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1
Liu, Yike, Bin He, Huiyi Lu, Zhendong Zhang, Xiao-Bi Xie, and Yingcai Zheng. "Full-intensity waveform inversion." GEOPHYSICS 83, no. 6 (November 1, 2018): R649—R658. http://dx.doi.org/10.1190/geo2017-0682.1.
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Many full-waveform inversion schemes are based on the iterative perturbation theory to fit the observed waveforms. When the observed waveforms lack low frequencies, those schemes may encounter convergence problems due to cycle skipping when the initial velocity model is far from the true model. To mitigate this difficulty, we have developed a new objective function that fits the seismic-waveform intensity, so the dependence of the starting model can be reduced. The waveform intensity is proportional to the square of its amplitude. Forming the intensity using the waveform is a nonlinear operation, which separates the original waveform spectrum into an ultra-low-frequency part and a higher frequency part, even for data that originally do not have low-frequency contents. Therefore, conducting multiscale inversions starting from ultra-low-frequency intensity data can largely avoid the cycle-skipping problem. We formulate the intensity objective function, the minimization process, and the gradient. Using numerical examples, we determine that the proposed method was very promising and could invert for the model using data lacking low-frequency information.
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Ha, Wansoo, and Changsoo Shin. "Laplace-domain full-waveform inversion of seismic data lacking low-frequency information." GEOPHYSICS 77, no. 5 (September 1, 2012): R199—R206. http://dx.doi.org/10.1190/geo2011-0411.1.
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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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Zhang, Tuo, and Christoph Sens-Schönfelder. "Adjoint envelope tomography for scattering and absorption using radiative transfer theory." Geophysical Journal International 229, no. 1 (November 11, 2021): 566–88. http://dx.doi.org/10.1093/gji/ggab457.
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SUMMARY To investigate the small-scale elastic structure of the subsurface at length scales below the resolution limits of waveform tomography, envelopes of high-frequency scattered seismic waveforms have been used with a variety of approaches. However, a rigorous framework for the iterative inversion of seismogram envelopes to image heterogeneity and high-frequency attenuation comparable to full waveform inversion (FWI) is missing. We present the mathematical framework for an iterative full envelope inversion using forward and adjoint simulations of the radiative transfer equations, in full analogy to FWI that is based on the wave equation. The forward and adjoint problems are solved by modelling 2-D multiple non-isotropic scattering in a random elastic medium with spatially variable heterogeneity and attenuation using the Monte Carlo method. Sensitivity kernels are derived for the squared difference between the full observed and modelled envelopes which is iteratively minimized with the L-BFGS method. We apply this algorithm in numerical tests in the acoustic approximation and show that it is possible to image the spatial distribution of small-scale heterogeneity and attenuation in iterative inversions. Our analysis shows that the relative importance of scattering and attenuation anomalies needs to be considered when the model resolution is assessed. The inversions confirm that the early coda is important for imaging the distribution of heterogeneity while later coda waves are more sensitive to intrinsic attenuation and we show that this dependency can be used to cope with the trade-off that exists between both material properties.
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AlTheyab, Abdullah, and G. T. Schuster. "Wavefront picking for 3D tomography and full-waveform inversion." GEOPHYSICS 81, no. 6 (November 2016): B201—B210. http://dx.doi.org/10.1190/geo2015-0544.1.
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We have developed an efficient approach for picking first-break wavefronts on coarsely sampled time slices of 3D shot gathers. Our objective was to compute a smooth initial velocity model for multiscale full-waveform inversion (FWI). Using interactive software, first-break wavefronts were geometrically modeled on time slices with a minimal number of picks. We picked sparse time slices, performed traveltime tomography, and then compared the predicted traveltimes with the data in-between the picked slices. The picking interval was refined with iterations until the errors in traveltime predictions fell within the limits necessary to avoid cycle skipping in early arrivals FWI. This approach was applied to a 3D ocean-bottom-station data set. Our results indicate that wavefront picking has 28% fewer data slices to pick compared with picking traveltimes in shot gathers. In addition, by using sparse time samples for picking, data storage is reduced by 88%, and therefore allows for a faster visualization and quality control of the picks. Our final traveltime tomogram is sufficient as a starting model for early arrival FWI.
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Smithyman, Brendan R., and Ronald M. Clowes. "Waveform tomography of field vibroseis data using an approximate 2D geometry leads to improved velocity models." GEOPHYSICS 77, no. 1 (January 2012): R33—R43. http://dx.doi.org/10.1190/geo2011-0076.1.
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Waveform tomography, a combination of traveltime tomography (or inversion) and waveform inversion, is applied to vibroseis first-arrival data to generate an interpretable model of P-wave velocity for a site in the Nechako Basin, south-central British Columbia, Canada. We use constrained 3D traveltime inversion followed by 2D full-waveform inversion to process long-offset (14.4 km) first-arrival refraction waveforms, resulting in a velocity model of significantly higher detail than a conventional refraction-statics model generated for a processing workflow. The crooked-line acquisition of the data set makes 2D full-waveform inversion difficult. Thus, a procedure that improves the tractability of waveform tomography processing of vibroseis data recorded on crooked roads is developed to generate a near-surface ([Formula: see text]) velocity model for the study area. The data waveforms are first static corrected using a time shift determined by 3D raytracing, which accounts for the crossline offsets produced by the crooked-line acquisition. The velocity model generated from waveform tomography exhibits substantial improvement when compared with a conventional refraction-statics model. It also shows improved resolution of sharp discontinuities and low-velocity regions when compared to the model from traveltime tomography alone, especially in regions where the geometry errors are moderate. Interpretation of the near-surface velocity model indicates possible subbasins in the Nechako Basin and delineates the Eocene volcanic rocks of the study area. This approach limits the ability of the full-waveform inversion to fit some propagation modes; however, the tractability of the inversion in the near-surface region is improved. This new development is especially useful in studies that do not warrant 3D seismic acquisition and processing.
