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Summer Research Fellowship Programme of India's Science Academies

Amplitude versus offset variations in gas sands

Sri Lakshmi Sunkara

Centre for Earth Ocean and Atmsopheric Sciences (CEOAS), University of Hyderabad, Prof. C.R.Rao Road, Gachibowli, Hyderabad 500046

Dr. Maheswar Ojha

National Geophysical Research Institute (CSIR-NGRI), Uppal Road, Hyderabad 500007

Abstract

The main objective of the present work was the Amplitude versus offset (AVO) analysis. AVO analysis is a very important tool for the detection of Hydrocarbons and free gas saturation in the sediments. There are various application of the AVO analysis such as., flat spot analysis, density estimation, pressure detection etc., The seismic reflection from gas sand shows a wide range of AVO characteristics. Generally, presence of gas in sediments is indicated by increasing amplitude with offset. According to Rutherford and Williams based on the normal incidence reflection coefficient, the Amplitude varies with offset for different classes of gas sands namely Class I, class II, Class III (increasing amplitude with offset) and gas sands of class IV (amplitude decreases with offset), is not explained by Rutherford and Williams. Castagna and Swan, 1998 explained the class IV gas sands by using the AVO cross plots on the basis of AVO gradient (B) and AVO intercept (A). Class IV gas sand has very high negative reflection coefficient with decreasing AVO. This may be due to the shear wave velocity of gas sand to be lower than the overlying formation.

Keywords: gas hydrates, AVO analysis, reflection coefficient, incidence angle, gas sand

INTRODUCTION

Gas Hydrate

In a country like India, there is a huge demand for natural gas and its supply, gas from gas hydrate may play a major role for mitigating this gap of demand-supply. Presently, a lot of focus is been shown on finding reservoirs of conventional hydrocarbons but also towards developing new, more efficient production and recovery techniques.

Gas hydrates are one of the serious economic and safety problems in petroleum industry during the exploration, production, processing and transportation of natural gas and liquid. Pipelines and processing equipment can be blocked by their formation. These blockages reduce and stop flow and can lead to production shut down.

Gas hydrates are solid ice-like crystalline structures which consist of natural gas molecules are entrapped within cavities of water molecules. The crystalline compounds typically form at low temperature and high pressure conditions.

Global Occurrence of Gas Hydrate

Gas hydrates occur in two discrete geological situations where the pressure-temperature conditions are within the hydrate stability field:

1. In Polar Regions, where temperatures are cold enough for onshore and offshore Permafrost to be present.

2. In offshore sediments of outer continental and insular margins where there are cold bottom water temperatures and deep water exceeding 300 – 500 meters.

The global locations of gas-hydrates have been established from geophysical, geochemical and geological methods, and sampling by the Deep Sea Drilling Program (DSDP) and Ocean Drilling Program (ODP). Fig. 1 shows the worldwide map of more than 90 documented hydrate occurrences.

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    Fig.1.Global Occurrence of Gas Hydrates (USGS)

    Stability Conditions for Occurrence of Gas Hydrate

    Gas hydrate stability is a function of water depth, bottom water temperature, pressure, thermal gradient, pore water salinity, gas availability, and composition. Gas hydrate are said to form at elevated pressure ~ 6-30MPa and at moderately cooled temperature (< 15°C) in shallow sediments. They are stable up to a few hundred meters below the seafloor, which is defined as the gas-hydrates stability zone (Sloan, 1998). They occur worldwide in two distinct regions namely - permafrost and outer continental margins (Sloan, 1998). The average thickness of the hydrate stability zone along continental margins is about 500 m. The gas-hydrates stability conditions both in permafrost and marine sediments are shown in the phase diagram (Fig.2).

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      Fig.2 Stability conditions of Gas hydrates – (a) permafrost region (b) oceanic environment (http://large.stanford.edu) 

      Detection of Gas Hydrates

      Bottom simulating reflector (BSR)

      Gas hydrate are mainly found by the seismic surveys. An anomalous reflector called “Bottom Simulating Reflector (BSR)” is mapped in the seismic data. Bottom Simulating Reflector (BSR) is caused by gas hydrates which are underlain either by brine or free gas sediments. The presence of free gas at BSR is not required, but possible, if there is over saturation of the pore fluids with methane within Hydrate Stability Zone (HSZ).

