Traveltime and relative geometric spreading approximation in elastic orthorhombic medium

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. C153-C162 ◽  
Author(s):  
Shibo Xu ◽  
Alexey Stovas ◽  
Hitoshi Mikada
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
P Wave ◽  
Form Expression ◽  
Amplitude Variation ◽  
Rational Form ◽  
Amplitude Variation With Offset ◽  
Practical Applications ◽  
Numerical Tests ◽  
Geometric Spreading

Wavefield properties such as traveltime and relative geometric spreading (traveltime derivatives) are highly essential in seismic data processing and can be used in stacking, time-domain migration, and amplitude variation with offset analysis. Due to the complexity of an elastic orthorhombic (ORT) medium, analysis of these properties becomes reasonably difficult, where accurate explicit-form approximations are highly recommended. We have defined the shifted hyperbola form, Taylor series (TS), and the rational form (RF) approximations for P-wave traveltime and relative geometric spreading in an elastic ORT model. Because the parametric form expression for the P-wave vertical slowness in the derivation is too complicated, TS (expansion in offset) is applied to facilitate the derivation of approximate coefficients. The same approximation forms computed in the acoustic ORT model also are derived for comparison. In the numerical tests, three ORT models with parameters obtained from real data are used to test the accuracy of each approximation. The numerical examples yield results in which, apart from the error along the y-axis in ORT model 2 for the relative geometric spreading, the RF approximations all are very accurate for all of the tested models in practical applications.

The Shuey-Radon transform

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. V197-V206 ◽  
Author(s):  
Ali Gholami ◽  
Milad Farshad
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Matching Pursuit ◽  
Real Data ◽  
Transform Domain ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Linear System Of Equations ◽  
Matching Pursuit Algorithm ◽  
Zero Offset

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.

Anisotropic 3D elastic full-wavefield inversion to directly estimate elastic properties and its role in interpretation

2021 ◽  
Vol 40 (4) ◽  
pp. 277-286
Author(s):  
Haiyang Wang ◽  
Olivier Burtz ◽  
Partha Routh ◽  
Don Wang ◽  
Jake Violet ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
P Wave ◽  
Quality Estimation ◽  
Amplitude Variation ◽  
Linear Inversion ◽  
Amplitude Variation With Offset ◽  
P Wave Velocity ◽  
Wavefield Inversion

Elastic properties from seismic data are important to determine subsurface hydrocarbon presence and have become increasingly important for detailed reservoir characterization that aids to derisk specific hydrocarbon prospects. Traditional techniques to extract elastic properties from seismic data typically use linear inversion of imaged products (migrated angle stacks). In this research, we attempt to get closer to Tarantola's visionary goal for full-wavefield inversion (FWI) by directly obtaining 3D elastic properties from seismic shot-gather data with limited well information. First, we present a realistic 2D synthetic example to show the need for elastic physics in a strongly elastic medium. Then, a 3D field example from deepwater West Africa is used to validate our workflow, which can be practically used in today's computing architecture. To enable reservoir characterization, we produce elastic products in a cascaded manner and run 3D elastic FWI up to 50 Hz. We demonstrate that reliable and high-resolution P-wave velocity can be retrieved in a strongly elastic setting (i.e., with a class 2 or 2P amplitude variation with offset response) in addition to higher-quality estimation of P-impedance and VP/VS ratio. These parameters can be directly used in interpretation, lithology, and fluid prediction.

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.

Velocity analysis in the presence of amplitude variation

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1664-1672 ◽  
Author(s):  
Debashish Sarkar ◽  
Robert T. Baumel ◽  
Ken L. Larner
Keyword(s):  
Seismic Data ◽  
Degrees Of Freedom ◽  
Velocity Analysis ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Numerical Tests ◽  
Class 1 ◽  
Signal Peak ◽  
Polarity Reversals

Conventional semblance velocity analysis is equivalent to modeling prestack seismic data with events that have hyperbolic moveout but no amplitude variation with offset (AVO). As a result of its assumption that amplitude is independent of offset, this method might be expected to perform poorly for events with strong AVO—especially for events with polarity reversals at large offset, such as reflections from tops of some class 1 and class 2 sands. We find that substantial amplitude variation and even phase change with offset do not compromise the conventional semblance measure greatly. Polarity reversal, however, causes conventional semblance to fail. The semblance method can be extended to take into account data with events that have amplitude variation, expressed by AVO intercept and gradient (i.e., the Shuey approximation). However, because of the extra degrees of freedom introduced in AVO‐sensitive semblance, resolution of the estimated velocities is decreased. This is because the data can be modeled acceptably with a range of combined erroneous velocity and AVO behavior. To address this problem, in addition to using the Shuey equation to describe the amplitude variation, we constrain the AVO parameters (intercept and gradient) to be related linearly within each semblance window. With this constraint we can preserve velocity resolution and improve the quality of velocity analysis in the presence of amplitude and even polarity variation with offset. Results from numerical tests suggest that the modified semblance is accurate in the presence of polarity reversals. Tests also indicate, however, that in the presence of noise, the signal peak in conventional semblance has better standout than does that in the modified semblance measures.