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Xing, Zhen, and Alfredo Mazzotti. "Two-grid full-waveform Rayleigh-wave inversion via a genetic algorithm — Part 2: Application to two actual data sets." GEOPHYSICS 84, no. 5 (September 1, 2019): R815—R825. http://dx.doi.org/10.1190/geo2018-0800.1.
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We have applied our two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI) to two actual data sets acquired in Luni (Italy) and Grenoble (France), respectively. Because our technique used 2D elastic finite-difference modeling for solving the forward problem, the observed data were 3D to 2D corrected prior to the inversion. To limit the computing time, both inversions focused on predicting low-resolution, smooth models by using quite coarse inversion grids. The wavelets for FWI were estimated directly from the observed data by using the Wiener method. In the Luni case, due to the strong dispersion effects on the data, to strengthen the inversion, envelopes and waveforms were considered in the objective function and an offset-marching strategy was applied. Though no a priori information was exploited, the outcomes of the Luni and Grenoble data inversion were fair. The predicted Luni [Formula: see text] model indicates a strong velocity increase from approximately 3 to 6 m, and velocity inversions have been detected at approximately 2 and 9 m depths. Analyzing the dispersion spectra, it results that the predicted Luni data reasonably reproduced the waveforms related to the fundamental mode and, likely, a small part of those related to the first higher mode. Concerning the Grenoble example, the predicted [Formula: see text] model coincides reasonably well with the long-wavelength structures presented in the [Formula: see text] profiles obtained from nearby boreholes. The data reconstruction is generally satisfactory, and when mismatches occur between the predicted and observed traces, the phase differences are always within half-periods. The fair inversion outcomes suggest that the predicted Luni and Grenoble models would likely be adequate initial models for local FWI, which could further increase the resolution and the details of the estimated [Formula: see text] models.
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Zhang, Zhen-dong, and Tariq Alkhalifah. "Local-crosscorrelation elastic full-waveform inversion." GEOPHYSICS 84, no. 6 (November 1, 2019): R897—R908. http://dx.doi.org/10.1190/geo2018-0660.1.
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Full-waveform inversion (FWI) in its classic form is a method based on minimizing the [Formula: see text] norm of the difference between the observed and simulated seismic waveforms at the receiver locations. The objective is to find a subsurface model that reproduces the full waveform including the traveltimes and amplitudes of the observed seismic data. However, the widely used [Formula: see text]-norm-based FWI faces many issues in practice. The point-wise comparison of waveforms fails when the phase difference between the compared waveforms of the predicted and observed data is larger than a half-cycle. In addition, amplitude matching is impractical considering the simplified physics that we often use to describe the medium. To avoid these known problems, we have developed a novel elastic FWI algorithm using the local-similarity attribute. It compares two traces within a predefined local time extension; thus, is not limited by the half-cycle criterion. The algorithm strives to maximize the local similarities of the predicted and observed data by stretching/squeezing the observed data. Phases instead of amplitudes of the seismic data are used in the comparison. The algorithm compares two data sets locally; thus, it performs better than the global correlation in matching multiple arrivals. Instead of picking/calculating one stationary stretching/squeezing curve, we used a weighted integral to find all possible stationary curves. We also introduced a polynomial-type weighting function, which is determined only by the predefined maximum stretching/squeezing and is guaranteed to be smoothly varying within the extension range. Compared with the previously used Gaussian or linear weighting functions, our polynomial one has fewer parameters to play around with. A modified synthetic elastic Marmousi model and the North Sea field data are used to verify the effectiveness of the developed approach and also reveal some of its limitations.
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Maurer, Hansruedi, Stewart A. Greenhalgh, Edgar Manukyan, Stefano Marelli, and Alan G. Green. "Receiver-coupling effects in seismic waveform inversions." GEOPHYSICS 77, no. 1 (January 2012): R57—R63. http://dx.doi.org/10.1190/geo2010-0402.1.
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Seismic waveform-inversion offers opportunities for detailed characterization of the subsurface. However, its full potential can only be exploited when any systematic source and receiver effects are either carefully avoided or appropriately accounted for during the inversions. Repeated crosshole measurements in the Mont Terri (Switzerland) underground laboratory have revealed that receiver coupling may significantly affect the seismic waveforms. More seriously, coupling conditions may vary during the course of a monitoring experiment. To address this problem, we have developed a novel scheme that estimates medium properties, frequency-dependent source functions, and frequency-dependent receiver-coupling factors. We demonstrate the efficacy of the new scheme via a synthetic 2D crosshole experiment in which realistic receiver-coupling factors are incorporated. Because determination of medium parameters and estimation of source functions and receiver-coupling factors are largely separated, the method can be easily adapted to any other waveform-inversion problem, including elastic, anisotropic, 2.5D, or 3D situations.
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Bleibinhaus, Florian, and Stéphane Rondenay. "Effects of surface scattering in full-waveform inversion." GEOPHYSICS 74, no. 6 (November 2009): WCC69—WCC77. http://dx.doi.org/10.1190/1.3223315.
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In full-waveform inversion of seismic body waves, often the free surface is ignored on grounds of computational efficiency. A synthetic study was performed to investigate the effects of this simplification. In terms of size and frequency, the test model and data conform to a real long-offset survey of the upper crust across the San Andreas fault. Random fractal variations are superimposed on a background model with strong lateral and vertical velocity variations ranging from 1200 to 6800 m/s. Synthetic data were computed and inverted for this model and different topographies. A fully viscoelastic time-domain code was used to synthesize the seismograms, and a viscoacoustic frequency-domain code was utilized to invert them. The inversion was focused on early arrivals, which are dominated by P-waves but also contain strong P-Rayleigh wave conversions from the near-field of the receiver. Resulting waveform models show artifacts and a loss of resolution from neglecting the free surface in the inversion, but the inversions are stable, and they still improve the resolution of kinematic models. The extent of deterioration depends more on the subsurface than on the surface structure. Inversion results were improved at no additional expense by introducing a weak contrast along a staircase function above shots and receivers.
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Charara, Marwan, and Christophe Barnes. "Constrained Full Waveform Inversion for Borehole Multicomponent Seismic Data." Geosciences 9, no. 1 (January 16, 2019): 45. http://dx.doi.org/10.3390/geosciences9010045.
