scholarly journals Full-waveform inversion using seislet regularization

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. A43-A49 ◽  
Author(s):  
Zhiguang Xue ◽  
Hejun Zhu ◽  
Sergey Fomel
Keyword(s):  
Wave Equations ◽  
Structural Information ◽  
Random Noise ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Optimization Approach ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
The Cost

Because of inaccurate, incomplete, and inconsistent waveform records, full-waveform inversion (FWI) in the framework of a local optimization approach may not have a unique solution, and thus it remains an ill-posed inverse problem. To improve the robustness of FWI, we have developed a new model regularization approach that enforced the sparsity of solutions in the seislet domain. The construction of seislet basis functions requires structural information that can be estimated iteratively from migration images. We implement FWI with seislet regularization using nonlinear shaping regularization and impose sparseness by applying soft thresholding on the updated model in the seislet domain at each iteration of the data-fitting process. The main extra computational cost of the method relative to standard FWI is the cost of applying forward and inverse seislet transforms at each iteration. This cost is almost negligible compared with the cost of solving wave equations. Numerical tests using the synthetic Marmousi model demonstrate that seislet regularization can greatly improve the robustness of FWI by recovering high-resolution velocity models, particularly in the presence of strong crosstalk artifacts from simultaneous sources or strong random noise in the data.

Full-waveform inversion for full-wavefield imaging: Decades in the making

2021 ◽  
Vol 40 (5) ◽  
pp. 324-334
Author(s):  
Rongxin Huang ◽  
Zhigang Zhang ◽  
Zedong Wu ◽  
Zhiyuan Wei ◽  
Jiawei Mei ◽  
...  
Keyword(s):  
Model Building ◽  
Seismic Imaging ◽  
Structural Information ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Types ◽  
Velocity Models ◽  
Full Waveform

Seismic imaging using full-wavefield data that includes primary reflections, transmitted waves, and their multiples has been the holy grail for generations of geophysicists. To be able to use the full-wavefield data effectively requires a forward-modeling process to generate full-wavefield data, an inversion scheme to minimize the difference between modeled and recorded data, and, more importantly, an accurate velocity model to correctly propagate and collapse energy of different wave modes. All of these elements have been embedded in the framework of full-waveform inversion (FWI) since it was proposed three decades ago. However, for a long time, the application of FWI did not find its way into the domain of full-wavefield imaging, mostly owing to the lack of data sets with good constraints to ensure the convergence of inversion, the required compute power to handle large data sets and extend the inversion frequency to the bandwidth needed for imaging, and, most significantly, stable FWI algorithms that could work with different data types in different geologic settings. Recently, with the advancement of high-performance computing and progress in FWI algorithms at tackling issues such as cycle skipping and amplitude mismatch, FWI has found success using different data types in a variety of geologic settings, providing some of the most accurate velocity models for generating significantly improved migration images. Here, we take a step further to modify the FWI workflow to output the subsurface image or reflectivity directly, potentially eliminating the need to go through the time-consuming conventional seismic imaging process that involves preprocessing, velocity model building, and migration. Compared with a conventional migration image, the reflectivity image directly output from FWI often provides additional structural information with better illumination and higher signal-to-noise ratio naturally as a result of many iterations of least-squares fitting of the full-wavefield data.

Accelerating full waveform inversion through Adaptive Gradient Optimization methods and Dynamic Simultaneous Sources

2020 ◽  
Author(s):  
Marcos Bernal-Romero ◽  
Ursula Iturrarán-Viveros
Keyword(s):  
Cost Function ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Step Length ◽  
Stochastic Gradient Descent ◽  
Physical Parameters ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Gradient Optimization

Summary Full-Waveform Inversion (FWI) is a procedure based on the minimization of a misfit (or cost) function applied to the difference between synthetic waveforms and real seismic traces that derives high-resolution velocity models. This is achieved through the iterative adjustment of the velocity model and/or some other physical parameters of the Earth’s subsurface, which generally implies large computational effort. In order to minimize this cost function we explore the use of Adaptive Gradient Optimization (AGO), a variant of Stochastic Gradient Descent (SGD) methods, combining them with a dynamic simultaneous sources strategy that allow us to reduce the computational cost involved in this process. AGO methods are computationally efficient, have little memory requirements and have the capability of adapting the step-length according to the optimization process’ evolution. Since a precise calibration of the step-length is needed to ensure efficiency, the AGOs are well-suited for this task because they are able to adapt the step-length according to the optimization’s development. In this work, we propose a simple non-linear relationship that allows an adjustment of the step-length with respect to the frequencies used in the multiscale FWI, avoiding the line-search strategy’s high computational burden. Additionally, the application of this new step-length rule into the AGO methods with a dynamic simultaneous sources strategy, allow us to concurrently accelerate and significantly improve the FWI’s numerical performance and results. We compare the performance and final results of seven AGO methods, using two different FWI misfit functionals (based on L1 and L2 norms) applied to estimate the final velocity models of two benchmark acoustic models: the Marmousi and the Canadian overthrust BP velocity models.

