Scale properties of the seismic wavefield perspectives for full-waveform matching

Starting from the nondimensionalization of equations of motion we partition the set of the velocity models in equivalence classes, such that the full waveform of an element in a given class can be calculated from the full waveform of any other element in the same class by scaling model parameters. We give a formal derivation of the seismic wavefield scale properties and we prove their capability through the use of numerical examples. Besides this, we introduce how the scale properties can be used to save computational time in full waveform modeling and inversion. In forward modeling we can use them for the calculation of the full waveform of any model in the same equivalence class of a model whose full waveform has been previously calculated. In full waveform inversion, scale properties can be used for full waveform matching: Given an experimental seismogram and a synthetic one, we can choose, in the same class of the synthetic model, another element whose waveform is closer to the experimental one.

Download Full-text

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

Geophysics ◽

10.1190/geo2018-0175.1 ◽

2019 ◽

Vol 84 (5) ◽

pp. R793-R804 ◽

Cited By ~ 3

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.

Download Full-text

Optimal coding of blended seismic sources for 2D full waveform inversion in time

CT&F - Ciencia Tecnología y Futuro ◽

10.29047/01225383.78 ◽

2018 ◽

Vol 8 (2) ◽

Author(s):

Katherine Flórez ◽

Sergio Alberto Abreo Carrillo ◽

Ana Beatriz Ramírez Silva

Keyword(s):

Waveform Inversion ◽

Velocity Model ◽

Computational Time ◽

Inversion Method ◽

Single Shot ◽

Full Waveform Inversion ◽

Velocity Models ◽

Full Waveform ◽

Seismic Image ◽

Blended Data

Full Waveform Inversion (FWI) schemes are gradually becoming more common in the oil and gas industry, as a new tool for studying complex geological zones, based on their reliability for estimating velocity models. FWI is a non-linear inversion method that iteratively estimates subsurface characteristics such as seismic velocity, starting from an initial velocity model and the preconditioned data acquired. Blended sources have been used in marine seismic acquisitions to reduce acquisition costs, reducing the number of times that the vessel needs to cross the exploration delineation trajectory. When blended or simultaneous without previous de-blending or separation, stage data are used in the reconstruction of the velocity model with the FWI method, and the computational time is reduced. However, blended data implies overlapping single shot-gathers, producing interference that affects the result of seismic approaches, such as FWI or seismic image migration. In this document, an encoding strategy is developed, which reduces the overlap areas within the blended data to improve the final velocity model with the FWI method.

Download Full-text

Edge-preserving smoothing for simultaneous-source full-waveform inversion model updates in high-contrast velocity models

Geophysics ◽

10.1190/geo2017-0563.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. A33-A37 ◽

Cited By ~ 5

Author(s):

Amsalu Y. Anagaw ◽

Mauricio D. Sacchi

Keyword(s):

Waveform Inversion ◽

Velocity Model ◽

Model Parameters ◽

Full Waveform Inversion ◽

High Contrast ◽

Edge Preserving ◽

Velocity Models ◽

Smoothing Filter ◽

Full Waveform ◽

Simultaneous Source

Full-waveform inversion (FWI) can provide accurate estimates of subsurface model parameters. In spite of its success, the application of FWI in areas with high-velocity contrast remains a challenging problem. Quadratic regularization methods are often adopted to stabilize inverse problems. Unfortunately, edges and sharp discontinuities are not adequately preserved by quadratic regularization techniques. Throughout the iterative FWI method, an edge-preserving filter, however, can gently incorporate sharpness into velocity models. For every point in the velocity model, edge-preserving smoothing assigns the average value of the most uniform window neighboring the point. Edge-preserving smoothing generates piecewise-homogeneous images with enhanced contrast at boundaries. We adopt a simultaneous-source frequency-domain FWI, based on quasi-Newton optimization, in conjunction with an edge-preserving smoothing filter to retrieve high-contrast velocity models. The edge-preserving smoothing filter gradually removes the artifacts created by simultaneous-source encoding. We also have developed a simple model update to prevent disrupting the convergence of the optimization algorithm. Finally, we perform tests to examine our algorithm.

Download Full-text

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

Geophysics ◽

10.1190/geo2015-0349.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. U25-U38 ◽

Cited By ~ 32

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.