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Full-waveform inversion for borehole seismic data is an ill-posed problem and constraining the problem is crucial. Constraints can be imposed on the data and model space through covariance matrices. Usually, they are set to a diagonal matrix. For the data space, signal polarization information can be used to evaluate the data uncertainties. The inversion forces the synthetic data to fit the polarization of observed data. A synthetic inversion for a 2D-2C data estimating a 1D elastic model shows a clear improvement, especially at the level of the receivers. For the model space, horizontal and vertical spatial correlations using a Laplace distribution can be used to fill the model space covariance matrix. This approach reduces the degree of freedom of the inverse problem, which can be quantitatively evaluated. Strong horizontal spatial correlation distances favor a tabular geological model whenever it does not contradict the data. The relaxation of the spatial correlation distances from large to small during the iterative inversion process allows the recovery of geological objects of the same size, which regularizes the inverse problem. Synthetic constrained and unconstrained inversions for 2D-2C crosswell data show the clear improvement of the inversion results when constraints are used.
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Brossier, Romain, Stéphane Operto, and Jean Virieux. "Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion." GEOPHYSICS 74, no. 6 (November 2009): WCC105—WCC118. http://dx.doi.org/10.1190/1.3215771.
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Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.
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Fichtner, Andreas, Jeannot Trampert, Paul Cupillard, Erdinc Saygin, Tuncay Taymaz, Yann Capdeville, and Antonio Villaseñor. "Multiscale full waveform inversion." Geophysical Journal International 194, no. 1 (April 29, 2013): 534–56. http://dx.doi.org/10.1093/gji/ggt118.
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Zhang, Xin, and Andrew Curtis. "Variational full-waveform inversion." Geophysical Journal International 222, no. 1 (April 11, 2020): 406–11. http://dx.doi.org/10.1093/gji/ggaa170.
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SUMMARY Seismic full-waveform inversion (FWI) can produce high-resolution images of the Earth’s subsurface. Since full-waveform modelling is significantly nonlinear with respect to velocities, Monte Carlo methods have been used to assess image uncertainties. However, because of the high computational cost of Monte Carlo sampling methods, uncertainty assessment remains intractable for larger data sets and 3-D applications. In this study, we propose a new method called variational FWI, which uses Stein variational gradient descent to solve FWI problems. We apply the method to a 2-D synthetic example and demonstrate that the method produces accurate approximations to those obtained by Hamiltonian Monte Carlo. Since variational inference solves the problem using optimization, the method can be applied to larger data sets and 3-D applications by using stochastic optimization and distributed optimization.
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van Herwaarden, Dirk Philip, Michael Afanasiev, Solvi Thrastarson, and Andreas Fichtner. "Evolutionary full-waveform inversion." Geophysical Journal International 224, no. 1 (September 26, 2020): 306–11. http://dx.doi.org/10.1093/gji/ggaa459.
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SUMMARY We present a new approach to full-waveform inversion (FWI) that enables the assimilation of data sets that expand over time without the need to reinvert all data. This evolutionary inversion rests on a reinterpretation of stochastic Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS), which randomly exploits redundancies to achieve convergence without ever considering the data set as a whole. Specifically for seismological applications, we consider a dynamic mini-batch stochastic L-BFGS, where the size of mini-batches adapts to the number of sources needed to approximate the complete gradient. As an illustration we present an evolutionary FWI for upper-mantle structure beneath Africa. Starting from a 1-D model and data recorded until 1995, we sequentially add contemporary data into an ongoing inversion, showing how (i) new events can be added without compromising convergence, (ii) a consistent measure of misfit can be maintained and (iii) the model evolves over times as a function of data coverage. Though applied retrospectively in this example, our method constitutes a possible approach to the continuous assimilation of seismic data volumes that often tend to grow exponentially.
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Yao, Gang, and Di Wu. "Reflection full waveform inversion." Science China Earth Sciences 60, no. 10 (September 18, 2017): 1783–94. http://dx.doi.org/10.1007/s11430-016-9091-9.
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Sinha, Mrinal, and Gerard T. Schuster. "Interferometric full-waveform inversion." GEOPHYSICS 84, no. 1 (January 1, 2019): R45—R60. http://dx.doi.org/10.1190/geo2018-0047.1.
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Velocity errors in the shallow part of the velocity model can lead to erroneous estimates of the full-waveform inversion (FWI) tomogram. If the location and topography of a reflector are known, then such a reflector can be used as a reference reflector to update the underlying velocity model. Reflections corresponding to this reference reflector are windowed in the data space. Windowed reference reflections are then crosscorrelated with reflections from deeper interfaces, which leads to partial cancellation of static errors caused by the overburden above the reference interface. Interferometric FWI (IFWI) is then used to invert the tomogram in the target region, by minimizing the normalized waveform misfit between the observed and predicted crosscorrelograms. Results with synthetic and field data with static errors above the reference interface indicate that an accurate tomogram can be inverted in areas lying within several wavelengths of the reference interface. IFWI can also be applied to synthetic time-lapse data to mitigate the nonrepeatability errors caused by time-varying overburden variations. The synthetic- and field-data examples demonstrate that IFWI can provide accurate tomograms when the near surface is ridden with velocity errors.
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Pratt, R. Gerhard. "Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model." GEOPHYSICS 64, no. 3 (May 1999): 888–901. http://dx.doi.org/10.1190/1.1444597.