scholarly journals Receiver-extension strategy for time-domain full waveform inversion using a relocalization approach

Geophysics ◽  
2021 ◽  
pp. 1-85
Author(s):  
Ludovic Métivier ◽  
Romain Brossier
Keyword(s):  
Time Domain ◽  
Field Data ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Geological Environment ◽  
Extension Method ◽  
Velocity Models ◽  
Full Waveform

A receiver-extension strategy is presented as an alternative to recently promoted source-extension strategies, in the framework of high resolution seismic imaging by full waveform inversion. This receiver-extension strategy is directly applicable in time-domain full waveform inversion, and unlike source-extension methods it incurs negligible extra computational cost. After connections between difference source-extension strategies are reviewed, the receiver-extension method is introduced and analyzed for single-arrival data. The method results in a misfit function convex with respect to the velocity model in this context. The method is then applied to three exploration scale synthetic case studies representative of different geological environment, based on: the Marmousi model, the BP 2004 salt model, and the Valhall model. In all three cases the receiver-extension strategy makes it possible to start full waveform inversion with crude initial models, and reconstruct meaningful subsurface velocity models. The good performance of the method even considering inaccurate amplitude prediction due to noise, imperfect modeling, and source wavelet estimation, bodes well for field data applications.

scholarly journals Full-waveform inversion via source-receiver extension

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R153-R171 ◽  
Author(s):  
Guanghui Huang ◽  
Rami Nammour ◽  
William Symes
Keyword(s):  
Model Updating ◽  
Quantitative Estimation ◽  
Time Lag ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Time Lags ◽  
Complex Data ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform

Full-waveform inversion produces highly resolved images of the subsurface and quantitative estimation of seismic wave velocity, provided that its initial model is kinematically accurate at the longest data wavelengths. If this initialization constraint is not satisfied, iterative model updating tends to stagnate at kinematically incorrect velocity models producing suboptimal images. The source-receiver extension overcomes this “cycle-skip” pathology by modeling each trace with its own proper source wavelet, permitting a good data fit throughout the inversion process. Because source wavelets should be constant (or vary systematically) across a shot gather, a measure of source trace dependence, for example, the mean square of the signature-deconvolved wavelet scaled by time lag, can be minimized to update the velocity model. For kinematically simple data, such measures of wavelet variance are mathematically equivalent to traveltime misfit. Thus, the model obtained by source-receiver extended inversion is close to that produced by traveltime tomography, even though the process uses no picked times. For more complex data, in which energy travels from source to receiver by multiple raypaths, Green’s function spectral notches may lead to slowly decaying trace-dependent wavelets with energy at time lags unrelated to traveltime error. Tikhonov regularization of the data-fitting problem suppresses these large-lag signals. Numerical examples suggest that this regularized formulation of source-receiver extended inversion is capable of recovering reasonably good velocity models from synthetic transmission and reflection data without stagnation at suboptimal models encountered by standard full-waveform inversion, but with essentially the same computational cost.

scholarly journals Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE101-VE117 ◽  
Author(s):  
Hafedh Ben-Hadj-Ali ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
High Resolution ◽  
Frequency Domain ◽  
Distributed Memory ◽  
Waveform Inversion ◽  
Steepest Descent Method ◽  
Frequency Domain Method ◽  
Full Waveform Inversion ◽  
Direct Solver ◽  
Velocity Models ◽  
Full Waveform

We assessed 3D frequency-domain (FD) acoustic full-waveform inversion (FWI) data as a tool to develop high-resolution velocity models from low-frequency global-offset data. The inverse problem was posed as a classic least-squares optimization problem solved with a steepest-descent method. Inversion was applied to a few discrete frequencies, allowing management of a limited subset of the 3D data volume. The forward problem was solved with a finite-difference frequency-domain method based on a massively parallel direct solver, allowing efficient multiple-shot simulations. The inversion code was fully parallelized for distributed-memory platforms, taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver. After validation on simple synthetic tests, FWI was applied to two targets (channel and thrust system) of the 3D SEG/EAGE overthrust model, corresponding to 3D domains of [Formula: see text] and [Formula: see text], respectively. The maximum inverted frequencies are 15 and [Formula: see text] for the two applications. A maximum of 30 dual-core biprocessor nodes with [Formula: see text] of shared memory per node were used for the second target. The main structures were imaged successfully at a resolution scale consistent with the inverted frequencies. Our study confirms the feasibility of 3D frequency-domain FWI of global-offset data on large distributed-memory platforms to develop high-resolution velocity models. These high-velocity models may provide accurate macromodels for wave-equation prestack depth migration.

scholarly journals Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Zhendong Zhang ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Yike Liu ◽  
Bin He ◽  
...  
Keyword(s):  
Field Data ◽  
Extreme Values ◽  
Time Lag ◽  
Waveform Inversion ◽  
Optimal Time ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

