Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

/pdf/an-overview-of-full-waveform-inversion-in-exploration-59sei7fzvh.pdf

An overview of full-waveform inversion in exploration geophysics

Introduction.- Numerical Solution of the Elastic Wave Equation.- Computing Sensitivity Kernels.- Seismological Data Functionals and their Associated Adjoint Sources.- Iterative Optimisation.- Full Waveform Tomography for Upper-mantle Structure in Australasian Region.- A Comparative Study of Local-scale full Waveform Tomographies.- Source Staking and Data Reduction in Global full Waveform Tomography.

Full Seismic Waveform Modelling and Inversion

Least-squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single-scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey-sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey-sinking (depth-oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning-based (surface-oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth-oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model-based data fitting.

http://www.trip.caam.rice.edu/reports/2007/geoprosp0207.pdf

Migration velocity analysis and waveform inversion

SUMMARY For the last 30 yr, since Tarantola’s pioneering theoretical study of waveform inversion, geophysicists and applied mathematicians have utilized a waveform inversion to delineate the earth’s structures. However, successful applications of waveform inversion to real data are nominal. The failures are mainly caused by the high non-linearity of the waveform inversion and the real data containing insufficient low-frequency components. We propose a waveform inversion algorithm that is robust and is not sensitive to the initial model by exploiting the wavefield in the Laplace domain and the adjoint property of the wave equation. The wavefield in the Laplace domain is equivalent to the zero frequency component of the damped wavefield. Therefore, the inversion of Poisson’s equation in electrical prospecting can be viewed as a waveform inversion problem, exploiting the zero frequency component of an undamped wavefield. Since our inversion algorithm in the Laplace domain is strongly associated with the nature of DC inversion for Poisson’s equation in electrical prospecting, our algorithm can generate a velocity model that is equivalent to a long-wavelength velocity model (a smooth velocity model). Through numerical tests, we found that the Laplace-transformed wavefields for optimally low Laplace damping constants are critically needed in our algorithm as the low-frequency components are necessary in the waveform inversion of the frequency domain. We note that the objective function by l2 norm of the logarithmic wavefield in the Laplace domain behaves as if it has no local minimum points in low and high Laplace damping constants. Moreover, we note that the forward modelling in the Laplace domain could be accurately calculated by using a coarser grid of several hundreds of metres than that of the frequency domain. Numerical tests of the salt dome model with high-velocity contrast demonstrate the robustness of our algorithm to both synthetic and real data. To apply our algorithm to real data more successfully, we need to improve the accuracy of the Laplace transformation for the wavefields in the time domain. However, our waveform inversion in the Laplace domain can be successfully applied to real data since our algorithm has more advantages in forward modelling and inversion than those in the frequency domain.

Waveform inversion in the Laplace domain

Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers...

3D prestack plane-wave, full-waveform inversion

Although waveform inversion has been studied extensively since its beginning 20 years ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our waveform inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noisefree synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below 5 Hz are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

/pdf/waveform-inversion-using-a-logarithmic-wavefield-2coiak7dam.pdf

Waveform inversion using a logarithmic wavefield

One of the applications of refraction-traveltime tomography is to provide an initial model for waveform inversion and Kirchhoff prestack migration. For such applications, we need a refraction-traveltime tomography method that is robust for complicated and high-velocity-contrast models. Of the many refraction-traveltime tomography methods available, we believe wave-based algorithms to be best suited for dealing with complicated models. We developed a new wave-based, refraction-tomography algorithm using a damped wave equation and a waveform-inversion back-propagation technique. The imaginary part of a complex angular frequency, which is generally introduced in frequency-domain wave modeling, acts as a damping factor. By choosing an optimal damping factor from the numerical-dispersion relation, we can suppress the wavetrains following the first arrival. The objective function of our algorithm consists of residuals between the respective phases of first arrivals in field data and in forward-modeled data. The...

