Ensemble-based seismic inversion for a stratified medium

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. R29-R39 ◽  
Author(s):  
Michael Gineste ◽  
Jo Eidsvik ◽  
York Zheng
Keyword(s):  
Waveform Inversion ◽  
Seismic Inversion ◽  
Stratified Medium ◽  
Elastic Parameters ◽  
Waveform Data ◽  
Optimization Task ◽  
Estimation Uncertainty ◽  
Seismic Waveform ◽  
Probabilistic Setting ◽  
Iterative Ensemble Smoother

Seismic waveform inversion is a nontrivial optimization task, which is often complicated by the nonlinear relationship between the elastic attributes of interest and the large amount of data obtained in seismic experiments. Quantifying the solution uncertainty can be even more challenging, and it requires considering the problem in a probabilistic setting. Consequently, the seismic inverse problem is placed in a Bayesian framework, using a sequential filtering approach to invert for the elastic parameters. The method uses an iterative ensemble smoother to estimate the subsurface parameters, and from the ensemble, a notion of estimation uncertainty is readily available. The ensemble implicitly linearizes the relation between the parameters and the observed waveform data; hence, it requires no tangent linear model. The approach is based on sequential conditioning on partitions of the whole data record (1) to regularize the inversion path and effectively drive the estimation process in a top-down manner and (2) to circumvent a consequence of the ensemble reduced rank approximation. The method is exemplified on a synthetic case, inverting for elastic parameters in a 1D medium using a seismic shot record. Our results indicate that the iterative ensemble method is applicable to seismic waveform inversion and that the ensemble representation indeed indicates estimation uncertainty.

scholarly journals Batch seismic inversion using the iterative ensemble Kalman smoother

2021 ◽  
Author(s):  
Michael Gineste ◽  
Jo Eidsvik
Keyword(s):  
Seismic Data ◽  
Time Windows ◽  
Seismic Inversion ◽  
Efficient Estimation ◽  
Solution Strategy ◽  
Adaptive Procedure ◽  
Waveform Data ◽  
Kalman Smoother ◽  
Seismic Waveform ◽  
Single Batch

AbstractAn ensemble-based method for seismic inversion to estimate elastic attributes is considered, namely the iterative ensemble Kalman smoother. The main focus of this work is the challenge associated with ensemble-based inversion of seismic waveform data. The amount of seismic data is large and, depending on ensemble size, it cannot be processed in a single batch. Instead a solution strategy of partitioning the data recordings in time windows and processing these sequentially is suggested. This work demonstrates how this partitioning can be done adaptively, with a focus on reliable and efficient estimation. The adaptivity relies on an analysis of the update direction used in the iterative procedure, and an interpretation of contributions from prior and likelihood to this update. The idea is that these must balance; if the prior dominates, the estimation process is inefficient while the estimation is likely to overfit and diverge if data dominates. Two approaches to meet this balance are formulated and evaluated. One is based on an interpretation of eigenvalue distributions and how this enters and affects weighting of prior and likelihood contributions. The other is based on balancing the norm magnitude of prior and likelihood vector components in the update. Only the latter is found to sufficiently regularize the data window. Although no guarantees for avoiding ensemble divergence are provided in the paper, the results of the adaptive procedure indicate that robust estimation performance can be achieved for ensemble-based inversion of seismic waveform data.

Enabling isotropic reflectivity modeling and inversion in anisotropic media

2021 ◽  
Vol 40 (4) ◽  
pp. 267-276
Author(s):  
Peter Mesdag ◽  
Leonardo Quevedo ◽  
Cătălin Tănase
Keyword(s):  
Synthetic Data ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Seismic Inversion ◽  
Stratified Medium ◽  
Effective Parameters ◽  
Elastic Parameters ◽  
Pp Wave ◽  
Anisotropic Elastic ◽  
And Inversion

Exploration and development of unconventional reservoirs, where fractures and in-situ stresses play a key role, call for improved characterization workflows. Here, we expand on a previously proposed method that makes use of standard isotropic modeling and inversion techniques in anisotropic media. Based on approximations for PP-wave reflection coefficients in orthorhombic media, we build a set of transforms that map the isotropic elastic parameters used in prestack inversion into effective anisotropic elastic parameters. When used in isotropic forward modeling and inversion, these effective parameters accurately mimic the anisotropic reflectivity behavior of the seismic data, thus closing the loop between well-log data and seismic inversion results in the anisotropic case. We show that modeling and inversion of orthorhombic anisotropic media can be achieved by superimposing effective elastic parameters describing the behavior of a horizontally stratified medium and a set of parallel vertical fractures. The process of sequential forward modeling and postinversion analysis is exemplified using synthetic data.