      The BSR results from the negative impedance contrast between sediment containing high velocity hydrate and underlying normal sediment that may contain free gas. BSR is approximately parallel the seafloor, and it cuts across stratigraphic reflectors (fig. 3). Other less conclusive criteria include suppression of general reflection amplitudes above the BSR relative to those below referred to as a “blanking zone”, and small scale reflection seismic effects such as the generation of hyperbola associated with a blocky structure at the base of the hydrate zone. The BSR reflection is generally a single symmetrical wavelet with a reversed polarity relative to the seafloor, indicating a sharp and negative impedance contrast downward across the BSR. No reflections from the top of the hydrate layer or bottom of the gas layer have been confidently identified (although there are some indications).

      This behavior is in contrast to the normal industry experience of “bright spots” at the top of gas layers. It has thus been inferred that the top of the hydrate accumulation and the base of the low-velocity free gas layer beneath the BSR must be gradational. The characteristic BSRs allow the regional distribution of hydrates to be mapped and the analyses of the BSRs and of the velocity structure can provide semi quantitative information on the amount and distribution of hydrates and underlying free gas.

      https://s3-us-west-2.amazonaws.com/assets.authorcafe.com/9013/assets/docxassets/insa_8_weekreport_2082019_5d47b95eeed54/media/image3.png
        Fig. 3. BSR showing negative reflection with wave form opposite to the seafloor. (Chandra and Surya, 2008)

        Blanking

        A second significant seismic characteristic of the gas-hydrate-bearing sediment is blanking, which is the reduction of the amplitude of seismic reflections caused by gas hydrate concentration.

        Attenuation

        Another important property to characterize the hydrate and gas-bearing sediments is the seismic quality factor (Q) or attenuation (Sain et al., 2009). Estimation of  Q is also required for compensating the effects of attenuation in the quest to improve the subsurface seismic images; to better interpret the effects of amplitude variation with offset (AVO); and to invert seismic data for deriving material properties. The extent of energy loss is a function of the physical property of the medium, commonly characterized by the attenuation, which is defined as the loss of energy per unit cycle (Aki and Richards 1980).

        Justification of the Work

        During the early 1970's, the hydrocarbon indicator was mostly foccussed on the detection of "Bright Spots". But the studies brought out that even the high amplitudes from hard rocks give the same indication as high amplitude from hydrocarbons. Chiburis et. al., 1993 studied that the AVO analysis can distuinguish the lithology changes from the fluid variations. The studies for hydrocarbons using AVO analysis were carried out extensively for few decades. The importance of the present study is to understand how the amplitude varies with offset depending on the constrasts of physical properties of rocks. Futhur this study also helps us to understand the various processing steps that are needed for the AVO analysis. This analysis helps us to understand and discriminate between the various fluid properties and lithologies. It also helps us to estimate the physical parameters of the rocks of the subsurface.

        Research Objectives

        The main objectives of the present work is,

        (i) To apply AVO analysis to identify the layers and their rock properties for the reservoir models.

        (ii) To identify the cause for the AVO behaviour in presence of fluids.

        (iii) To study the various AVO classes in a reservoir, especially the behaviour when there is presence of gas in the sediments.

        LITERATURE REVIEW

        Seismic amplitude-versus offset (AVO) analysis has become one of the powerful geophysical method for the direct detection of gas from seismic data. The method is based on the estimation of the effective elastic parameters of a hydrocarbon reservoir using elastic reflection coefficient. It mainly focusses on the estimation of the subsurface rock properties, thereby helps in determination of the lithology, fluid saturation and porosity. This is done by solving the Knott energy equations (or Zoeppritz equations) that the energy reflected from an elastic boundary varies with the angle of incidence of the incident wave. This behavior was studied further by Koefoed (1955, 1962), by studying the change in reflection coefficient with the incident angle which is dependent on the Poisson’s ratio difference across an elastic boundary. In 1984, Ostrander introduced a practical application of the amplitude variation with incident angle phenomenon. He used the Zoeppritz amplitude equations (e.g. Aki and Richards, 1980) to analyze the reflection coefficients as a function of the angle of incidence for a simple three-layer, gas-sand model, i.e. a sand layer encased in two shale layers. AVO analysis requires accurate determination of the angle of incidence at an interface, the accuracy of which depends on an accurate velocity model (Coulombe et al., 1993).

