The convexity of optimal transport-based waveform inversion for certain structured velocity models

AbstractThis study comprehensively investigates the source mechanisms associated with the mainshock and aftershocks of the Mw = 6.3 Yogyakarta earthquake which occurred on May 27, 2006. The process involved using moment tensor inversion to determine the fault plane parameters and joint inversion which were further applied to understand the spatial and temporal slip distributions during the earthquake. Moreover, coseismal slip distribution was overlaid with the relocated aftershock distribution to determine the stress field variations around the tectonic area. Meanwhile, the moment tensor inversion made use of near-field data and its Green’s function was calculated using the extended reflectivity method while the joint inversion used near-field and teleseismic body wave data which were computed using the Kikuchi and Kanamori methods. These data were filtered through a trial-and-error method using a bandpass filter with frequency pairs and velocity models from several previous studies. Furthermore, the Akaike Bayesian Information Criterion (ABIC) method was applied to obtain more stable inversion results and different fault types were discovered. Strike–slip and dip-normal were recorded for the mainshock and similar types were recorded for the 8th aftershock while the 9th and 16th June were strike slips. However, the fault slip distribution from the joint inversion showed two asperities. The maximum slip was 0.78 m with the first asperity observed at 10 km south/north of the mainshock hypocenter. The source parameters discovered include total seismic moment M0 = 0.4311E + 19 (Nm) or Mw = 6.4 with a depth of 12 km and a duration of 28 s. The slip distribution overlaid with the aftershock distribution showed the tendency of the aftershock to occur around the asperities zone while a normal oblique focus mechanism was found using the joint inversion.

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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.

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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.

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Laplace-domain full-waveform inversion of seismic data lacking low-frequency information

Geophysics ◽

10.1190/geo2011-0411.1 ◽

2012 ◽

Vol 77 (5) ◽

pp. R199-R206 ◽

Cited By ~ 31

Author(s):

Wansoo Ha ◽

Changsoo Shin

Keyword(s):

Seismic Data ◽

Field Data ◽

Waveform Inversion ◽

Low Frequency ◽

Single Frequency ◽

Frequency Content ◽

Laplace Domain ◽

Frequency Information ◽

Velocity Models ◽

Gaussian Source

The lack of the low-frequency information in field data prohibits the time- or frequency-domain waveform inversions from recovering large-scale background velocity models. On the other hand, Laplace-domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions. In theory, frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the Laplace domain. Because the constant can be retrieved using the source estimation process, the frequency content of the seismic data does not affect the gradient direction of the Laplace-domain waveform inversion. We obtained inversion results of the frequency-filtered field data acquired in the Gulf of Mexico and two synthetic data sets obtained using a first-derivative Gaussian source wavelet and a single-frequency causal sine function. They demonstrated that Laplace-domain inversion yielded consistent results regardless of the frequency content within the seismic data.

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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.

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A Graph-Space Optimal Transport Approach for Full Waveform Inversion

80th EAGE Conference and Exhibition 2018 ◽

10.3997/2214-4609.201801031 ◽

2018 ◽

Author(s):

L. Metivier ◽

A. Allain ◽

R. Brossier ◽

Q. Merigot ◽

E. Oudet ◽

...

Keyword(s):

Optimal Transport ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Full Waveform ◽

Transport Approach

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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.

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Passive seismic event estimation using multiscattering waveform inversion

Geophysics ◽

10.1190/geo2018-0358.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. KS59-KS69 ◽

Cited By ~ 8

Author(s):

Chao Song ◽

Zedong Wu ◽

Tariq Alkhalifah

Keyword(s):

Seismic Data ◽

Waveform Inversion ◽

Velocity Model ◽

Source Image ◽

Time Inversion ◽

Multiple Sources ◽

Origin Time ◽

Secondary Sources ◽

Velocity Models ◽

Passive Seismic

Passive seismic monitoring has become an effective method to understand underground processes. Time-reversal-based methods are often used to locate passive seismic events directly. However, these kinds of methods are strongly dependent on the accuracy of the velocity model. Full-waveform inversion (FWI) has been used on passive seismic data to invert the velocity model and source image, simultaneously. However, waveform inversion of passive seismic data uses mainly the transmission energy, which results in poor illumination and low resolution. We developed a waveform inversion using multiscattered energy for passive seismic to extract more information from the data than conventional FWI. Using transmission wavepath information from single- and double-scattering, computed from a predicted scatterer field acting as secondary sources, our method provides better illumination of the velocity model than conventional FWI. Using a new objective function, we optimized the source image and velocity model, including multiscattered energy, simultaneously. Because we conducted our method in the frequency domain with a complex source function including spatial and wavelet information, we mitigate the uncertainties of the source wavelet and source origin time. Inversion results from the Marmousi model indicate that by taking advantage of multiscattered energy and starting from a reasonably acceptable frequency (a single source at 3 Hz and multiple sources at 5 Hz), our method yields better inverted velocity models and source images compared with conventional FWI.

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RETRACTED ARTICLE: Estimation of the source process and forward simulation of long-period ground motion of the 2018 Hokkaido Eastern Iburi, Japan, earthquake

Earth Planets and Space ◽

10.1186/s40623-019-1079-6 ◽

2019 ◽

Vol 71 (1) ◽

Cited By ~ 1

Author(s):

Hisahiko Kubo ◽

Asako Iwaki ◽

Wataru Suzuki ◽

Shin Aoi ◽

Haruko Sekiguchi

Keyword(s):

Ground Motion ◽

Velocity Structure ◽

Time Window ◽

Waveform Inversion ◽

Strong Motion ◽

Source Model ◽

Multiple Time ◽

Velocity Models ◽

Long Period ◽

Slip Area

Abstract In this study, we investigate the source rupture process of the 2018 Hokkaido Eastern Iburi earthquake in Japan (MJMA 6.7) and how the ground motion can be reproduced using available source and velocity models. First, we conduct a multiple-time-window kinematic waveform inversion using strong-motion waveforms, which indicates that a large-slip area located at a depth of 25–30 km in the up-dip direction from the hypocenter was caused by a rupture propagating upward 6–12 s after its initiation. Moreover, the high-seismicity area of aftershocks did not overlap with the large-slip area. Subsequently, using the obtained source model and a three-dimensional velocity structure model, we conduct a forward long-period (< 0.5 Hz) ground-motion simulation. The simulation was able to reproduce the overall ground-motion characteristics in the sedimentary layers of the Ishikari Lowland.

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