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.

Bayesian linearized rock-physics inversion

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. D625-D641 ◽  
Author(s):  
Dario Grana
Keyword(s):  
Granular Media ◽  
Computational Cost ◽  
Rock Physics ◽  
Real Data ◽  
Data Sets ◽  
New Approach ◽  
Amplitude Variation With Offset ◽  
Fluid Properties ◽  
Rock Physics Modeling ◽  
Physics Modeling

The estimation of rock and fluid properties from seismic attributes is an inverse problem. Rock-physics modeling provides physical relations to link elastic and petrophysical variables. Most of these models are nonlinear; therefore, the inversion generally requires complex iterative optimization algorithms to estimate the reservoir model of petrophysical properties. We have developed a new approach based on the linearization of the rock-physics forward model using first-order Taylor series approximations. The mathematical method adopted for the inversion is the Bayesian approach previously applied successfully to amplitude variation with offset linearized inversion. We developed the analytical formulation of the linearized rock-physics relations for three different models: empirical, granular media, and inclusion models, and we derived the formulation of the Bayesian rock-physics inversion under Gaussian assumptions for the prior distribution of the model. The application of the inversion to real data sets delivers accurate results. The main advantage of this method is the small computational cost due to the analytical solution given by the linearization and the Bayesian Gaussian approach.

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.

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.

Whole Earth Full-Waveform Inversion With Wavefield Adapted Meshes

2020 ◽  
Author(s):  
Solvi Thrastarson ◽  
Dirk-Philip van Herwaarden ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Martin van Driel ◽  
...  
Keyword(s):  
Stochastic Optimization ◽  
High Performance ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Real Data ◽  
Global Scale ◽  
Full Waveform Inversion ◽  
Optimization Scheme ◽  
Continental Scale ◽  
Full Waveform

<p>With the steadily increasing availability and density of seismic data, full-waveform inversion (FWI) can reveal the Earth's subsurface with unprecedented resolution. FWI, however, carries a significant computational burden. Even with the ever-increasing power of high-performance computing resources, these massive compute requirements inhibit substantial progress, and require algorithmic and technological innovations for global and continental scale inversions.<br>In this contribution, we present an approach to FWI where we achieve significant computational savings through wavefield adapted meshing [1] combined with a stochastic optimization scheme [2]. This twofold strategy allows us (a) to solve the wave equation at lower costs, and (b) to reduce the number of required simulations. In laterally smooth media, we can construct meshes which are adapted to the expected complexity of the wavefield. By optimally designing a unique mesh for each source, we can reduce the computational cost of the forward and adjoint simulations by an order of magnitude. The stochastic optimization scheme is based on a dynamic mini-batch L-BFGS approach, which adaptively subsamples the event catalogue and requires significantly fewer wavefield simulations to converge to a model than conventional FWI. An additional benefit of the dynamic mini-batches is that they seamlessly allow for the inclusion of more sources in an inversion without a considerable additional computational cost.<br>We demonstrate a prototype FWI for this approach towards a global scale inversion with real data.<br><br>[1] Thrastarson, S., van Driel, M., Krischer, L., Afanasiev, M., Boehm, C., van Herwaarden, DP., Fichtner, A., 2019. Accelerating numerical wave propagation by wavefield adapted meshes, Part II: Full-waveform inversion. <em>Submitted to Geophysical Journal International</em><br>[2] van Herwaarden, DP., Boehm, C., Afanasiev, M., Krischer, L., van Driel, M., Thrastarson, S., Trampert, J., Fichtner, A. 2019. Accelerated full-waveform inversion using dynamic mini-batches. <em>Submitted to Geophysical Journal International</em></p>

Least‐squares DMO and migration

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1364-1371 ◽  
Author(s):  
Shuki Ronen ◽  
Christopher L. Liner
Keyword(s):  
Least Squares ◽  
Survey Design ◽  
A Priori ◽  
Computational Cost ◽  
Earth Model ◽  
Data Sampling ◽  
Sampled Data ◽  
Amplitude Variation With Offset ◽  
And Migration ◽  
Irregularly Sampled Data

