Approximations to the Zoeppritz equations and their use in AVO analysis

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1920-1927 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Linear Approximation ◽  
Wave Velocity ◽  
Order Approximation ◽  
Quadratic Function ◽  
P Wave ◽  
S Wave ◽  
Elastic Parameters ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Analysis

To efficiently invert seismic amplitudes for elastic parameters, pseudoquartic approximations to the Zoeppritz equations are derived to calculate P-P-wave reflection and transmission coefficients as a function of the ray parameter p. These explicit expressions have a compact form in which the coefficients of the p2 and p4 terms are given in terms of the vertical slownesses. The amplitude coefficients are also represented as a quadratic function of the elastic contrasts at an interface and are compared to the linear approximation used in conventional amplitude variation with offset (AVO) analysis, which can invert for only two elastic parameters. Numerical analysis with the second‐order approximation shows that the condition number of the Fréchet matrix for three elastic parameters is improved significantly from using a linear approximation. Therefore, those quadratic approximations can be used directly with amplitude information to estimate not only two but three parameters: P-wave velocity contrast, S-wave velocity contrast, and the ratio of S-wave and P-wave velocities at an interface.

Shear‐wave velocity and density estimation from PS-wave AVO analysis: Application to an OBS dataset from the North Sea

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1446-1454 ◽  
Author(s):  
Side Jin ◽  
G. Cambois ◽  
C. Vuillermoz
Keyword(s):  
Wave Velocity ◽  
North Sea ◽  
Random Noise ◽  
P Wave ◽  
S Wave ◽  
Data Set ◽  
Avo Analysis ◽  
The North ◽  
Avo Inversion ◽  
The North Sea

S-wave velocity and density information is crucial for hydrocarbon detection, because they help in the discrimination of pore filling fluids. Unfortunately, these two parameters cannot be accurately resolved from conventional P-wave marine data. Recent developments in ocean‐bottom seismic (OBS) technology make it possible to acquire high quality S-wave data in marine environments. The use of (S)-waves for amplitude variation with offset (AVO) analysis can give better estimates of S-wave velocity and density contrasts. Like P-wave AVO, S-wave AVO is sensitive to various types of noise. We investigate numerically and analytically the sensitivity of AVO inversion to random noise and errors in angles of incidence. Synthetic examples show that random noise and angle errors can strongly bias the parameter estimation. The use of singular value decomposition offers a simple stabilization scheme to solve for the elastic parameters. The AVO inversion is applied to an OBS data set from the North Sea. Special prestack processing techniques are required for the success of S-wave AVO inversion. The derived S-wave velocity and density contrasts help in detecting the fluid contacts and delineating the extent of the reservoir sand.

Fracture-porosity inversion from P-wave AVOA data along 2D seismic lines: An example from the Austin Chalk of southeast Texas

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. B1-B7 ◽  
Author(s):  
Abdullatif A. Al-Shuhail
Keyword(s):  
Aspect Ratio ◽  
Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
Amplitude Variation ◽  
Fracture Porosity ◽  
Amplitude Variation With Offset ◽  
P Wave Velocity ◽  
Austin Chalk ◽  
Southeast Texas

Vertical aligned fractures can significantly enhance the horizontal permeability of a tight reservoir. Therefore, it is important to know the fracture porosity and direction in order to develop the reservoir efficiently. P-wave AVOA (amplitude variation with offset and azimuth) can be used to determine these fracture parameters. In this study, I present a method for inverting the fracture porosity from 2D P-wave seismic data. The method is based on a modeling result that shows that the anisotropic AVO (amplitude variation with offset) gradient is negative and linearly dependent on the fracture porosity in a gas-saturated reservoir, whereas the gradient is positive and linearly dependent on the fracture porosity in a liquid-saturated reservoir. This assumption is accurate as long as the crack aspect ratio is less than 0.1 and the ratio of the P-wave velocity to the S-wave velocity is greater than 1.8 — two conditions that are satisfied in most naturally fractured reservoirs. The inversion then uses the fracture strike, the crack aspect ratio, and the ratio of the P-wave velocity to the S-wave velocity to invert the fracture porosity from the anisotropic AVO gradient after inferring the fluid type from the sign of the anisotropic AVO gradient. When I applied this method to a seismic line from the oil-saturated zone of the fractured Austin Chalk of southeast Texas, I found that the inversion gave a median fracture porosity of 0.21%, which is within the fracture-porosity range commonly measured in cores from the Austin Chalk.

