young’s Modulus is 6. The value of Shear Modulus is 7. The value of Density is 8. The Value of Porosity is
5.2 R ECOMMENDATION For the next experiment, we have several reccomendations such as : 1. The need for assistance from the lecturer or lecturer assitance during the experiment 2. More detailed explanation about step of experiment and usabilit y of tool
BIBLIOGRAPHY http://www.bbc.co.uk/schools/gcsebitesize/science/aqa/waves/generalwavesrev1.shtml . (2015). Holmes, C. W. (1978). Distributin of Selected Element in Surficial Marine Sediment of the Northern Gulf of Mexico Continental Shelf and Slope . Geological Survey , 38. Sari, D. N. (t.thn.). PENGUKURAN KECEPATAN GELOMBANG S PADA SAMPEL BATUAN. Schon, J. H. (2011). PHYSICAL PROPERTIES OF ROCKS : A WORKBOOK. Oxford: Elsevier B.V. Schon, J. H. (2015). PHYSICAL PROPERTIES OF ROCKS : FUDAMENTALAND PRINCIPLES OF PETROPHYISICS SECOND EDITION. Oxford: Elsevier B.V.
