Amplitude-variation-with-offset and prestack waveform inversion- a direct comparison using a real data example

2014 ◽  
Author(s):  
Subhashis Mallick* ◽  
Samar Adhikari ◽  
Josiane Pafeng
Keyword(s):  
Waveform Inversion ◽  
Real Data ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset

Linearized amplitude variation with offset (AVO) inversion with supercritical angles

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. E49-E55 ◽  
Author(s):  
Jonathan E. Downton ◽  
Charles Ursenbach
Keyword(s):  
Reflection Coefficient ◽  
Critical Angle ◽  
Waveform Inversion ◽  
Phase Variation ◽  
Reflection Coefficients ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion ◽  
Angle Data

Contrary to popular belief, a linearized approximation of the Zoeppritz equations may be used to estimate the reflection coefficient for angles of incidence up to and beyond the critical angle. These supercritical reflection coefficients are complex, implying a phase variation with offset in addition to amplitude variation with offset (AVO). This linearized approximation is then used as the basis for an AVO waveform inversion. By incorporating this new approximation, wider offset and angle data may be incorporated in the AVO inversion, helping to stabilize the problem and leading to more accurate estimates of reflectivity, including density reflectivity.

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.

The vertical image projection method for migration stretch compensation

2021 ◽  
pp. 1-55
Author(s):  
Arash JafarGandomi
Keyword(s):  
Real Data ◽  
Amplitude Variation ◽  
Seismic Migration ◽  
Amplitude Variation With Offset ◽  
Amplitude Inversion ◽  
Image Projection ◽  
And Migration ◽  
Avo Attributes ◽  
Conditioning Approach ◽  
The Impact

True amplitude inversion is often carried out without taking into account migration distortions to the wavelet. Seismic migration leaves a dip-dependent effect on the wavelet that can cause significant inaccuracies in the inverted impedances obtained from conventional inversion approaches based on 1D vertical convolutional modelling. Neglecting this effect causes misleading inversion results and leakage of dipping noise and migration artifacts from higher frequency bands to the lower frequencies. I have observed that despite dip-dependency of this effect, low-dip and flat events may also suffer if they are contaminated with cross-cutting noise, steep migration artifacts, and smiles. In this paper I propose an efficient, effective and reversible data pre-conditioning approach that accounts for dip-dependency of the wavelet and is applied to migrated images prior to inversion. My proposed method consists of integrating data with respect to the total wavenumber followed by the differentiation with respect to the vertical wavenumber. This process is equivalent to applying a deterministic dip-consistent pre-conditioning that projects the data from the total wavenumber to the vertical wavenumber axis. This preconditioning can be applied to both pre- and post-stack data as well as to amplitude variation with offset (AVO) attributes such as intercept and gradient before inversion. The vertical image projection methodology that I propose here reduces the impact of migration artifacts such as cross-cutting noise and migration smiles and improves inverted impedances in both synthetic and real data examples. In particular I show that neglecting the proposed pre-conditioning leads to anomalously higher impedance values along the steeply dipping structures.

Prestack waveform inversion of three-dimensional seismic data — An example from the Rock Springs Uplift, Wyoming, USA

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. B1-B12 ◽  
Author(s):  
Josiane Pafeng ◽  
Subhashis Mallick ◽  
Hema Sharma
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Waveform Inversion ◽  
Three Dimensional ◽  
Seismic Inversion ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Seismic Waveform ◽  
Rock Springs Uplift ◽  
Rock Springs

Applying seismic inversion to estimate subsurface elastic earth properties for reservoir characterization is a challenge in exploration seismology. In recent years, waveform-based seismic inversions have gained popularity, but due to high computational costs, their applications are limited, and amplitude-variation-with-offset/angle inversion is still the current state-of-the-art. We have developed a genetic-algorithm-based prestack seismic waveform inversion methodology. By parallelizing at multiple levels and assuming a locally 1D structure such that forward computation of wave equation synthetics is computationally efficient, this method is capable of inverting 3D prestack seismic data on parallel computers. Applying this inversion to a real prestack seismic data volume from the Rock Springs Uplift (RSU) located in Wyoming, USA, we determined that our method is capable of inverting the data in a reasonable runtime and producing much higher quality results than amplitude-variation-with-offset/angle inversion. Because the primary purpose for seismic data acquisition at the RSU was to characterize the subsurface for potential targets for carbon dioxide sequestration, we also identified and analyzed some potential primary and secondary storage formations and their associated sealing lithologies from our inversion results.

Iterative multiparameter waveform inversion of precritical reflection data using prestack time Kirchhoff approximation

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. R15-R27 ◽  
Author(s):  
Hassan Khaniani ◽  
John C. Bancroft ◽  
Eric von Lunen
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Real Data ◽  
Forward Modeling ◽  
Kirchhoff Approximation ◽  
Amplitude Variation With Offset ◽  
Reflection Data ◽  
Elastic Wave Scattering ◽  
Iterative Inversion ◽  
And Migration

We have studied elastic wave scattering and iterative inversion in the context of the Kirchhoff approximation. The approach is more consistent with the weak-contrast reflectivity functions of Zoeppritz equations as compared to the Born approximation. To reduce the computational cost associated with inversion, we demonstrated the use of amplitude-variation-with-offset (AVO) analysis, prestack time migrations (PSTMs), and the corresponding forward modeling in an iterative scheme. Forward modeling and migration/inversion operators are based on the double-square-root (DSR) equations of PSTM and linearized reflectivity functions. All operators involved in the inversion, including the background model for DSR and AVO, are defined in P-to-P traveltime and are updated at each iteration. Our method is practical for real data applications because all operators of the inversion are known to be applicable for standard methods. We have evaluated the inversion on synthetic and real data using the waveform characteristics of P-to-P and P-to-S data.