Multiscale seismic waveform inversion

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1457-1473 ◽  
Author(s):  
Carey Bunks ◽  
Fatimetou M. Saleck ◽  
S. Zaleski ◽  
G. Chavent
Keyword(s):  
Iterative Methods ◽  
Global Minimum ◽  
Multigrid Method ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
Local Minima ◽  
Data Set ◽  
Seismic Waveform ◽  
Inversion Methods ◽  
Iterative Inversion

Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low‐frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.

Data-driven Prestack Waveform Inversion Using Genetic Algorithm- Methodology and Examples

2021 ◽  
pp. 1-97
Author(s):  
Lingxiao Jia ◽  
Subhashis Mallick ◽  
Cheng Wang
Keyword(s):  
Genetic Algorithm ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
P Wave ◽  
Data Driven ◽  
Initial Model ◽  
Reservoir Properties ◽  
Well Control ◽  
Seismic Waveform

The choice of an initial model for seismic waveform inversion is important. In matured exploration areas with adequate well control, we can generate a suitable initial model using well information. However, in new areas where well control is sparse or unavailable, such an initial model is compromised and/or biased by the regions with more well controls. Even in matured exploration areas, if we use time-lapse seismic data to predict dynamic reservoir properties, an initial model, that we obtain from the existing preproduction wells could be incorrect. In this work, we outline a new methodology and workflow for a nonlinear prestack isotropic elastic waveform inversion. We call this method a data driven inversion, meaning that we derive the initial model entirely from the seismic data without using any well information. By assuming a locally horizonal stratification for every common midpoint and starting from the interval P-wave velocity, estimated entirely from seismic data, our method generates pseudo wells by running a two-pass one-dimensional isotropic elastic prestack waveform inversion that uses the reflectivity method for forward modeling and genetic algorithm for optimization. We then use the estimated pseudo wells to build the initial model for seismic inversion. By applying this methodology to real seismic data from two different geological settings, we demonstrate the usefulness of our method. We believe that our new method is potentially applicable for subsurface characterization in areas where well information is sparse or unavailable. Additional research is however necessary to improve the compute-efficiency of the methodology.

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.

Long-Wavelength Earth Model via Accelerated Full-Waveform Inversion

2021 ◽  
Author(s):  
Solvi Thrastarson ◽  
Dirk-Philip van Herwaarden ◽  
Lion Krischer ◽  
Martin van Driel ◽  
Christian Boehm ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Large Data ◽  
Earth Model ◽  
Full Waveform Inversion ◽  
Waveform Data ◽  
Long Wavelength ◽  
Computational Overhead ◽  
Full Dataset ◽  
Full Waveform ◽  
Seismic Waveform

<p>As the volume of available seismic waveform data increases, the responsibility to use the data in an effective way emerges. This requires computational efficiency as well as maximizing the exploitation of the information associated with the data.</p><p>In this contribution, we present a long-wavelength Earth model, created by using the data recorded from over a thousand earthquakes, starting from a simple one-dimensional background (PREM). The model is constructed with an accelerated full-waveform inversion (FWI) method which can seamlessly include large data volumes with a significantly reduced computational overhead. Although we present a long-wavelength model, the approach has the potential to go to much higher frequencies, while maintaining a reasonable cost.</p><p>Our approach combines two novel FWI variants. (1) The dynamic mini-batch approach which uses adaptively defined subsets of the full dataset in each iteration, detaching the direct scaling of inversion cost from the number of earthquakes included. (2) Wavefield-adapted meshes which utilize the azimuthal smoothness of the wavefield to design meshes optimized for each individual source location. Using wavefield adapted meshes can drastically reduce the cost of both forward and adjoint simulations as well as it makes the scaling of the computing cost to modelled frequencies more favourable.</p>

A discrepancy-based penalty method for extended waveform inversion

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. R287-R298 ◽  
Author(s):  
Lei Fu ◽  
William W. Symes
Keyword(s):  
Born Approximation ◽  
Degrees Of Freedom ◽  
Linear Models ◽  
Waveform Inversion ◽  
Constant Density ◽  
Inversion Process ◽  
Waveform Data ◽  
Seismic Waveform ◽  
Optimization Formulation ◽  
Penalty Weight

Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These extra degrees of freedom must be curtailed at the solution, for example, by penalizing them as part of an optimization formulation. For separable (partly linear) models, a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical (linear) degrees of freedom. The linear variables are eliminated in an inner optimization step, leaving a function of the outer (nonlinear) variables to be optimized. This variable projection method is convenient for computation, but it requires that the penalty weight be increased as the estimated model tends to the (physical) solution. We describe an algorithm based on discrepancy, that is, maintaining the data residual at the inner optimum within a prescribed range, to control the penalty weight during the outer optimization. We evaluate this algorithm in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting bandlimited waveform data in the Born approximation.

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