Constrained nonlinear amplitude variation with offset inversion using Zoeppritz equations

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R245-R255 ◽  
Author(s):  
Ali Gholami ◽  
Hossein S. Aghamiry ◽  
Mostafa Abbasi
Keyword(s):  
Nonlinear Equations ◽  
Wave Velocity ◽  
Seismic Data ◽  
P Wave ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion

The inversion of prestack seismic data using amplitude variation with offset (AVO) has received increased attention in the past few decades because of its key role in estimating reservoir properties. AVO is mainly governed by the Zoeppritz equations, but traditional inversion techniques are based on various linear or quasilinear approximations to these nonlinear equations. We have developed an efficient algorithm for nonlinear AVO inversion of precritical reflections using the exact Zoeppritz equations in multichannel and multi-interface form for simultaneous estimation of the P-wave velocity, S-wave velocity, and density. The total variation constraint is used to overcome the ill-posedness while solving the forward nonlinear model and to preserve the sharpness of the interfaces in the parameter space. The optimization is based on a combination of Levenberg’s algorithm and the split Bregman iterative scheme, in which we have to refine the data and model parameters at each iteration. We refine the data via the original nonlinear equations, but we use the traditional cost-effective linearized AVO inversion to construct the Jacobian matrix and update the model. Numerical experiments show that this new iterative procedure is convergent and converges to a solution of the nonlinear problem. We determine the performance and optimality of our nonlinear inversion algorithm with various simulated and field seismic data sets.

Wavefield and AVO modeling using elastic thin-slab method

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. C57-C67 ◽  
Author(s):  
Xian-Yun Wu ◽  
Ru-Shan Wu
Keyword(s):  
Finite Difference ◽  
Wave Velocity ◽  
Finite Difference Methods ◽  
P Wave ◽  
Thin Slab ◽  
Slab Method ◽  
S Wave ◽  
Amplitude Variation With Offset ◽  
Local Variance ◽  
Parameter Perturbations

We propose a dual-domain, one-way, elastic thin-slab method for fast and accurate amplitude variation with offset (AVO) modeling. In this method, the wavefield propagates in the wavenumber domain and interacts with heterogeneity in the space domain. The approach requires much less memory and is two to three orders of magnitude faster than a full-wave method using finite difference or finite element. The thin-bed AVO and AVOs with lateral parameter variations have been conducted using the thin-slab method and compared with reflectivity and finite-difference methods, respectively. It is shown that the thin-slab method can be used to accurately model reflections for most sedimentary rocks that have intermediate parameter perturbations ([Formula: see text] for P-wave velocity and [Formula: see text] for S-wave velocity). The combined effects of overburden structure and the scattering associated with heterogeneities on AVO have been investigated using the thin-slab method. Properties of the target zone and overburden structure control the AVO trends at overall offsets. Scattering associated with heterogeneities increases local variance in the reflected amplitudes and becomes significant for the sedimentary models with weak reflections. Interpretation of AVO observations based on homogeneous elastic models would therefore bias the estimated properties of the target. Furthermore, these effects can produce different apparent AVO trends in different offset ranges.

Sediments with gas hydrates: Internal structure from seismic AVO

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1659-1669 ◽  
Author(s):  
Christine Ecker ◽  
Jack Dvorkin ◽  
Amos Nur
Keyword(s):  
Internal Structure ◽  
Wave Velocity ◽  
Seismic Data ◽  
Pore Space ◽  
Rock Physics ◽  
P Wave ◽  
S Wave ◽  
High Concentration ◽  
Amplitude Variation With Offset ◽  
Bottom Simulating Reflector

We interpret amplitude variation with offset (AVO) data from a bottom simulating reflector (BSR) offshore Florida by using rock‐physics‐based synthetic seismic models. A previously conducted velocity and AVO analysis of the in‐situ seismic data showed that the BSR separates hydrate‐bearing sediments from sediments containing free methane. The amplitude at the BSR are increasingly negative with increasing offset. This behavior was explained by P-wave velocity above the BSR being larger than that below the BSR, and S-wave velocity above the BSR being smaller than that below the BSR. We use these AVO and velocity results to infer the internal structure of the hydrated sediment. To do so, we examine two micromechanical models that correspond to the two extreme cases of hydrate deposition in the pore space: (1) the hydrate cements grain contacts and strongly reinforces the sediment, and (2) the hydrate is located away from grain contacts and does not affect the stiffness of the sediment frame. Only the second model can qualitatively reproduce the observed AVO response. Thus inferred internal structure of the hydrate‐bearing sediment means that (1) the sediment above the BSR is uncemented and, thereby, mechanically weak, and (2) its permeability is very low because the hydrate clogs large pore‐space conduits. The latter explains why free gas is trapped underneath the BSR. The seismic data also indicate the absence of strong reflections at the top of the hydrate layer. This fact suggests that the high concentration of hydrates in the sediment just above the BSR gradually decreases with decreasing depth. This effect is consistent with the fact that the low‐permeability hydrated sediments above the BSR prevent free methane from migrating upwards.