        METHODOLOGY

        Amplitude Variation with Offset (AVO)

        The Amplitude versus offset (AVO) or amplitude variation with offset is defined as the variation in seismic reflection amplitude with variation in offset (distance between shot point and receiver). Seismic amplitude-versus offset (AVO) analysis is very important geophysical method for the direct search of gas from seismic records. The AVO analysis is based on the estimation of the elastic parameters of a hydrocarbon reservoir using elastic reflection coefficients. Koefoed (1955, 1962), studied that across an elastic boundary, the change in reflection coefficient with the incident angle is dependent on the Poisson’s ratio difference. Koefoed (1955) also proposed that analyzing the shape of the reflection coefficient vs. angle of incidence curve can be an important tool for interpreting lithology.

        Ostrander, 1984 has introduced the application of the amplitude variation with incident angle phenomenon. He used the Zoeppritz amplitude equations (e.g. Aki and Richards, 1980) to analyze the reflection coefficients as a function of the angle of incidence for a simple three-layer, gas-sand model. The model consisted of sand layer encased in two shale layers. By using published values of Poisson’s ratio for shale, brine saturated sands, and gas saturated sands, he determined that there is a significant enough change in reflection coefficient with angle of incidence to discriminate between gas saturated sands and brine saturated sands. The variation in amplitude is an important parameter from the AVO analysis, and is in the form of function (amp = A + Bsin2θ), where A is the AVO intercept, B is the AVO gradient and θ, angle of incidence.

        The variation of reflection and transmission coefficients with angle of incidence (AVA) (and corresponding increasing offset) is often referred to as offset-dependent reflectivity and is the fundamental basis for amplitude-versus-offset (AVO) analysis. Recently AVO analysis is used mostly in lithology studies, hydrocarbon detection and fluid parameter analysis.

        AVO Theory

        The reflectivity with offset distance with the partitioning of energy at an interface is given by Castagna and Backus, 1993. The angles for incident, reflected and transmitted rays at the boundary are related according to Snell’s law by equation 1:

        p=sinθ1vp1=sinθ2vp2=sinϕ1=vs1sinϕ2vs2………………………… (1)

        where, VP1 = P-wave velocity in medium 1, VP2 = P-wave velocity in medium 2, VS1 = S-wave velocity in medium , V S2 = S-wave velocity in medium, θ1 = incident P-wave angle, θ2 = transmitted P-wave angle, φ1 = reflected S-wave angle, φ 2 = transmitted S-wave angle, p = is the ray parameter.

        At a particular interface, after the ray path, the amplitude of the reflected energy is calculated using the Zoeppritz equations. The Zoeppritz equations determine the transformation of an incident plane wave upon striking a plane reflector. As shown in Figure 4, an incident p-wave produces four resulting waves, consisting of two reflected waves and two transmitted waves.

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          Fig. 4. Reflection and transmission at an interface between two infinite elastic half-spaces for an incident P-wave (Castagna and Backus, 1993).

          Aki and Richards (1980) gave an easily solved matrix form given in equation 2:

          Q=P-1R……...................(2)

          Where P is the matrix

          P=(sinθ1sinϕ1sinθ2cosϕ2cosθ1sinϕ1cosθ2sinϕ2sin2θ1Vp1Vs1cos2ϕ1ρ2Vs22Vp1ρ1Vs12Vp2cos2ϕ1ρ2Vs2Vp1ρ1Vs12cos2ϕ2cos2ϕ1Vs1Vp1sin2ϕ1ρ2Vp2ρ1Vp1cos2ϕ2ρ2Vs2ρ1Vp1sin2ϕ2)P={\begin{pmatrix}-\sin\theta_1&-\sin\phi_1&\sin\theta_2&\cos\phi_2\\\cos\theta_1&-\sin\phi_1&\cos\theta_2&-\sin\phi_2\\\sin2\theta_1&\frac{V_{p1}}{V_{s1}}\cos2\phi_1&\frac{\rho_2V_{s2}^2V_{p1}}{\rho_1V_{s1}^2V_{p2}}\cos2\phi_1&\frac{\rho_2V_{s2}V_{p1}}{\rho_1V_{s1}^2}\cos2\phi_2\\-\cos2\phi_1&\frac{V_{s1}}{V_{p1}}\sin2\phi_1&\frac{\rho_2V_{p2}}{\rho_1V_{p1}}\cos2\phi_2&\frac{\rho_2V_{s2}}{\rho_1V_{p1}}\sin2\phi_2\end{pmatrix}}_{}…(3)

          And R is the matrix

          R=sinθ1cosθ1sin2θ1cos2ϕ1.....................(4)

          Here P and R are the two complex matrices consisting of elements which are functions of Vs, Vp, ρ (density), θ (incident angle), ϕ (emergence angle).