An integrated broadband preprocessing method for towed-streamer seismic data

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V201-V221 ◽  
Author(s):  
Mehdi Aharchaou ◽  
Erik Neumann
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Pressure Data ◽  
Amplitude Variation ◽  
Field Source ◽  
Amplitude Variation With Offset ◽  
Ringing Artifacts ◽  
Joint Application ◽  
Amplitude Compensation ◽  
Unified Method

Broadband preprocessing has become widely used for marine towed-streamer seismic data. In the standard workflow, far-field source designature, receiver and source-side deghosting, and redatuming to mean sea level are applied in sequence, with amplitude compensation for background [Formula: see text] delayed until the imaging or postmigration stages. Thus, each step is likely to generate its own artifacts, quality checking can be time-consuming, and broadband data are only obtained late in this chained workflow. We have developed a unified method for broadband preprocessing — called integrated broadband preprocessing (IBP) — which enables the joint application of all the above listed steps early in the processing sequence. The amplitude, phase, and amplitude-variation-with-offset fidelity of IBP are demonstrated on pressure data from the shallow, deep, and slanted streamers. The integration allows greater sparsity to emerge in the representation of seismic data, conferring clear benefits over the sequential application. Moreover, time sparsity, full dimensionality, and early amplitude [Formula: see text] compensation all have an impact on broadband data quality, in terms of reduced ringing artifacts, improved wavelet integrity at large crossline angles, and fewer residual high-frequency multiples.

Traveltime approximation for converted waves in elastic orthorhombic media

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. C229-C237 ◽  
Author(s):  
Shibo Xu ◽  
Alexey Stovas
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Processing Parameters ◽  
Model Parameters ◽  
Seismic Data Processing ◽  
Converted Wave ◽  
Rational Form ◽  
Time Migration ◽  
Taylor Series Approximation ◽  
Anisotropy Parameters

The moveout approximations are commonly used in seismic data processing such as velocity analysis, modeling, and time migration. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from the real data. To approximate the traveltime in an elastic orthorhombic (ORT) medium, we defined an explicit rational-form approximation for the traveltime of the converted [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves. To obtain the expression of the coefficients, the Taylor-series approximation is applied in the corresponding vertical slowness for three pure-wave modes. By using the effective model parameters for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves, the coefficients in the converted-wave traveltime approximation can be represented by the anisotropy parameters defined in the elastic ORT model. The accuracy in the converted-wave traveltime for three ORT models is illustrated in numerical examples. One can see from the results that, for converted [Formula: see text]- and [Formula: see text]-waves, our rational-form approximation is very accurate regardless of the tested ORT model. For a converted [Formula: see text]-wave, due to the existence of cusps, triplications, and shear singularities, the error is relatively larger compared with PS-waves.

Value of information analysis and Bayesian inversion for closed skew-normal distributions: Applications to seismic amplitude variation with offset data

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R151-R163 ◽  
Author(s):  
Javad Rezaie ◽  
Jo Eidsvik ◽  
Tapan Mukerji
Keyword(s):  
Seismic Data ◽  
Value Of Information ◽  
Bayesian Inversion ◽  
Information Analysis ◽  
Amplitude Variation ◽  
Mean Values ◽  
Amplitude Variation With Offset ◽  
Seismic Amplitude ◽  
Value Of Information Analysis ◽  
Skew Normal

Information analysis can be used in the context of reservoir decisions under uncertainty to evaluate whether additional data (e.g., seismic data) are likely to be useful in impacting the decision. Such evaluation of geophysical information sources depends on input modeling assumptions. We studied results for Bayesian inversion and value of information analysis when the input distributions are skewed and non-Gaussian. Reservoir parameters and seismic amplitudes are often skewed and using models that capture the skewness of distributions, the input assumptions are less restrictive and the results are more reliable. We examined the general methodology for value of information analysis using closed skew normal (SN) distributions. As an example, we found a numerical case with porosity and saturation as reservoir variables and computed the value of information for seismic amplitude variation with offset intercept and gradient, all modeled with closed SN distributions. Sensitivity of the value of information analysis to skewness, mean values, accuracy, and correlation parameters is performed. Simulation results showed that fewer degrees of freedom in the reservoir model results in higher value of information, and seismic data are less valuable when seismic measurements are spatially correlated. In our test, the value of information was approximately eight times larger for a spatial-dependent reservoir variable compared with the independent case.

Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T613-T625 ◽  
Author(s):  
Qizhen Du ◽  
Bo Zhang ◽  
Xianjun Meng ◽  
Chengfeng Guo ◽  
Gang Chen ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Coefficient Matrix ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reflectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reflectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

Amplitude variation with offset inversion using the reflectivity method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. R185-R195 ◽  
Author(s):  
Hongxing Liu ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Bo Hou ◽  
Li Chen
Keyword(s):  
Wave Velocity ◽  
P Wave ◽  
Transmission Losses ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Propagation Effects ◽  
Reflectivity Method ◽  
Internal Multiples

Most existing amplitude variation with offset (AVO) inversion methods are based on the Zoeppritz’s equation or its approximations. These methods assume that the amplitude of seismic data depends only on the reflection coefficients, which means that the wave-propagation effects, such as geometric spreading, attenuation, transmission loss, and multiples, have been fully corrected or attenuated before inversion. However, these requirements are very strict and can hardly be satisfied. Under a 1D assumption, reflectivity-method-based inversions are able to handle transmission losses and internal multiples. Applications of these inversions, however, are still time-consuming and complex in computation of differential seismograms. We have evaluated an inversion methodology based on the vectorized reflectivity method, in which the differential seismograms can be calculated from analytical expressions. It is computationally efficient. A modification is implemented to transform the inversion from the intercept time and ray-parameter domain to the angle-gather domain. AVO inversion is always an ill-posed problem. Following a Bayesian approach, the inversion is stabilized by including the correlation of the P-wave velocity, S-wave velocity, and density. Comparing reflectivity-method-based inversion with Zoeppritz-based inversion on a synthetic data and a real data set, we have concluded that reflectivity-method-based inversion is more accurate when the propagation effects of transmission losses and internal multiples are not corrected. Model testing has revealed that the method is robust at high noise levels.

Determination of the principal directions of azimuthal anisotropy from P-wave seismic data

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 692-706 ◽  
Author(s):  
Subhashis Mallick ◽  
Kenneth L. Craft ◽  
Laurent J. Meister ◽  
Ronald E. Chambers
Keyword(s):  
Anisotropic Medium ◽  
Seismic Data ◽  
Principal Direction ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Amplitude Variation ◽  
S Waves ◽  
Wave Data ◽  
Principal Directions ◽  
Qualitative Measure

In an azimuthally anisotropic medium, the principal directions of azimuthal anisotropy are the directions along which the quasi-P- and the quasi-S-waves propagate as pure P and S modes. When azimuthal anisotropy is induced by oriented vertical fractures imposed on an azimuthally isotropic background, two of these principal directions correspond to the directions parallel and perpendicular to the fractures. S-waves propagating through an azimuthally anisotropic medium are sensitive to the direction of their propagation with respect to the principal directions. As a result, primary or mode‐converted multicomponent S-wave data are used to obtain the principal directions. Apart from high acquisition cost, processing and interpretation of multicomponent data require a technology that the seismic industry has not fully developed. Anisotropy detection from conventional P-wave data, on the other hand, has been limited to a few qualitative studies of the amplitude variation with offset (AVO) for different azimuthal directions. To quantify the azimuthal AVO, we studied the amplitude variation with azimuth for P-wave data at fixed offsets. Our results show that such amplitude variation with azimuth is periodic in 2θ, θ being the orientation of the shooting direction with respect to one of the principal directions. For fracture‐induced anisotropy, this principal direction corresponds to the direction parallel or perpendicular to the fractures. We use this periodic azimuthal dependence of P-wave reflection amplitudes to identify two distinct cases of anisotropy detection. The first case is an exactly determined one, where we have observations from three azimuthal lines for every common‐midpoint (CMP) location. We derive equations to compute the orientation of the principal directions for such a case. The second case is an overdetermined one where we have observations from more than three azimuthal lines. Orientation of the principal direction from such an overdetermined case can be obtained from a least‐squares fit to the reflection amplitudes over all the azimuthal directions or by solving many exactly determined problems. In addition to the orientation angle, a qualitative measure of the degree of azimuthal anisotropy can also be obtained from either of the above two cases. When azimuthal anisotropy is induced by oriented vertical fractures, this qualitative measure of anisotropy is proportional to fracture density. Using synthetic seismograms, we demonstrate the robustness of our method in evaluating the principal directions from conventional P-wave seismic data. We also apply our technique to real P-wave data, collected over a wide source‐to‐receiver azimuth distribution. Computations using our method gave an orientation of the principal direction consistent with the general fracture orientation in the area as inferred from other geological and geophysical evidence.

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