Amplitude-variation-with-offset and prestack-waveform inversion: A direct comparison using a real data example from the Rock Springs Uplift, Wyoming, USA

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. B45-B59 ◽  
Author(s):  
Subhashis Mallick ◽  
Samar Adhikari
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Quantitative Estimation ◽  
Waveform Inversion ◽  
Forward Modeling ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Rock Springs Uplift ◽  
Rock Springs

Recent advances in seismic data acquisition and processing allow routine extraction of offset-/angle-dependent reflection amplitudes from prestack seismic data for quantifying subsurface lithologic and fluid properties. Amplitude-variation-with-offset (AVO) inversion is the most commonly used practice for such quantification. Although quite successful, AVO has a few shortcomings primarily due to the simplicity in its inherent assumptions, and for any quantitative estimation of reservoir properties, they are generally interpreted in combination with other information. In recent years, waveform-based inversions have gained popularity in reservoir characterization and depth imaging. Going beyond the simple assumptions of AVO and using wave equation solutions, these methods have been effective in accurately predicting the subsurface properties. Developments of these waveform inversions have so far been along two lines: (1) the methods that use a locally 1D model of the subsurface for each common midpoint and use an analytical solution to the wave equation for forward modeling and (2) the methods that do not make any 1D assumption but use an approximate numerical solution to the wave equation in 2D or 3D for forward modeling. Routine applications of these inversions are, however, still computationally demanding. We described a multilevel parallelization of elastic-waveform inversion methodology under a 1D assumption that allowed its application in a reasonable time frame. Applying AVO and waveform inversion on a single data set from the Rock Springs Uplift, Wyoming, USA, and comparing them with one another, we also determined that the waveform-based method was capable of obtaining a much superior description of subsurface properties compared with AVO. We concluded that the waveform inversions should be the method of choice for reservoir property estimation as high-performance computers become commonly available.

scholarly journals A direct inverse method for subsurface properties: The conceptual and practical benefit and added value in comparison with all current indirect methods, for example, amplitude-variation-with-offset and full-waveform inversion

2017 ◽  
Vol 5 (3) ◽  
pp. SL89-SL107 ◽  
Author(s):  
Arthur B. Weglein
Keyword(s):  
Success Rate ◽  
Waveform Inversion ◽  
Forward Problem ◽  
Inversion Method ◽  
Elastic Model ◽  
Full Waveform Inversion ◽  
Amplitude Variation ◽  
Indirect Methods ◽  
Amplitude Variation With Offset ◽  
Full Waveform

Direct inverse methods solve the problem of interest; in addition, they communicate whether the problem of interest is the problem that we (the seismic industry) need to be interested in. When a direct solution does not result in an improved drill success rate, we know that the problem we have chosen to solve is not the right problem — because the solution is direct and cannot be the issue. On the other hand, with an indirect method, if the result is not an improved drill success rate, then the issue can be either the chosen problem, or the particular choice within the plethora of indirect solution methods, or both. The inverse scattering series (ISS) is the only direct inversion method for a multidimensional subsurface. Solving a forward problem in an inverse sense is not equivalent to a direct inverse solution. All current methods for parameter estimation, e.g., amplitude-variation-with-offset and full-waveform inversion, are solving a forward problem in an inverse sense and are indirect inversion methods. The direct ISS method for determining earth material properties defines the precise data required and the algorithms that directly output earth mechanical properties. For an elastic model of the subsurface, the required data are a matrix of multicomponent data, and a complete set of shot records, with only primaries. With indirect methods, any data can be matched: one trace, one or several shot records, one component, multicomponent, with primaries only or primaries and multiples. Added to that are the innumerable choices of cost functions, generalized inverses, and local and global search engines. Direct and indirect parameter inversion are compared. The direct ISS method has more rapid convergence and a broader region of convergence. The difference in effectiveness increases as subsurface circumstances become more realistic and complex, in particular with band-limited noisy data.

Nonlinear amplitude-variation-with-offset inversion for Lamé parameters using a direct inversion method

2017 ◽  
Vol 5 (3) ◽  
pp. SL57-SL67 ◽  
Author(s):  
Guangsen Cheng ◽  
Xingyao Yin ◽  
Zhaoyun Zong
Keyword(s):  
Nonlinear Equation ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Reservoir Prediction ◽  
Amplitude Variation ◽  
Linear Inversion ◽  
Amplitude Variation With Offset ◽  
Avo Inversion

Prestack seismic inversion is widely used in fluid indication and reservoir prediction. Compared with linear inversion, nonlinear inversion is more precise and can be applied to high-contrast situations. The inversion results can be affected by the parameters’ sensitivity, so the parameterization of nonlinear equations is very significant. Considering the poor nonlinear amplitude-variation-with-offset (AVO) inversion results of impedance and velocity parameters, we adjust the parameters of the nonlinear equation, avoid the inaccuracy caused by parameters sensitivity and get the ideal nonlinear AVO inversion results of the Lamé parameters. The feasibility and stability of the nonlinear equation based on the Lamé parameters and method are verified by the model and the real data examples. The resolution and the lateral continuity of nonlinear inversion results are better compared with the linear inversion results.

A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. U25-U38 ◽  
Author(s):  
Nuno V. da Silva ◽  
Andrew Ratcliffe ◽  
Vetle Vinje ◽  
Graham Conroy
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Radiation Patterns ◽  
Data Set ◽  
Full Waveform ◽  
Seismic Image ◽  
Central North Sea

Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.

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