          RESULTS AND DISCUSSION

          AVO governed by Zeoppritz Equation

          Zeoppritz, 1919 derived the particle motion amplitude of the reflected and transmitted waves using the conversion of stress and displacement across the interface, which yield four equations as described in the before section. Figures 5-10 & 12-13 are generated with MATLAB script.

          Table 1. Parameters of first layer for two Zeoppritz model from Richards (1961) for Paleozoic Limestone structure in Western Canada.
          Overburden ModelVp (Km/s)Vs (Km/s)Density (gm/cc)
          First Layer (model A)1.8290.9142.02
          First Layer (Model B)2.5211.562.12
          Second Layer6.0963.0482.65
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            Fig. 5. Variation of reflected and transmitted coefficient with angle of incidence for Model A (Table 1), (Rp=P-wave Reflection Coefficient; Rs=S-wave Reflection coefficient; Tp= P-wave Transmission Coefficient; Ts=S-wave Transmission coefficient).
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              Fig.6. Variation of reflected and transmitted coefficient with angle of incidence for Model B (Table 1), (Rp=P-wave Reflection Coefficient; Rs=S-wave Reflection coefficient; Tp= P-wave Transmission Coefficient; Ts=S-wave Transmission coefficient).
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                Fig.7. Variation of reflected and transmitted coefficient with angle of incidence for Model A (where first layer values are Vp=6.096 m/s; Vs=3.048 Km/s; density=2.65 gm/c.c and second layer values are is Vp=1.829 m/s; Vs=0.914 Km/s; density=2.02 gm/c.c. (Rp=P-wave Reflection Coefficient; Rs=S-wave Reflection coefficient; Tp= P-wave Transmission Coefficient; Ts=S-wave Transmission coefficient).
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                  Fig. 8. P-wave reflection versus incident angle for six models given in Table 2 (after Richards, 1961).
                  Table.2. Parameters of first layer for six Zeoppritz models from Richards (1961) for Paleozoic Limestone structures in Western Canada. These models correspond to reflection coefficient curves given in Figure 8 when the second layer has the parameters: Vp=6096 m/s; Vs=3048 m/s and ρ=2.65 gm/c.c. Note that Vp/vs =2 for all layers.
                  Overburden ModelVp (m/s)Vs (m/s)Density (gm/cc)
                  A18299142.02
                  B252112602.12
                  C304815242.20
                  E426721332.38
                  F487724382.47
                  G548627432.56

                  Some important observations made from Figure 8 are:

                  (i) The Amplitude of the reflected P-wave occur at normal incidence, the first critical angle.

                  (ii) The change of reflection coefficient with respect to angle of incidence is small at ow angles.

                  (iii) At near normal incidence, Rpp decreases slightly with increasing angle.

                  The Aki and Richards equation is an important linear approximation of thezeoppritz equations. It is valid for reflection angles up to about 40°. An even simpler approximation is the Shuey (1985) approximation.

                  AVO – Shuey Two-term & Shuey Three-term Approximation

                  Shuey’s second order approximation: The Shuey’s second order approximation is valid for short and medium offsets upto about 20°or even to 30°. The reflection coefficient of P-wave in terms of incidence angle (θ) is given by:

                  Rpp(θ)A+Bsin2θ……………………. (5)

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                    Fig. 9. Plane-wave reflection coefficient versus angle of incidence for the top of class IV (quadrant II) gas sand, and the corresponding brine-sand reflection. The model parameters are: shale—VP = 3.24 km/s, VS =1.62 km/s, ρ= 2.34 gm/cm3 ; brine sand—VP = 2.59 km/s, Vs =1.06 km/s, ρ= 2.21 gm/cm3 ; gas sand—Vp = 1.65 km/s, Vs = 1.09 km/s, ρ= 2.07 gm/cm3 . The solid lines are the full Zoeppritz solution. The dashed lines are the two-term Shuey (1985) approximation (after Castagna et. al., 1998)

                    Figure 9 shows the effect of a low-impedance brine sand. The reflection coefficients are large, but the Shuey (1985) two-term approximation is good to about 30°angle of incidence. For angles less than this, B is positive for both brine and gas sands, and magnitude decreases with increasing offset in both cases.