On-the-Fly Full Hessian Kernel Calculations Based upon Seismic-Wave Simulations

2021 ◽  
Author(s):  
Yujiang Xie ◽  
Catherine A. Rychert ◽  
Nicholas Harmon ◽  
Qinya Liu ◽  
Dirk Gajewski
Keyword(s):  
Wave Equations ◽  
Convergence Rates ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Random Access ◽  
Spectral Element ◽  
Source Codes ◽  
Full Waveform ◽  
Trade Offs ◽  
Adjoint Tomography

Abstract Full waveform inversion or adjoint tomography has routinely been performed to image the internal structure of the Earth at high resolution. This is typically done using the Fréchet kernels and the approximate Hessian or the approximate inverse Hessian because of the high-computational cost of computing and storing the full Hessian. Alternatively, the full Hessian kernels can be used to improve inversion resolutions and convergence rates, as well as possibly to mitigate interparameter trade-offs. The storage requirements of the full Hessian kernel calculations can be reduced by compression methods, but often at a price of accuracy depending on the compression factor. Here, we present open-source codes to compute both Fréchet and full Hessian kernels on the fly in the computer random access memory (RAM) through simultaneously solving four wave equations, which we call Quad Spectral-Element Method (QuadSEM). By recomputing two forward fields at the same time that two adjoint fields are calculated during the adjoint simulation, QuadSEM constructs the full Hessian kernels using the exact forward and adjoint fields. In addition, we also implement an alternative approach based on the classical wavefield storage method (WSM), which stores forward wavefields every kth (k≥1) timestep during the forward simulation and reads required fields back into memory during the adjoint simulation for kernel construction. Both Fréchet and full Hessian kernels can be computed simultaneously through the QuadSEM or the WSM code, only doubling the computational cost compared with the computation of Fréchet kernels alone. Compared with WSM, QuadSEM can reduce the disk space and input/output cost by three orders of magnitude in the presented examples that use 15,000 timesteps. Numerical examples are presented to demonstrate the functionality of the methods, and the computer codes are provided with this contribution.

Full-waveform inversion of salt models using shape optimization and simulated annealing

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R793-R804 ◽  
Author(s):  
Debanjan Datta ◽  
Mrinal K. Sen ◽  
Faqi Liu ◽  
Scott Morton
Keyword(s):  
Simulated Annealing ◽  
Least Squares ◽  
Level Set ◽  
Waveform Inversion ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Starting Model

A good starting model is imperative in full-waveform inversion (FWI) because it solves a least-squares inversion problem using a local gradient-based optimization method. A suboptimal starting model can result in cycle skipping leading to poor convergence and incorrect estimation of subsurface properties. This problem is especially crucial for salt models because the strong velocity contrasts create substantial time shifts in the modeled seismogram. Incorrect estimation of salt bodies leads to velocity inaccuracies in the sediments because the least-squares gradient aims to reduce traveltime differences without considering the sharp velocity jump between sediments and salt. We have developed a technique to estimate velocity models containing salt bodies using a combination of global and local optimization techniques. To stabilize the global optimization algorithm and keep it computationally tractable, we reduce the number of model parameters by using sparse parameterization formulations. The sparse formulation represents sediments using a set of interfaces and velocities across them, whereas a set of ellipses represents the salt body. We use very fast simulated annealing (VFSA) to minimize the misfit between the observed and synthetic data and estimate an optimal model in the sparsely parameterized space. The VFSA inverted model is then used as a starting model in FWI in which the sediments and salt body are updated in the least-squares sense. We partition model updates into sediment and salt updates in which the sediments are updated like conventional FWI, whereas the shape of the salt is updated by taking the zero crossing of an evolving level set surface. Our algorithm is tested on two 2D synthetic salt models, namely, the Sigsbee 2A model and a modified SEG Advanced Modeling Program (SEAM) Phase I model while fixing the top of the salt. We determine the efficiency of the VFSA inversion and imaging improvements from the level set FWI approach and evaluate a few sources of uncertainty in the estimation of salt shapes.

scholarly journals Full-waveform inversion, Part 3: Optimization

2018 ◽  
Vol 37 (2) ◽  
pp. 142-145 ◽  
Author(s):  
Philipp Witte ◽  
Mathias Louboutin ◽  
Keegan Lensink ◽  
Michael Lange ◽  
Navjot Kukreja ◽  
...  
Keyword(s):  
Objective Function ◽  
Wave Equations ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Acoustic Wave Equation ◽  
Automated Generation ◽  
Domain Specific ◽  
Full Waveform ◽  
Adjoint State ◽  
Adjoint State Method

This tutorial is the third part of a full-waveform inversion (FWI) tutorial series with a step-by-step walkthrough of setting up forward and adjoint wave equations and building a basic FWI inversion framework. For discretizing and solving wave equations, we use Devito ( http://www.opesci.org/devito-public ), a Python-based domain-specific language for automated generation of finite-difference code ( Lange et al., 2016 ). The first two parts of this tutorial ( Louboutin et al., 2017 , 2018 ) demonstrated how to solve the acoustic wave equation for modeling seismic shot records and how to compute the gradient of the FWI objective function using the adjoint-state method. With these two key ingredients, we will now build an inversion framework that can be used to minimize the FWI least-squares objective function.

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