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Seismic waveforms contain much information that is ignored under standard processing schemes; seismic waveform inversion seeks to use the full information content of the recorded wavefield. In this paper I present, apply, and evaluate a frequency‐space domain approach to waveform inversion. The method is a local descent algorithm that proceeds from a starting model to refine the model in order to reduce the waveform misfit between observed and model data. The model data are computed using a full‐wave equation, viscoacoustic, frequency‐domain, finite‐difference method. Ray asymptotics are avoided, and higher‐order effects such as diffractions and multiple scattering are accounted for automatically. The theory of frequency‐domain waveform/wavefield inversion can be expressed compactly using a matrix formalism that uses finite‐difference/finite‐element frequency‐domain modeling equations. Expressions for fast, local descent inversion using back‐propagation techniques then follow naturally. Implementation of these methods depends on efficient frequency‐domain forward‐modeling solutions; these are provided by recent developments in numerical forward modeling. The inversion approach resembles prestack, reverse‐time migration but differs in that the problem is formulated in terms of velocity (not reflectivity), and the method is fully iterative. I illustrate the practical application of the frequency‐domain waveform inversion approach using tomographic seismic data from a physical scale model. This allows a full evaluation and verification of the method; results with field data are presented in an accompanying paper. Several critical processes contribute to the success of the method: the estimation of a source signature, the matching of amplitudes between real and synthetic data, the selection of a time window, and the selection of suitable sequence of frequencies in the inversion. An initial model for the inversion of the scale model data is provided using standard traveltime tomographic methods, which provide a robust but low‐resolution image. Twenty‐five iterations of wavefield inversion are applied, using five discrete frequencies at each iteration, moving from low to high frequencies. The final results exhibit the features of the true model at subwavelength scale and account for many of the details of the observed arrivals in the data.
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Zhang, Chao, Ting Lei, and Yi Wang. "Two-Dimensional Full-Waveform Joint Inversion of Surface Waves Using Phases and Z/H Ratios." Applied Sciences 11, no. 15 (July 22, 2021): 6712. http://dx.doi.org/10.3390/app11156712.
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Surface-wave dispersion and the Z/H ratio are important parameters used to resolve the Earth’s structure, especially for S-wave velocity. Several previous studies have explored using joint inversion of these two datasets. However, all of these studies used a 1-D depth-sensitivity kernel, which lacks precision when the structure is laterally heterogeneous. Adjoint tomography (i.e., full-waveform inversion) is a state-of-the-art imaging method with a high resolution. It can obtain better-resolved lithospheric structures beyond the resolving ability of traditional ray-based travel-time tomography. In this study, we present a systematic investigation of the 2D sensitivities of the surface wave phase and Z/H ratio using the adjoint-state method. The forward-modeling experiments indicated that the 2D phase and Z/H ratio had different sensitivities to the S-wave velocity. Thus, a full-waveform joint-inversion scheme of surface waves with phases and a Z/H ratio was proposed to take advantage of their complementary sensitivities to the Earth’s structure. Both applications to synthetic data sets in large- and small-scale inversions demonstrated the advantage of the joint inversion over the individual inversions, allowing for the creation of a more unified S-wave velocity model. The proposed joint-inversion scheme offers a computationally efficient and inexpensive alternative to imaging fine-scale shallow structures beneath a 2D seismic array.
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Pan, Guangdong, Lin Liang, and Tarek M. Habashy. "A numerical study of 3D frequency-domain elastic full-waveform inversion." GEOPHYSICS 84, no. 1 (January 1, 2019): R99—R108. http://dx.doi.org/10.1190/geo2017-0727.1.
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We have developed a 3D elastic full-waveform inversion (FWI) algorithm with forward modeling and inversion performed in the frequency domain. The Helmholtz equation is solved with a second-order finite-difference method using an iterative solver equipped with an efficient complex-shifted incomplete LU-based preconditioner. The inversion is based on the minimization of the data misfit functional and a total variation regularization for the unknown model parameters. We implement the Gauss-Newton method as the optimization engine for the inversions. The codes are parallelized with a message passing interface based on the number of shots and receivers. We examine the performance of this elastic FWI algorithm and workflow on synthetic examples including surface seismic and vertical seismic profile configurations. With various initial models, we manage to obtain high-quality velocity images for 3D earth models.
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Ha, Wansoo, and Changsoo Shin. "Why do Laplace-domain waveform inversions yield long-wavelength results?" GEOPHYSICS 78, no. 4 (July 1, 2013): R167—R173. http://dx.doi.org/10.1190/geo2012-0365.1.
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Laplace-domain inversions generate long-wavelength velocity models from synthetic and field data sets, unlike full-waveform inversions in the time or frequency domain. By examining the gradient directions of Laplace-domain inversions, we explain why they result in long-wavelength velocity models. The gradient direction of the inversion is calculated by multiplying the virtual source and the back-propagated wavefield. The virtual source has long-wavelength features because it is the product of the smooth forward-modeled wavefield and the partial derivative of the impedance matrix, which depends on the long-wavelength initial velocity used in the inversion. The back-propagated wavefield exhibits mild variations, except for near the receiver, in spite of the short-wavelength components in the residual. The smooth back-propagated wavefield results from the low-wavenumber pass-filtering effects of Laplace-domain Green’s function, which attenuates the high-wavenumber components of the residuals more rapidly than the low-wavenumber components. Accordingly, the gradient direction and the inversion results are smooth. Examples of inverting field data acquired in the Gulf of Mexico exhibit long-wavelength gradients and confirm the generation of long-wavelength velocity models by Laplace-domain inversion. The inversion of moving-average filtered data without short-wavelength features shows that the Laplace-domain inversion is not greatly affected by the high-wavenumber components in the field data.
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Lyu, Chao, Yann Capdeville, David Al-Attar, and Liang Zhao. "Intrinsic non-uniqueness of the acoustic full waveform inverse problem." Geophysical Journal International 226, no. 2 (April 6, 2021): 795–802. http://dx.doi.org/10.1093/gji/ggab134.
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SUMMARY In the context of seismic imaging, full waveform inversion (FWI) is increasingly popular. Because of its lower numerical cost, the acoustic approximation is often used, especially at the exploration geophysics scale, both for tests and for real data. Moreover, some research domains such as helioseismology face true acoustic media for which FWI can be useful. In this work, an argument that combines particle relabelling and homogenization is used to show that the general acoustic inverse problem based on band-limited data is intrinsically non-unique. It follows that the results of such inversions should be interpreted with caution. To illustrate these ideas, we consider 2-D numerical FWI examples based on a Gauss–Newton iterative inversion scheme and demonstrate effects of this non-uniqueness in the local optimization context.