                    Shuey’s third order approximation: In Shuey’s third order approximation, the first term gives the amplitude at normal incidence, the second term characterizes R(θ) at intermediate angles, and the third term describes the approach to the critical angle. The coefficients of Shuey’s approximation form the basis of various weighted stacking procedures. The reflection coefficient of P-wave in terms of incidence angle (θ) is given by:

                    Rpp(θ)A+Bsin2θ+Csin2θtan2θ……………………. (6)

                    Where , Vp2=Vp2Vp1;Vs2=Vs2Vs1;ρ2=(ρ2+ρ1)/2;Vp=(Vp2+Vp1)/2;θ=(θ2+θ1)/2;\begin{array}{l}\triangle V_{p2=}V_{p2}-V_{p1};\\\triangle V_{s2=}V_{s2}-V_{s1};\\\rho_{2=}(\rho_2+\rho_1)/2;\\V_{p=}(V_{p2}+V_{p1})/2;\\\theta=(\theta_2+\theta_1)/2;\\\end{array},

                    and P is the ray parameter.

                    A is the zero-offset stack, B is commonly referred to as the AVO slope or gradient, and the third term becomes significant in the far-offset stack.

                    AVO Response for gas sand and brine sand over shale:

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                      Fig.10. AVO behaviour for brine sand underlain by Shale shown in Table 3. The figure shows that the AVO behaviour are same upto 15°for Two-Term, Three term and Zeoppritz equation (i.e amplitude decrease with offset at the same rate) after that the AVO gradient of the “two-term Shuey approximation” is more than that of three-term and Zeoppritz equation.
                      Table 3. Parameters of Shale and brine sand.
                      ModelVp (Km/s)Vs (Km/s)Density (gm/cc)
                      Shale2.2501.1252.00
                      Brine sand2.5001.2502.11

                      AVO Response Classification

                      The standard classification of bright spot, phase reversal, and dim out was the Rutherford and Williams’s classification of the reflection coefficient curves. This classification was developed for reflections from hydrocarbon saturated formations. According to Rutherford and Williams’s classification, the slope of the reflection coefficient curve is negative for all classes. The reflection amplitude decreases with the angle of incidence. The absolute amplitude that increase with angle of incidence as classified as Class II and III AVO gas saturated anomalies. Castagna et al. (1998) found that some Class III gas saturated anomalies can have slowly decreasing amplitudes with offset. These were named Class IV AVO anomalies (Figure 11). However, the Class IV anomalies are still considered as the large amplitudes associated with the hydrocarbons. Table 4 shows the various models for different lithologies that were generated for the study of class I - class IV AVO Classification.

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                        Fig.11. AVO classifications defined by Rutherford, et al. (1989) and Castagna, et al. (1998), and typical flat spot behaviour.
                        Table.4. Parameters of shale brine sand and gas sand showing variations for the Class I-class IV AVO responses:
                        LithologyVp1 (m/s)Vp2 (m/s)Vs1 (m/s)Vs2 (m/s)ρ1 (gm/cc)ρ2 (gm/cc)
                        shale over brine sand (class I)29003250133017802.292.44
                        shale over gas sand (class III)29002540133016202.292.09
                        brine sand over gas sand (class III)25901650106010902.212.07
                        shale over gas sand (class II)27492835139417622.062.04
                        shale over brine sand (class IV)32502540162010602.342.21
                        shale over gas sand (class IV)32401650162010902.342.07
                        shale over brine sand (class IV32402540162016802.342.21
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                          Fig.12. Various classes of AVO response based on the normal incidence reflection coefficient. P-wave reflection coefficients at the top of each Rutherford and Williams (1989) classification of gas sands. Class IV sands not discussed by Rutherford and Williams, have negative normal-incidence reflection coefficient, but decrease in amplitude with offset.

                          The cross plot of AVO Intercept (A) versus AVO Gradient (B) reveal different AVO behaviours as shown in Figure 13 (Castagna et al., 1998). The background trend line in the cross-plot of A versus B is a function of the background Vp /Vs ratio. The deviation from the background trend line indicates the presence of hydrocarbon. Using the cross-plot of A versus B, the hydrocarbon-saturated sands can be classified according to their locations in the A -B plane.

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                            Fig.13. New AVO classifications identical to Rutherford and Williams (1989) for class I and class II sands. But the Class II is further subdivided into two classes III and Class IV.

