scholarly journals A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE119-VE133 ◽  
Author(s):  
Changsoo Shin ◽  
Wansoo Ha
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Frequency Component ◽  
Inversion Method ◽  
Local Minima ◽  
Objective Functions ◽  
Laplace Domain ◽  
Velocity Models ◽  
Domain Inversion

In the frequency domain, gradient-based local-optimization methods of waveform inversions have been unsuccessful at inverting subsurface parameters without an accurate starting model. Such methods could not correct automatically for poor starting models because multiple local minima made it difficult to approach the true global minimum. In this study, we compared the behavior of objective functions in the frequency and Laplace domains. Wavefields in the Laplace domain correspond to the zero-frequency component of a damped wavefield; thus, the Laplace-domain waveform inversion can image smooth velocity models. Objective functions in the Laplace-domain inversion have a smoother surface and fewer local minima than in the frequency-domain inversion. We applied the waveform inversion to a 2D slice of the acoustic SEG/EAGE salt model in the Laplace domain and recovered smooth velocity models from inaccurate initial velocity conditions. We also successfully imaged velocities of the salt, SEG overthrust, and Institut Francais du Petrole Marmousi models with the frequency-domain inversion method by using the inverted velocity model of the Laplace-domain inversion as the initial model.

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

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.

Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R223-R233 ◽  
Author(s):  
Yong Ma ◽  
Dave Hale
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Local Minima ◽  
Low Frequencies ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Dynamic Warping

In reflection seismology, full-waveform inversion (FWI) can generate high-wavenumber subsurface velocity models but often suffers from an objective function with local minima caused mainly by the absence of low frequencies in seismograms. These local minima cause cycle skipping when the low-wavenumber component in the initial velocity model for FWI is far from the true model. To avoid cycle skipping, we discovered a new wave-equation reflection traveltime inversion (WERTI) to update the low-wavenumber component of the velocity model, while using FWI to only update high-wavenumber details of the model. We implemented the low- and high-wavenumber inversions in an alternating way. In WERTI, we used dynamic image warping (DIW) to estimate the time shifts between recorded data and synthetic data. When compared with correlation-based techniques often used in traveltime estimation, DIW can avoid cycle skipping and estimate the time shifts accurately, even when shifts vary rapidly. Hence, by minimizing traveltime shifts estimated by dynamic warping, WERTI reduces errors in reflection traveltime inversion. Then, conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high-wavenumber details. The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.

3D Laplace-domain waveform inversion using a low-frequency time-domain modeling algorithm

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R1-R13 ◽  
Author(s):  
Wansoo Ha ◽  
Seung-Goo Kang ◽  
Changsoo Shin
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Domain Modeling ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Domain Inversion

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

First-arrival traveltime inversion of seismic diving waves observed on undulant surface

2021 ◽  
Vol 225 (2) ◽  
pp. 1020-1031
Author(s):  
Huachen Yang ◽  
Jianzhong Zhang ◽  
Kai Ren ◽  
Changbo Wang
Keyword(s):  
Turning Points ◽  
Analytical Formula ◽  
Velocity Model ◽  
Western China ◽  
Inversion Method ◽  
Mountain Area ◽  
Traveltime Inversion ◽  
Static Correction ◽  
Velocity Models ◽  
First Arrival

SUMMARY A non-iterative first-arrival traveltime inversion method (NFTI) is proposed for building smooth velocity models using seismic diving waves observed on irregular surface. The new ray and traveltime equations of diving waves propagating in smooth media with undulant observation surface are deduced. According to the proposed ray and traveltime equations, an analytical formula for determining the location of the diving-wave turning points is then derived. Taking the influence of rough topography on first-arrival traveltimes into account, the new equations for calculating the velocities at turning points are established. Based on these equations, a method is proposed to construct subsurface velocity models from the observation surface downward to the bottom using the first-arrival traveltimes in common offset gathers. Tests on smooth velocity models with rugged topography verify the validity of the established equations, and the superiority of the proposed NFTI. The limitation of the proposed method is shown by an abruptly-varying velocity model example. Finally, the NFTI is applied to solve the static correction problem of the field seismic data acquired in a mountain area in the western China. The results confirm the effectivity of the proposed NFTI.

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.

Traveltime information-based wave-equation inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC27-WCC36 ◽  
Author(s):  
Yu Zhang ◽  
Daoliu Wang
Keyword(s):  
Wave Equation ◽  
Conventional Method ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Data Fitting ◽  
Inversion Method ◽  
New Wave ◽  
Seismic Record

We propose a new wave-equation inversion method that mainly depends on the traveltime information of the recorded seismic data. Unlike the conventional method, we first apply a [Formula: see text] transform to the seismic data to form the delayed-shot seismic record, back propagate the transformed data, and then invert the velocity model by maximizing the wavefield energy around the shooting time at the source locations. Data fitting is not enforced during the inversion, so the optimized velocity model is obtained by best focusing the source energy after a back propagation. Therefore, inversion accuracy depends only on the traveltime information embedded in the seismic data. This method may overcome some practical issues of waveform inversion; in particular, it relaxes the dependency of the seismic data amplitudes and the source wavelet.

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

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. R199-R206 ◽  
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.

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.

scholarly journals Passive seismic event estimation using multiscattering waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. KS59-KS69 ◽  
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.

Nonlinear velocity inversion by a two‐step Monte Carlo method.

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Side Jin ◽  
Raul Madariaga
Keyword(s):  
Monte Carlo ◽  
Velocity Model ◽  
Small Scale ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Ray Theory ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Reference Velocity

Seismic reflection data contain information on small‐scale impedance variations and a smooth reference velocity model. Given a reference velocity model, the reflectors can be obtained by linearized migration‐inversion. If the reference velocity is incorrect, the reflectors obtained by inverting different subsets of the data will be incoherent. We propose to use the coherency of these images to invert for the background velocity distribution. We have developed a two‐step iterative inversion method in which we separate the retrieval of small‐scale variations of the seismic velocity from the longer‐period reference velocity model. Given an initial background velocity model, we use a waveform misfit‐functional for the inversion of small‐scale velocity variations. For this linear step we use the linearized migration‐inversion method based on ray theory that we have recently developed with Lambaré and Virieux. The reference velocity model is then updated by a Monte Carlo inversion method. For the nonlinear inversion of the velocity background, we introduce an objective functional that measures the coherency of the short wavelength components obtained by inverting different common shot gathers at the same locations. The nonlinear functional is calculated directly in migrated data space to avoid expensive numerical forward modeling by finite differences or ray theory. Our method is somewhat similar to an iterative migration velocity analysis, but we do an automatic search for relatively large‐scale 1-D reference velocity models. We apply the nonlinear inversion method to a marine data set from the North Sea and also show that nonlinear inversion can be applied to realistic scale data sets to obtain a laterally heterogeneous velocity model with a reasonable amount of computer time.

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