Simultaneous inversion for model geometry and elastic parameters

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 182-190 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Joint Inversion ◽  
Real Data ◽  
Structural Effect ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Elastic Parameters ◽  
Simultaneous Inversion ◽  
Avo Analysis ◽  
The North

Both traveltimes and amplitudes in reflection seismology are used jointly in an inversion to simultaneously invert for the interface geometry and the elastic parameters at the reflectors. The inverse problem has different physical dimensions in both data and model spaces. Practical approaches are proposed to tackle the dimensional difficulties. In using the joint inversion, which may properly take care of the structural effect, one potentially improves the estimates of the subsurface elastic parameters in the traditional analysis of amplitude variation with offset (AVO). Analysis of the elastic parameters estimated, using the ratio of s-wave to P-wave velocity contrasts and the deviation of this parameter from a normal background trend, promises to have application in AVO analysis. The inversion method is demonstrated by application to real data from the North Sea.

Interpretation of AVO anomalies

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A3-75A13 ◽  
Author(s):  
Douglas J. Foster ◽  
Robert G. Keys ◽  
F. David Lane
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
P Wave ◽  
Rock Properties ◽  
Light Hydrocarbons ◽  
S Wave ◽  
Amplitude Variation With Offset ◽  
P Wave Velocity ◽  
Fluid Properties ◽  
Porosity Changes

We investigate the effects of changes in rock and fluid properties on amplitude-variation-with-offset (AVO) responses. In the slope-intercept domain, reflections from wet sands and shales fall on or near a trend that we call the fluid line. Reflections from the top of sands containing gas or light hydrocarbons fall on a trend approximately parallel to the fluid line; reflections from the base of gas sands fall on a parallel trend on the opposing side of the fluid line. The polarity standard of the seismic data dictates whether these reflections from the top of hydrocarbon-bearing sands are below or above the fluid line. Typically, rock properties of sands and shales differ, and therefore reflections from sand/shale interfaces are also displaced from the fluid line. The distance of these trends from the fluid line depends upon the contrast of the ratio of P-wave velocity [Formula: see text] and S-wave velocity [Formula: see text]. This ratio is a function of pore-fluid compressibility and implies that distance from the fluid line increases with increasing compressibility. Reflections from wet sands are closer to the fluid line than hydrocarbon-related reflections. Porosity changes affect acoustic impedance but do not significantly impact the [Formula: see text] contrast. As a result, porosity changes move the AVO response along trends approximately parallel to the fluid line. These observations are useful for interpreting AVO anomalies in terms of fluids, lithology, and porosity.

AVA inversion of the top Utsira Sand reflection at the Sleipner field

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. C53-C63 ◽  
Author(s):  
Tor Erik Rabben ◽  
Bjørn Ursin
Keyword(s):  
Wave Impedance ◽  
P Wave ◽  
Damping Factor ◽  
S Wave ◽  
Elastic Parameters ◽  
Zoeppritz Equations ◽  
Gassmann’S Equation ◽  
Inversion Procedure ◽  
Global Scaling ◽  
Amplitude Variation With Angle

Amplitude variation with angle (AVA) inversion is performed on the top Utsira Sand reflector at the Sleipner field, North Sea, Norway. This interface is of particular interest because of the accumulation of [Formula: see text] injected from a point deeper in the Utsira Sand. The focus is on the postmigration processing of angle gathers together with the actual inversion procedure. The processing treats amplitude extraction, offset-to-angle mapping, and global scaling in detail. Two algorithms are used for the inversion of AVA data, one that assesses uncertainties and one fast least-squares variant. Both are very suitable for this type of problem because of their covariance matrices and built-in regularization. In addition, two three-parameter approximations of the Zoeppritz equations are used. One is linear approximation and the other is quadratic. The results show significant signals for all three elastic parameters, but the substitution of brine by [Formula: see text] using Gassmann’s equation indicates that the contrasts in S-wave impedance and density are overestimated. For the contrasts in P-wave impedance the results are in agreement with the fluid substitution. A simple sensitivity analysis shows that the offset-to-angle mapping and the damping factor in the inversion are the most plausible explanations of the discrepancy.