                            AVO Analysis for Synthetic Layered Model

                            A layered velocity model A (of 6 layers whose elastic parameters described+ below in Figure 14 and in table 5) that represents the subsurface was built. The model represents a low velocity layer encased in shale. The AVO effects for the sandstone reservoirs is analysed using the Zoeppritz P-wave reflection coefficients was written in MATLAB script. The ray-tracing technique of CREWES (written in MATLAB) was applied to calculate the wave paths and compute the travel times and amplitudes along the paths (Margrave, 2000). Ray-tracing is a significant approach to model the 2-dimensional and 3-dimensional geologic structures. This method was first applied in the study of high-frequency elastic waves by Babich (1956), Babich and Alexeyev (1958) and later on for detection of gas in sand stone reservoir for Prinos basin (Choustoulakis, 2015). Table 5 shows the various P-wave velocities (Vp in m/s); S-wave velocities (Vs in m/s; densities (gm/cc) of different shale, sandstone layers of different interfaces.

                            Table 5. The elastic parameters of six layered model A
                            LayersDepth (m)P-Velocity (m/s)S-Velocity (m/s)Density (g/cc)
                            10300021002.6
                            2600330023002.4
                            31400280015002.1
                            41900300017002.3
                            52500320019002.4
                            63000370029002.7
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                              Fig.14. Vp, Vs and density versus depth for the model A.

                              The calculated ray parameters are then used to calculate travel times, reflectivity coefficients and incidence angles for each interface. The reflectivity values are computed on the basis of Zeoppritz’s equations (1919). The travel times and incidence angle are used to create a synthetic seismogram by convolving the reflectivity with a 30 Hz Ricker wavelet. The travel time for each medium and the corresponding synthetic seismogram generated is shown in Figure 15 and Figure 16 respectively.

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                                Fig.15. Travel time plot calculated from the ray parameters obtained from ray tracing algorithm.
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                                  Fig. 16. Synthetic seismogram created by convolving the reflectivity calculated from incidence angle with 30Hz Ricker wavelet.

                                  From Figure 16, it is clearly seen that the second interface presents highly negative amplitudes, while the above and deeper interface presents highly positive amplitudes. As the offset increases, the amplitudes decrease and not easily observed. The correction of amplitude (Figure 17) is necessary for a stronger signal, because as the offset increases, the signal becomes weak. The exact image of the subsurface is necessary for interpretation. Hence the correction for amplitude losses need to be applied for the seismogram. The amplitude correction (Figure 17) is done by multiplying the seismic trace amplitude with the time independent variable which has a power of time.

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                                    Fig. 17. Synthetic seismogram with spherical divergence correction

                                    Normal move out correction (NMO) is a function of time and offset that can be used in seismic processing to compensate the effects of normal move out or delay in arrival travel times when geophones and shot points are offset from each other. The NMO correction is applied to the seismic record to remove the delay in the travel time (Figure 18). NMO stretching happened when two points belonging to the same event present a time difference (a) before the NMO correction and (b) after the NMO correction. The b will be greater than a (b>a) because the upper point will undergo a larger NMO correction than the other point which is lower, i.e. stretching is a frequency distortion in which events are shifted to lower frequencies. The stretching is mostly confined to larger offsets and shallow times (Figure 18). Hence muting needs to be applied for the stretching.

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                                      Fig.18. NMO correction and stretching.

                                      We have tested the by converting the Root Mean Square velocities to interval velocities and we have obtained the following values given in Table 6. The P-wave velocities almost match with the initial model.

                                      Table 6 The P-wave velocities of the initial model A and values obtained after the velocity analysis.
                                      LayersDepth (m)

                                      P-Velocity (m/s)

                                      Assumed

                                      P-Velocity (m/s)

                                      Obtained after the velocity analysis

                                      1030003100
                                      260033002890
                                      3140028003000
                                      4190030003100
                                      5250032003050
                                      6300037003100
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                                        Reflection Coefficients versus angle of incidence using the Zeoppritz approximations for the five different layers of the model A.

                                        Figure 20 shows the set of reflection coefficient AVO curves for the five interfaces calculated for the Incidence angle. The AVO curves shows that the first, third, fourth, fifth interfaces belong to class II and class I of AVO class. This is because all these curves have a positive reflection coefficient curve at zero offset/angle of incidence and the amplitude decrease with increase in offset/angle.