Conventional processing, such as Kirchhoff dip moveout (DMO) and prestack full migration, are based on independent imaging of subsets of the data before stacking or amplitude variation with offset (AVO) analysis. Least‐squares DMO (LSDMO) and least‐squares migration (LSMig) are a family of developing processing methods which are based on inversion of reverse DMO and demigration operators. LSDMO and LSMig find the earth model that best fits the data and a priori assumptions which can be imposed as constraints. Such inversions are more computer intensive, but have significant advantages compared to conventional processing when applied to irregularly sampled data. Various conventional processes are approximations of the inversions in LSDMO and LSMig. Often, processing is equivalent to using the transpose of a matrix which LSDMO/LSMig inverts. Such transpose processing is accurate when the data sampling is adequate. In practice, costly survey design, real‐time coverage quality control, in‐fill acquisition, redundancy editing, and prestack interpolation, are used to create a survey geometry such that the transpose is a good approximation of the inverse. Normalized DMO and migration are approximately equivalent to following the application of the above transpose processing by a diagonal correction. However, in most cases, the required correction is not actually diagonal. In such cases LSDMO and LSMig can produce earth models with higher resolution and higher fidelity than normalized DMO and migration. The promise of LSMig and LSDMO is reduced acquisition cost, improved resolution, and reduced acquisition footprint. The computational cost, and more importantly turn‐around time, is a major factor in the commercialization of these methods. With parallel computing, these methods are now becoming practical.

scholarly journals Seismic shot-encoding schemes for waveform inversion

2020 ◽  
Vol 17 (5) ◽  
pp. 906-913 ◽  
Author(s):  
Edwin Fagua Duarte ◽  
Carlos A N da Costa ◽  
João M de Araújo ◽  
Yanghua Wang ◽  
Ying Rao
Keyword(s):  
Waveform Inversion ◽  
Random Phase ◽  
Computational Cost ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Seismic Waveform ◽  
Rotation Scheme ◽  
Iterative Inversion ◽  
Inversion Procedure ◽  
The Time Domain

Abstract A shot-encoding technique can be used in seismic waveform inversion to significantly reduce the computational cost by reducing the number of seismic simulations in the inversion procedure. Here we developed two alternative shot-encoding schemes to perform simultaneous-sources waveform inversion. The first scheme (I) encodes shot gathers with random-phase rotations applied to seismic traces. The second scheme (II) encodes shot gathers with random static time shifts. The well-known polarity encoding scheme (III) is just a special case of the random-phase rotation scheme. The second scheme is a variation of the conventional static shift encoding (IV), but the static time shifts in the second scheme are limited to one period of the dominant frequency. All encoded shot gathers are added up into a single super-shot gather for seismic waveform inversion. We perform the time-domain waveform inversion, using these shot-encoding schemes in conjunction with a restarted L-BFGS algorithm in the iterative inversion. The effectiveness and efficiency analyses demonstrate that the two shot-encoding schemes (I and II) proposed in this paper may improve the convergence of the iterative inversion, reduce the crosstalk effect among shots and consequently produce a subsurface velocity model with a high resolution.

scholarly journals Simulating migrated and inverted seismic data by filtering a geologic model

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. T1-T10 ◽  
Author(s):  
Gerrit Toxopeus ◽  
Jan Thorbecke ◽  
Kees Wapenaar ◽  
Steen Petersen ◽  
Evert Slob ◽  
...  
Keyword(s):  
Spatial Resolution ◽  
Computational Cost ◽  
Synthetic Data ◽  
Real Data ◽  
Earth Model ◽  
Karst Collapse ◽  
Convolution Model ◽  
Geologic Model ◽  
And Migration ◽  
And Inversion