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van Herwaarden, Dirk Philip, Christian Boehm, Michael Afanasiev, Solvi Thrastarson, Lion Krischer, Jeannot Trampert, and Andreas Fichtner. "Accelerated full-waveform inversion using dynamic mini-batches." Geophysical Journal International 221, no. 2 (February 21, 2020): 1427–38. http://dx.doi.org/10.1093/gji/ggaa079.
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SUMMARY We present an accelerated full-waveform inversion based on dynamic mini-batch optimization, which naturally exploits redundancies in observed data from different sources. The method rests on the selection of quasi-random subsets (mini-batches) of sources, used to approximate the misfit and the gradient of the complete data set. The size of the mini-batch is dynamically controlled by the desired quality of the gradient approximation. Within each mini-batch, redundancy is minimized by selecting sources with the largest angular differences between their respective gradients, and spatial coverage is maximized by selecting candidate events with Mitchell’s best-candidate algorithm. Information from sources not included in a specific mini-batch is incorporated into each gradient calculation through a quasi-Newton approximation of the Hessian, and a consistent misfit measure is achieved through the inclusion of a control group of sources. By design, the dynamic mini-batch approach has several main advantages: (1) The use of mini-batches with adaptive size ensures that an optimally small number of sources is used in each iteration, thus potentially leading to significant computational savings; (2) curvature information is accumulated and exploited during the inversion, using a randomized quasi-Newton method; (3) new data can be incorporated without the need to re-invert the complete data set, thereby enabling an evolutionary mode of full-waveform inversion. We illustrate our method using synthetic and real-data inversions for upper-mantle structure beneath the African Plate. In these specific examples, the dynamic mini-batch approach requires around 20 per cent of the computational resources in order to achieve data and model misfits that are comparable to those achieved by a standard full-waveform inversion where all sources are used in each iteration.
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Gao, Guozhong, Aria Abubakar, and Tarek M. Habashy. "Joint petrophysical inversion of electromagnetic and full-waveform seismic data." GEOPHYSICS 77, no. 3 (May 1, 2012): WA3—WA18. http://dx.doi.org/10.1190/geo2011-0157.1.
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Accurate determination of reservoir petrophysical parameters is of great importance for reservoir monitoring and characterization. We developed a joint inversion approach for the direct estimation of in situ reservoir petrophysical parameters such as porosity and fluid saturations by jointly inverting electromagnetic and full-waveform seismic measurements. Full-waveform seismic inversions allow the exploitation of the full content of the data so that a more accurate geophysical model can be inferred. Electromagnetic data are linked to porosity and fluid saturations through Archie’s equations, whereas seismic data are linked to them through rock-physics fluid-substitution equations. For seismic modeling, we used an acoustic approximation. Sensitivity studies combined with inversion tests show that seismic data are mainly sensitive to porosity distribution, whereas electromagnetic data are more sensitive to fluid-saturation distribution. The separate inversion of electromagnetic or seismic data is highly nonunique and thus leads to great ambiguity in the determination of porosity and fluid saturations. In our approach, we used a Gauss-Newton algorithm equipped with the multiplicative regularization and proper data-weighting scheme. We tested the implemented joint petrophysical inversion method using various synthetic models for surface and crosswell measurements. We found that the joint inversion approach provides substantial advantage for an improved estimation of porosity and fluid-saturation distributions over the one obtained from the separate inversion of electromagnetic and seismic data. This advantage is achieved by significantly reducing the ambiguity on the determination of porosity and fluid saturations using multiphysics measurements. We also carried out a study on the effects of using inaccurate petrophysical transform parameters on the inversion results. Our study demonstrated that up to 20% errors in the saturation and porosity exponents in Archie’s equations do not cause significant errors in the inversion results. On the other hand, if the bulk modulus and density of the rock matrix have a large percentage of errors (i.e., more than 5%), the inversion results will be significantly degraded. However, if the density of the rock matrix has an error of less than 2%, the joint inversion can tolerate a large percentage of errors in the bulk modulus of the rock matrix.
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Moghaddam, Peyman P., Henk Keers, Felix J. Herrmann, and Wim A. Mulder. "A new optimization approach for source-encoding full-waveform inversion." GEOPHYSICS 78, no. 3 (May 1, 2013): R125—R132. http://dx.doi.org/10.1190/geo2012-0090.1.
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Waveform inversion is the method of choice for determining a highly heterogeneous subsurface structure. However, conventional waveform inversion requires that the wavefield for each source is computed separately. This makes it very expensive for realistic 3D seismic surveys. Source-encoding waveform inversion, in which the sources are modeled simultaneously, is considerably faster than conventional waveform inversion but suffers from artifacts. These artifacts can partly be removed by assigning random weights to the source wavefields. We found that the misfit function, and therefore also its gradient, for source-encoding waveform inversion is an unbiased random estimation of the misfit function used in conventional waveform inversion. We found a new method of source-encoding waveform inversion that takes into account the random nature of the gradients used in the optimization. In this new method, the gradient at each iteration is a weighted average of past gradients such that the most recent gradients have the largest weights with exponential decay. This way we damped the random fluctuations of the gradient by incorporating information from the previous iterations. We compared this new method with existing source-encoding waveform inversion methods as well as conventional waveform inversion and found that the model misfit reduction is faster and smoother than those of existing source-encoding waveform inversion methods, and it approaches the model misfit reduction obtained in conventional waveform inversion.
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Habashy, T. M., A. Abubakar, G. Pan, and A. Belani. "Source-receiver compression scheme for full-waveform seismic inversion." GEOPHYSICS 76, no. 4 (July 2011): R95—R108. http://dx.doi.org/10.1190/1.3590213.