Numerical and Theoretical Investigation on the Origin of the Multiple Peaks of the H/V Ratio Curve

2021 ◽  
Author(s):  
Wanbo Xiao ◽  
Siqi Lu ◽  
Yanbin Wang
Keyword(s):  
Rayleigh Wave ◽  
Wave Velocity ◽  
Subsurface Layer ◽  
P Wave ◽  
Theoretical Formula ◽  
S Wave ◽  
Multiple Peaks ◽  
Ratio Curve ◽  
Multiple Layer ◽  
Wave Resonance

<p>Despite the popularity of the horizontal to vertical spectral ratio (HVSR) method in site effect studies, the origin of the H/V peaks has been controversial since this method was proposed. Many previous studies mainly focused on the explanation of the first or single peak of the H/V ratio, trying to distinguish between the two hypotheses — the S-wave resonance and ellipticity of Rayleigh wave. However, it is common both in numerical simulations and practical experiments that the H/V ratio exhibits multiple peaks, which is essential to explore the origin of the H/V peaks.</p><p>The cause for the multiple H/V peaks has not been clearly figured out, and once was simply explained as the result of multi subsurface layers. Therefore, we adopted numerical method to simulate the ambient noise in various layered half-space models and calculated the H/V ratio curves for further comparisons. The peak frequencies of the H/V curves accord well with the theoretical frequencies of S-wave resonance in two-layer models, whose frequencies only depend on the S wave velocity and the thickness of the subsurface layer. The same is true for models with varying model parameters. Besides, the theoretical formula of the S-wave resonance in multiple-layer models is proposed and then supported by numerical investigations as in the cases of two-layer models. We also extended the S-wave resonance to P-wave resonance and found that its theoretical frequencies fit well with the V/H peaks, which could be an evidence to support the S-wave resonance theory from a new perspective. By contrast, there are obvious differences between the higher orders of the H/V ratio peaks and the higher orders of Rayleigh wave ellipticity curves both in two-layer and multiple-layer models. The Rayleigh wave ellipticity curves are found to be sensitive to the Poisson’s ratio and the thickness of the subsurface layer, so the variation of the P wave velocity can affect the peak frequencies of the Rayleigh wave ellipticity curves while the H/V peaks show slight change. The Rayleigh wave ellipticity theory is thus proved to be inappropriate for the explanation of the multiple H/V peaks, while the possible effects of the Rayleigh wave on the fundamental H/V peak still cannot be excluded.</p><p>Based on the analyses above, we proposed a new evidence to support the claim that the peak frequencies of the H/V ratio curve, except the fundamental peaks, are caused by S-wave resonance. The relationship between the P-wave resonance and the V/H peaks may also find further application.</p>

Using Seismic Data to Predict Shale Pore Pressure and Overpressure Sweet Spots: A Case Study from the Lower Silurian Longmaxi Formation in Sichuan Basin, China

2021 ◽  
Author(s):  
Sheng Chen ◽  
Qingcai Zeng ◽  
Xiujiao Wang ◽  
Qing Yang ◽  
Chunmeng Dai ◽  
...  
Keyword(s):  
Prediction Model ◽  
Wave Velocity ◽  
Shale Gas ◽  
Seismic Data ◽  
P Wave ◽  
Formation Pressure ◽  
S Wave ◽  
P Wave Velocity ◽  
New Formation ◽  
Sweet Spots

Abstract Practices of marine shale gas exploration and development in south China have proved that formation overpressure is the main controlling factor of shale gas enrichment and an indicator of good preservation condition. Accurate prediction of formation pressure before drilling is necessary for drilling safety and important for sweet spots predicting and horizontal wells deploying. However, the existing prediction methods of formation pore pressures all have defects, the prediction accuracy unsatisfactory for shale gas development. By means of rock mechanics analysis and related formulas, we derived a formula for calculating formation pore pressures. Through regional rock physical analysis, we determined and optimized the relevant parameters in the formula, and established a new formation pressure prediction model considering P-wave velocity, S-wave velocity and density. Based on regional exploration wells and 3D seismic data, we carried out pre-stack seismic inversion to obtain high-precision P-wave velocity, S-wave velocity and density data volumes. We utilized the new formation pressure prediction model to predict the pressure and the spatial distribution of overpressure sweet spots. Then, we applied the measured pressure data of three new wells to verify the predicted formation pressure by seismic data. The result shows that the new method has a higher accuracy. This method is qualified for safe drilling and prediction of overpressure sweet spots for shale gas development, so it is worthy of promotion.

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