                                        Comparing Figure 20 with the Figure 11 of AVO classification each medium of the model can be categorized to an AVO class as shown in Table 7.

                                        Table 7 AVO classification of the model’s interfaces.
                                        Medium AVO class
                                        1: Layers 1-2 II
                                        2: Layers 2-3 IV
                                        3: Layers 3-4 I
                                        4: Layers 4-5 I
                                        5: Layers 5-6 I

                                        The crossplot of AVO gradient and intercept is plotted in Figure 20.

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                                          Crossplot of AVO gradient (B) and AVO intercept (A) with the background trend plotted with dashed line.

                                          As it can be observed in Figure 20, the brine sand anomaly is evident, with the point corresponding to the first medium being plotted to the right of the background trend. The brine anomaly belongs to class IV, which confirms the results from the reflection coefficient curves. The cross-plot of Intercept versus Gradient from AVO analysis shows clear marked separation of anomalous points from background trend (shale/wet (brine) sand) which has been identified as class IV AVO anomaly.

                                          CONCLUSIONS AND RECOMMENDATIONS

                                          Conclusions

                                          AVO analysis is an important tool for the interpretation of subsurface rock properties. In this study we have produced AVO curves using the Zoeppritz equation for the interface between different media, and we have analyzed the variation of amplitude reflections with respect to incidence angle for various synthetic models.

                                          From the above work, it can be concluded that:

                                          1. The changes in reflection coefficient is function of incidence angle.

                                          2. Analysis of seismic reflection amplitude versus offset can distinguish between gas-related amplitude anomalies and other type of amplitude anomalies

                                          3. The seismic reflection from gas sand shows a wide range of AVO characteristics. Generally, presence of gas in sediments is indicated by increasing amplitude with offset.

                                          4. Class IV gas sand has very high negative reflection coefficient with decreasing AVO. This may be due to the shear wave velocity of gas sand to be lower than the overlying formation.

                                          5. The change in lithology, porosity and fluid affects the AVO classification.

                                          This report comprehensively covers the Amplitude versus offset analysis for sandstone environments. Amplitude Versus Offset (AVO) modelling was carried out for synthetic models for the study and identification of various AVO classes and also studying the gas sand of AVO Class 3 and Class 4 type. The variation in seismic reflection amplitudewith offset indicates the changes in lithology and fluid content in rocks above and below the reflector. AVO analysis is an important technique to determine rock properties in subsurface. A gas-filled sandstone might show increasing amplitude with offset. One common misconception is the failure to distinguish a gas-filled reservoir from a brine-filled reservoir, but Rutherford-Williams new AVO classification clearly demarcates the gas-filled sand from the brine-filled sand of class IV anomaly.

                                          REFERENCES

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                                          Babich, V. M ., 1956. Ray Method of the Computation of the Intensity of Wavefronts: Doklady Akad. Nauk. SSSR, 110,355-57.

                                          Babich, V. M. and Alexeyev, A. S., 1958. On the Ray Method of the Computation of the Intensity of Wavefronts: Izv. Akad. Nauk. SSSR, Geop. Series, 1, 9-15.

                                          Castagna, J. P. and Backus, M. M., 1993, Offset dependent reflectivity: Theory and Practice of AVO analysis; Soc. Expl. Geophys.

                                          Castagna, J. P., H. W. Swan, and D. J. Foster, 1998, A Framework for AVO gradient and intercept interpretation: Geophysics, 63, 948-956.

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                                          Chandra R., and Surya, S., 2008. Techniques in Exploration and Formation Evaluation for Gas Hydrates, 7th International conference and Exposition on Petroleum Geophysics, Hyderabad, p-177.

                                          Choustoulakis, E Emmanouil, 2015. Detection of gas in sandstone reservoir using AVO analysis in Prinos Basin, M.Sc dissertation Report.

                                          Koefoed, O., 1962. Reflection and transmission coefficients for plane longitudinal and incident waves: Geophysical Prospecting., 10, 304-351.

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                                          ACKNOWLEDGEMENTS

                                          I would like to thank and express my gratitude towards my guide Dr. Maheswar Ojha for his kind help and constant support, guidance and clarifying queries during the Fellowship. I m extremely thankful for the Director, National Geophysical Research Institute for providing the facilities to carry out this work. I also thank the Head, Centre for Earth Ocean & Atmospheric Sciences, University of Hyderabad for allowing me to carry out the fellowship. INSA is kindly acknowledged for sanction of the fellowship.

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