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We have developed a source-receiver compression approach for reducing the computational time and memory usage of the acoustic and elastic full-waveform inversions. By detecting and quantifying the extent of redundancy in the data, we assembled a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers used in the survey. Because the numbers of these simultaneous sources and receivers could be significantly less than those of the physical sources and receivers, the computational time and memory usage of any gradient-type inversion method such as steepest descent, nonlinear conjugate gradient, contrast-source inversion, and quasi-Newton methods could be reduced. The scheme is based on decomposing the data into their principal components using a singular-value decomposition approach, and the data reduction is done through the elimination of the small eigenvalues. Consequently, this would suppress the effect of noise in the data. Moreover, taking advantage of the redundancy in the data, this compression scheme effectively stacks the redundant data, resulting in an increased signal-to-noise ratio. For demonstration of the concept, we produced inversion results for the 2D acoustic Marmousi and BP models for surface measurements and an elastic model for crosswell measurements. We found that this approach has the potential to significantly reduce computational time and memory usage of the Gauss-Newton method by 1–2 orders of magnitude.
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Cao, D., W. B. Beydoun, S. C. Singh, and A. Tarantola. "A simultaneous inversion for background velocity and impedance maps." GEOPHYSICS 55, no. 4 (April 1990): 458–69. http://dx.doi.org/10.1190/1.1442855.
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Full‐waveform inversion of seismic reflection data is highly nonlinear because of the irregular form of the function measuring the misfit between the observed and the synthetic data. Since the nonlinearity results mainly from the parameters describing seismic velocities, an alternative to the full nonlinear inversion is to have an inversion method which remains nonlinear with respect to velocities but linear with respect to impedance contrasts. The traditional approach is to decouple the nonlinear and linear parts by first estimating the background velocity from traveltimes, using either traveltime inversion or velocity analysis, and then estimating impedance contrasts from waveforms, using either waveform inversion or conventional migration. A more sophisticated strategy is to obtain both the subsurface background velocities and impedance contrasts simultaneously by using a single least‐squares norm waveform‐fit criterion. The background velocity that adequately represents the gross features of the medium is parameterized using a sparse grid, whereas the impedance contrasts use a dense grid. For each updated velocity model, the impedance contrasts are computed using a linearized inversion algorithm. For a 1-D velocity background, it is very efficient to perform inversion in the f-k domain by using the WKBJ and Born approximations. The method performs well both with synthetic and field data.
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Romanowicz, Barbara, Li-Wei Chen, and Scott W. French. "Accelerating full waveform inversion via source stacking and cross-correlations." Geophysical Journal International 220, no. 1 (October 21, 2019): 308–22. http://dx.doi.org/10.1093/gji/ggz437.
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SUMMARY Accurate synthetic seismic wavefields can now be computed in 3-D earth models using the spectral element method (SEM), which helps improve resolution in full waveform global tomography. However, computational costs are still a challenge. These costs can be reduced by implementing a source stacking method, in which multiple earthquake sources are simultaneously triggered in only one teleseismic SEM simulation. One drawback of this approach is the perceived loss of resolution at depth, in particular because high-amplitude fundamental mode surface waves dominate the summed waveforms, without the possibility of windowing and weighting as in conventional waveform tomography. This can be addressed by redefining the cost-function and computing the cross-correlation wavefield between pairs of stations before each inversion iteration. While the Green’s function between the two stations is not reconstructed as well as in the case of ambient noise tomography, where sources are distributed more uniformly around the globe, this is not a drawback, since the same processing is applied to the 3-D synthetics and to the data, and the source parameters are known to a good approximation. By doing so, we can separate time windows with large energy arrivals corresponding to fundamental mode surface waves. This opens the possibility of designing a weighting scheme to bring out the contribution of overtones and body waves. It also makes it possible to balance the contributions of frequently sampled paths versus rarely sampled ones, as in more conventional tomography. Here we present the results of proof of concept testing of such an approach for a synthetic 3-component long period waveform data set (periods longer than 60 s), computed for 273 globally distributed events in a simple toy 3-D radially anisotropic upper mantle model which contains shear wave anomalies at different scales. We compare the results of inversion of 10 000 s long stacked time-series, starting from a 1-D model, using source stacked waveforms and station-pair cross-correlations of these stacked waveforms in the definition of the cost function. We compute the gradient and the Hessian using normal mode perturbation theory, which avoids the problem of cross-talk encountered when forming the gradient using an adjoint approach. We perform inversions with and without realistic noise added and show that the model can be recovered equally well using one or the other cost function. The proposed approach is computationally very efficient. While application to more realistic synthetic data sets is beyond the scope of this paper, as well as to real data, since that requires additional steps to account for such issues as missing data, we illustrate how this methodology can help inform first order questions such as model resolution in the presence of noise, and trade-offs between different physical parameters (anisotropy, attenuation, crustal structure, etc.) that would be computationally very costly to address adequately, when using conventional full waveform tomography based on single-event wavefield computations.
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Cheng, C. H. "Full waveform inversion ofPwaves forVsandQp." Journal of Geophysical Research: Solid Earth 94, B11 (November 10, 1989): 15619–25. http://dx.doi.org/10.1029/jb094ib11p15619.
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Qu, Yingming, Zhenchun Li, Jianping Huang, and Jinli Li. "Viscoacoustic anisotropic full waveform inversion." Journal of Applied Geophysics 136 (January 2017): 484–97. http://dx.doi.org/10.1016/j.jappgeo.2016.12.001.
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He, Bin, Yike Liu, Huiyi Lu, and Zhendong Zhang. "Correlative Full-Intensity Waveform Inversion." IEEE Transactions on Geoscience and Remote Sensing 58, no. 10 (October 2020): 6983–94. http://dx.doi.org/10.1109/tgrs.2020.2978433.
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Warner, Michael, Andrew Ratcliffe, Tenice Nangoo, Joanna Morgan, Adrian Umpleby, Nikhil Shah, Vetle Vinje, et al. "Anisotropic 3D full-waveform inversion." GEOPHYSICS 78, no. 2 (March 1, 2013): R59—R80. http://dx.doi.org/10.1190/geo2012-0338.1.
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We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7 km, with reduced coverage to a maximum offset of about 11 km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000 m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5 Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model building including anisotropic reflection tomography, and contained epsilon values as high as 20%. The final FWI velocity model shows a network of shallow high-velocity channels that match similar features in the reflection data. Deeper in the section, the FWI velocity model reveals a sharper and more-intense low-velocity region associated with the gas cloud in which low-velocity fingers match the location of gas-filled faults visible in the reflection data. The resulting velocity model provides a better match to well logs, and better flattens common-image gathers, than does the starting model. Reverse-time migration, using the FWI velocity model, provides significant uplift to the migrated image, simplifying the planform of the reservoir section at depth. The workflows, inversion strategy, and algorithms that we have used have broad application to invert a wide-range of analogous data sets.