The simulation of migrated and inverted data is hampered by the high computational cost of generating 3D synthetic data, followed by processes of migration and inversion. For example, simulating the migrated seismic signature of subtle stratigraphic traps demands the expensive exercise of 3D forward modeling, followed by 3D migration of the synthetic seismograms. This computational cost can be overcome using a strategy for simulating migrated and inverted data by filtering a geologic model with 3D spatial-resolution and angle filters, respectively. A key property of the approach is this: The geologic model that describes a target zone is decoupled from the macrovelocity model used to compute the filters. The process enables a target-orientedapproach, by which a geologically detailed earth model describing a reservoir is adjusted without having to recalculate the filters. Because a spatial-resolution filter combines the results of the modeling and migration operators, the simulated images can be compared directly to a real migration image. We decompose the spatial-resolution filter into two parts and show that applying one of those parts produces output directly comparable to 1D inverted real data. Two-dimensional synthetic examples that include seismic uncertainties demonstrate the usefulness of the approach. Results from a real data example show that horizontal smearing, which is not simulated by the 1D convolution model result, is essential to understand the seismic expression of the deformation related to sulfate dissolution and karst collapse.

scholarly journals Source-independent efficient wavefield inversion

2020 ◽  
Vol 222 (1) ◽  
pp. 697-714
Author(s):  
Chao Song ◽  
Tariq Alkhalifah
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Real Data ◽  
Velocity Model ◽  
Data Set ◽  
Full Waveform ◽  
Source Estimation ◽  
Reference Trace ◽  
New Formulation ◽  
Wavefield Inversion

SUMMARY Full-waveform inversion (FWI) is an effective tool to retrieve a high-resolution subsurface velocity model. The source wavelet accuracy plays an important role in reaching that goal. So we often need to estimate the source function before or within the inversion process. Source estimation requires additional computational cost, and an inaccurate source estimation can hamper the convergence of FWI. We develop a source-independent waveform inversion utilizing a recently introduced wavefield reconstruction based method, which we refer to as efficient wavefield inversion (EWI). In EWI, we essentially reconstruct the wavefield by fitting it to the observed data as well as a wave equation based on iterative Born scattering. However, a wrong source wavelet will induce errors in the reconstructed wavefield, which may lead to a divergence of this optimization problem. We use a convolution-based source-independent misfit function to replace the conventional data fitting term in EWI to formulate a source-independent EWI (SIEWI) objective function. By convolving the observed data with a reference trace from the predicted data and convolving the predicted data with a reference trace from the observed data, the influence of the source wavelet on the optimization is mitigated. In SIEWI, this new formulation is able to mitigate the cycle-skipping issue and the source wavelet uncertainty simultaneously. We demonstrate those features on the Overthrust model and a modified Marmousi model. Application on a 2-D real data set also shows the effectiveness of the proposed method.

Wavefield reconstruction in attenuating media: A checkpointing-assisted reverse-forward simulation method

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R349-R362 ◽  
Author(s):  
Pengliang Yang ◽  
Romain Brossier ◽  
Ludovic Métivier ◽  
Jean Virieux
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Simulation Method ◽  
Forward Modeling ◽  
Seismic Attenuation ◽  
Practical Implementation ◽  
Forward Simulation ◽  
Reverse Time ◽  
Time Migration

Three-dimensional implementations of reverse time migration (RTM) and full-waveform inversion (FWI) require efficient schemes to access the incident field to apply the imaging condition of RTM or build the gradient of FWI. Wavefield reconstruction by reverse propagation using final snapshot and saved boundaries appears quite efficient but unstable in attenuating media, whereas the checkpointing strategy is a stable alternative at the expense of increased computational cost through repeated forward modeling. We have developed a checkpointing-assisted reverse-forward simulation (CARFS) method in the context of viscoacoustic wave propagation with a generalized Maxwell body. At each backward reconstruction step, the CARFS algorithm makes a smart decision between forward modeling using checkpoints and reverse propagation based on the minimum time-stepping cost and an energy measure. Numerical experiments demonstrated that the CARFS method allows accurate wavefield reconstruction using less timesteppings than optimal checkpointing, even if seismic attenuation is very strong. For RTM and FWI applications involving a huge number of independent sources and/or applications on architectures with limited memory, CARFS will provide an efficient tool with adequate accuracy in practical implementation.

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