/pdf/refraction-tomography-using-a-waveform-inversion-back-2hq8uf2yz8.pdf

Refraction tomography using a waveform-inversion back-propagation technique

For scaling of the gradient of misfit function, we develop a new pseudo-Hessian matrix constructed by combining amplitude field and pseudo-Hessian matrix. Since pseudoHessian matrix neglects the calculation of the zero-lag auto-correlation of impulse responses in the approximate Hessian matrix, the pseudo-Hessian matrix has a limitation to scale the gradient of misfit function compared to the approximate Hessian matrix. To validate the new pseudoHessian matrix, we perform frequency-domain elastic full waveform inversion using this Hessian matrix. By synthetic experiments, we show that the new pseudo-Hessian matrix can give better convergence to the true model than the old one does. Furthermore, since the amplitude fields are intrinsically obtained in forward modeling procedure, we do not have to pay any extra cost to compute the new pseudo-Hessian. We think that the new pseudo-Hessian matrix can be used as an alternative of the approximate Hessian matrix of the Gauss-Newton method.

Frequency Domain Elastic Full Waveform Inversion Using the New Pseudo-Hessian Matrix: Elastic Marmousi-2 Synthetic Test

Waveform inversion is one of the valuable methods for seismic interpretation. Most of the waveform inversion algorithms employ common shot gathers. Since we obtain stacked data in general seismic data processing, there are needs to develop a waveform inversion algorithm that can be applied to stacked data. We design a waveform inversion algorithm using exploding reflectors, which is applied to stacked data. Our algorithm is constructed under the assumptions that there exist many exploding reflectors and waves excited at the reflectors propagate with half a velocity as in poststack migration. In our inversion algorithm, we choose the steepest-descent method, and compute the steepest-descent direction by introducing a backpropagation technique and virtual source concept, which are popularly used in frequencydomain waveform inversion these days. The virtual source is regarded as a source for partial derivative wavefield with respect to subsurface velocity, therefore we compute the virtual source by taking the derivative of the modeling operator with respect to subsurface velocity. In the conventional waveform inversion using the steepest-descent method, since original sources, used in forward modeling, are independent of subsurface velocity, the virtual source does not include any original source-related term. In our waveform inversion, however, we use subsurface exploding reflectors for original sources in forward modeling. Since the exploding reflectors are expressed by subsurface velocity contrasts, the virtual source has terms generated by taking the derivative of original sources with respect to subsurface velocity. Numerical structure of our waveform inversion is really similar to that of the conventional one except for different virtual source and different velocity (i.e., half a velocity). We apply our algorithm to a field data set, which was gathered in the Korean continental shelf. In our inversion results, we could observe an anticlinal structure clearly, which is already known to be gas reservoir.

/pdf/waveform-inversion-of-a-stacked-section-using-an-exploding-fneevsl481.pdf

Waveform inversion of a stacked section using an exploding reflector concept

We applied two wave-based refraction traveltime tomography algorithms to a real, field data set obtained in Congo, Africa. The two wave-based refraction tomography methods extract traveltimes by taking the logarithm of damped wavefield. The damped wavefield can be assumed to have a single, first arrival when we choose an optimal damping factor in complex angular frequency. The main differences between two methods exist in computing the steepest-descent directions. One method computes Frechet derivative of traveltime directly; The other method introduces a backpropagation algorithm and virtual source concept, which is commonly employed in waveform inversion and reverse time migration. The two methods have already proven to give similar, good results for synthetic data. After applying the two wavebased tomography method to the real, field data, we can know that both of them describe high-velocity salt dome structure very clearly and give reliable solutions for real data. Having used the inverted velocity model in prestack Kirchhoff migration successfully, we can also confirm that the inverted velocity model obtained by the refraction tomography method can be effectively applied in prestack Kirchhoff migration.

Application of refraction tomography algorithms to real data

Popular Tasks used by Researchers

How can I help with your research?

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

We encountered an error while loading the panel. Please try refreshing the page.

Something went wrong

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

Anyone with the link can view this chat. You can switch it back to private anytime.

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Dong-Joo Min

Author Tools

Chat about Author