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da Silva, Nuno V., Gang Yao, and Michael Warner. "Semiglobal viscoacoustic full-waveform inversion." GEOPHYSICS 84, no. 2 (March 1, 2019): R271—R293. http://dx.doi.org/10.1190/geo2017-0773.1.
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Full-waveform inversion deals with estimating physical properties of the earth’s subsurface by matching simulated to recorded seismic data. Intrinsic attenuation in the medium leads to the dispersion of propagating waves and the absorption of energy — media with this type of rheology are not perfectly elastic. Accounting for that effect is necessary to simulate wave propagation in realistic geologic media, leading to the need to estimate intrinsic attenuation from the seismic data. That increases the complexity of the constitutive laws leading to additional issues related to the ill-posed nature of the inverse problem. In particular, the joint estimation of several physical properties increases the null space of the parameter space, leading to a larger domain of ambiguity and increasing the number of different models that can equally well explain the data. We have evaluated a method for the joint inversion of velocity and intrinsic attenuation using semiglobal inversion; this combines quantum particle-swarm optimization for the estimation of the intrinsic attenuation with nested gradient-descent iterations for the estimation of the P-wave velocity. This approach takes advantage of the fact that some physical properties, and in particular the intrinsic attenuation, can be represented using a reduced basis, substantially decreasing the dimension of the search space. We determine the feasibility of the method and its robustness to ambiguity with 2D synthetic examples. The 3D inversion of a field data set for a geologic medium with transversely isotropic anisotropy in velocity indicates the feasibility of the method for inverting large-scale real seismic data and improving the data fitting. The principal benefits of the semiglobal multiparameter inversion are the recovery of the intrinsic attenuation from the data and the recovery of the true undispersed infinite-frequency P-wave velocity, while mitigating ambiguity between the estimated parameters.
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Zhu, Weiqiang, Kailai Xu, Eric Darve, Biondo Biondi, and Gregory C. Beroza. "Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification." GEOPHYSICS 87, no. 1 (December 6, 2021): R93—R109. http://dx.doi.org/10.1190/geo2020-0933.1.
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Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. The velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.
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Yuan, Shihao, Nobuaki Fuji, and Satish C. Singh. "High-frequency localized elastic full-waveform inversion for time-lapse seismic surveys." GEOPHYSICS 86, no. 3 (March 18, 2021): R277—R292. http://dx.doi.org/10.1190/geo2020-0286.1.
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Seismic full-waveform inversion (FWI) is a powerful method used to estimate the elastic properties of the subsurface. To mitigate the nonlinearity and cycle-skipping problems, in a hierarchical manner, one first inverts the low-frequency content to determine long- and medium-wavelength structures and then increases the frequency content to obtain detailed information. However, the inversion of higher frequencies can be computationally very expensive, especially when the target of interest, such as oil/gas reservoirs and axial melt lens, is at a great depth, far away from source and receiver arrays. To address this problem, we have developed a localized FWI algorithm in which iterative modeling is performed locally, allowing us to extend inversions for higher frequencies with little computation effort. Our method is particularly useful for time-lapse seismic, where the changes in elastic parameters are local due to fluid extraction and injection in the subsurface. In our method, the sources and receivers are extrapolated to a region close to the target area, allowing forward modeling and inversion to be performed locally after low-frequency full-model inversion for the background model, which by nature only represents long- to medium-wavelength features. Numerical tests show that the inversion of low-frequency data for the overburden is sufficient to provide an accurate high-frequency estimation of elastic parameters of the target region.
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Tao, Kai, Stephen P. Grand, and Fenglin Niu. "Full-waveform inversion of triplicated data using a normalized-correlation-coefficient-based misfit function." Geophysical Journal International 210, no. 3 (June 7, 2017): 1517–24. http://dx.doi.org/10.1093/gji/ggx249.
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Summary In seismic full-waveform inversion (FWI), the choice of misfit function determines what information in data is used and ultimately affects the resolution of the inverted images of the Earth's structure. Misfit functions based on traveltime have been successfully applied in global and regional tomographic studies. However, wave propagation through the upper mantle results in multiple phases arriving at a given receiver in a narrow time interval resulting in complicated waveforms that evolve with distance. To extract waveform information as well as traveltime, we use a misfit function based on the normalized correlation coefficient (CC). This misfit function is able to capture the waveform complexities in both phase and relative amplitude within the measurement window. It is also insensitive to absolute amplitude differences between modeled and recorded data, which avoids problems due to uncertainties in source magnitude, radiation pattern, receiver site effects or even miscalibrated instruments. These features make the misfit function based on normalized CC a good candidate to achieve high-resolution images of complex geological structures when interfering phases coexist in the measurement window, such as triplication waveforms. From synthetic tests, we show the advantages of this misfit function over the cross-correlation traveltime misfit function. Preliminary inversion of data from an earthquake in Northeast China images a sharper and stronger amplitude slab stagnant in the middle of the transition zone than FWI of cross-correlation traveltime.
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Dantas, Renato R. S., Walter E. Medeiros, and Jessé C. Costa. "A multiscale approach to full-waveform inversion using a sequence of time-domain misfit functions." GEOPHYSICS 84, no. 4 (July 1, 2019): R539—R551. http://dx.doi.org/10.1190/geo2018-0291.1.