Download Full-text

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

Geophysics ◽

10.1190/1.2957948 ◽

2008 ◽

Vol 73 (5) ◽

pp. VE101-VE117 ◽

Cited By ~ 93

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.

Download Full-text

Target-oriented inversion using the Patched Green′s function method

Geophysics ◽

10.1190/geo2020-0640.1 ◽

2021 ◽

pp. 1-77

Author(s):

Danyelle da Silva ◽

Edwin Fagua Duarte ◽

Wagner Almeida ◽

Mauro Ferreira ◽

Francisco Alirio Moura ◽

...

Keyword(s):

Condensed Matter ◽

Waveform Inversion ◽

Time Lapse ◽

Velocity Model ◽

Dyson Equation ◽

Computational Time ◽

Green Functions ◽

Target Area ◽

Computational Domain ◽

Full Waveform

We have designed a target-oriented methodology to perform Full Waveform Inversion using a frequency-domain wave propagator based on the so-called Patched Greens Function (PGF) technique. Originally developed in condensed matter physics to describe electronic waves in materials, the PGF technique is easily adaptable to the case of wave propagation in a spatially variable media in general. By dividing the entire computational domain into two sections, namely the target area and the outside target area, we calculate the Green Functions related to each section separately. The calculations related to the section outside the target are performed only once at the beginning of inversion, whereas the calculations in the target area are performed repeatedly for each iteration of the inversion process. With the Green Functions of the separate areas, we calculate the Green Functions of the two systems patched together through the application of a Recursive Dyson equation. By performing 2D and time-lapse experiments on the Marmousi model and a Brazilian Pre-salt velocity model, we demonstrate that the target-oriented PGF reduces the computational time of the inversion without compromising accuracy. In fact, when compared with conventional FWI results, the PGF-based calculations are identical but done in a fraction of the time.

Download Full-text

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽

10.1190/geo2020-0331.1 ◽

2021 ◽

pp. 1-37

Author(s):

Xinhai Hu ◽

Wei Guoqi ◽

Jianyong Song ◽

Zhifang Yang ◽

Minghui Lu ◽

...

Keyword(s):

Waveform Inversion ◽

Nonlinear Least Squares ◽

Real Data ◽

Model Parameters ◽

Full Waveform Inversion ◽

Linear Inversion ◽

Near Surface ◽

Model Parameter ◽

Full Waveform ◽

Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

Download Full-text

Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽

10.1190/geo2018-0082.1 ◽

2019 ◽

Vol 84 (1) ◽

pp. R1-R10 ◽

Cited By ~ 11

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.

Download Full-text

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

The Leading Edge ◽

10.1190/tle40050324.1 ◽

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.

Download Full-text

Optimized Model Parameterization using Compact Full Waveform Inversion

Geophysical Journal International ◽

10.1093/gji/ggaa175 ◽

2020 ◽

Author(s):

Linan Xu ◽

Edgar Manukyan ◽

Hansruedi Maurer

Keyword(s):

Large Scale ◽

Waveform Inversion ◽

Gradient Methods ◽

Significant Loss ◽

Inverse Model ◽

Eigenvalue Decomposition ◽

Model Parameters ◽

Full Waveform Inversion ◽

Full Waveform ◽

Model Parameterization

Summary Seismic Full Waveform Inversion (FWI) has the potential to produce high-resolution subsurface images, but the computational resources required for realistically sized problems can be prohibitively large. In terms of computational costs, Gauss-Newton algorithms are more attractive than the commonly employed conjugate gradient methods, because the former have favorable convergence properties. However, efficient implementations of Gauss-Newton algorithms require an excessive amount of computer memory for larger problems. To address this issue, we introduce Compact Full Waveform Inversion (CFWI). Here, a suitable inverse model parameterization is sought that allows representing all subsurface features, potentially resolvable by a particular source-receiver deployment, but using only a minimum number of model parameters. In principle, an inverse model parameterization, based on the Eigenvalue decomposition, would be optimal, but this is computationally not feasible for realistic problems. Instead, we present two alternative parameter transformations, namely the Haar and the Hartley transformations, with which similarly good results can be obtained. By means of a suite of numerical experiments, we demonstrate that these transformations allow the number of model parameters to be reduced to only a few percent of the original parameterization without any significant loss of spatial resolution. This facilitates efficient solutions of large-scale FWI problems with explicit Gauss-Newton algorithms.

Download Full-text