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Most of the approaches designed to avoid cycle skipping in full-waveform inversion (FWI) involve calculating a sequence of inversions in a multiscale fashion. We have adopted an alternative strategy, which is inverting a sequence of different misfit functions in the time domain. This is an implicit multiscale approach in the sense that the used misfit functions are sensitive to different wavelengths, but all of the inversion steps use the same modeling algorithm and the same model grid. In the first and third inversion steps, the transmitted (early arrivals) and reflected (late arrivals) components of the wavefield envelopes are respectively fitted. The second step promotes a smooth transition between the first and third steps, by using the envelope of the complete waveform. Because fitting just the envelope of the reflected waves has a minor effect on the misfit function of the whole data set, the phases of the reflected waves are mostly fitted in the fourth step, which is based on the waveform misfit function preserving only the late arrivals. The third and fourth steps are of crucial importance to fit the reflected events. We test the sequential inversion approach with the Marmousi model using data sets with different frequencies, obtaining better estimates of the velocity field than those obtained with the classic FWI. The solutions obtained with classic FWI and sequential inversion approach degrade with a progressively higher peak frequency data set, but the classic FWI solution degrades more rapidly.
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Garg, Aayush, and D. J. Verschuur. "From surface seismic data to reservoir elastic parameters using a full-wavefield redatuming approach." Geophysical Journal International 221, no. 1 (December 18, 2019): 115–28. http://dx.doi.org/10.1093/gji/ggz557.
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SUMMARY Traditionally, reservoir elastic parameters inversion suffers from the overburden multiple scattering and transmission imprint in the local input data used for the target-oriented inversion. In this paper, we present a full-wavefield approach, called reservoir-oriented joint migration inversion (JMI-res), to estimate the high-resolution reservoir elastic parameters from surface seismic data. As a first step in JMI-res, we reconstruct the fully redatumed data (local impulse responses) at a suitable depth above the reservoir from the surface seismic data, while correctly accounting for the overburden interal multiples and transmission losses. Next, we apply a localized elastic full waveform inversion on the estimated impulse responses to get the elastic parameters. We show that JMI-res thus provides much more reliable local target impulse responses, thus yielding high-resolution elastic parameters, compared to a standard redatuming procedure based on time reversal of data. Moreover, by using this kind of approach we avoid the need to apply a full elastic full waveform inversion-type process for the whole subsurface, as within JMI-res elastic full waveform inversion is only restricted to the reservoir target domain.
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Borisov, Dmitry, Fuchun Gao, Paul Williamson, and Jeroen Tromp. "Application of 2D full-waveform inversion on exploration land data." GEOPHYSICS 85, no. 2 (January 9, 2020): R75—R86. http://dx.doi.org/10.1190/geo2019-0082.1.
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Estimating subsurface seismic properties is an important topic in civil engineering, oil and gas exploration, and global seismology. We have developed an application of 2D elastic waveform inversion with an active-source on-shore data set, as is typically acquired in exploration seismology on land. The maximum offset is limited to 12 km, and the lowest available frequency is 5 Hz. In such a context, surface waves are generally treated as noise and are removed as a part of data processing. In contrast to the conventional approach, our workflow starts by inverting surface waves to constrain shallow parts of the shear wavespeed model. To mitigate cycle skipping, frequency- and offset-continuation approaches are used. To accurately take into account free-surface effects (and irregular topography), a spectral-element-based wave propagation solver is used for forward modeling. To reduce amplitude influences, a normalized crosscorrelation (NC) objective function is used in conjunction with systematic updates of the source wavelet during the inversion process. As the inversion proceeds, body waves are gradually incorporated in the process. At the final stage, surface and body waves are inverted together using the entire offset range over the band between 5 and 15 Hz. The inverted models include high-resolution features in the first 500 m of compressional and shear wavespeeds, with some model updates down to 4.0 km in the first parameter. The inversion results confirmed by well-log information, indicate a better fit of compressional to shear wavespeeds ratios compared with the initial model. The final data fit is also noticeably improved compared to the initial one. Although our results confirm previous studies demonstrating that an NC norm combined with a source time function correction can partly stabilize purely elastic inversions of viscoelastic data, we believe that including an attenuation depth model in the forward simulation gives better results.
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Métivier, L., R. Brossier, and J. Virieux. "Combining asymptotic linearized inversion and full waveform inversion." Geophysical Journal International 201, no. 3 (April 14, 2015): 1682–703. http://dx.doi.org/10.1093/gji/ggv106.
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Pérez Solano, Carlos, and René-Édouard Plessix. "Velocity-model building with enhanced shallow resolution using elastic waveform inversion — An example from onshore Oman." GEOPHYSICS 84, no. 6 (November 1, 2019): R977—R988. http://dx.doi.org/10.1190/geo2018-0736.1.
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Full-waveform inversion is a powerful data-fitting technique that is used for velocity-model building in seismic exploration. The inversion approach exploits the sensitivity of long-offset, wide-aperture, low-frequency data to the P-wave velocity properties in the subsurface. In the geologically complex land context in which different lithologies interleave and create large elastic property contrasts, acoustic waveform inversion is challenged due to the elastic nature of the data. The large elastic property contrasts create mode conversions. At low-to-intermediate frequencies, due to tuning/interference effects, the changes in the amplitudes of the different events affect amplitude and phase of the waveforms. We found that elastic waveform inversion of the long-offset, wide-aperture, low-frequency data leads to better retrieval of the compressional velocity model than the acoustic inversion and it is more stable. To obtain a good resolution in the shallow part of the model in an efficient manner, we have developed a two-stage inversion workflow that combines offset and frequency continuation. We have evaluated the relevance of this workflow with a challenging data set from South Oman.
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Zhao, Xinglei, Jianfei Gao, Hui Xia, and Fengnian Zhou. "Retrieval of Suspended Sediment Concentration from Bathymetric Bias of Airborne LiDAR." Sensors 22, no. 24 (December 19, 2022): 10005. http://dx.doi.org/10.3390/s222410005.
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In addition to depth measurements, airborne LiDAR bathymetry (ALB) has shown usefulness in suspended sediment concentration (SSC) inversion. However, SSC retrieval using ALB based on waveform decomposition or near-water-surface penetration by green lasers requires access to full-waveform data or infrared laser data, which are not always available for users. Thus, in this study we propose a new SSC inversion method based on the depth bias of ALB. Artificial neural networks were used to build an empirical inversion model by connecting the depth bias and SSC. The proposed method was verified using an ALB dataset collected through Optech coastal zone mapping and imaging LiDAR systems. The results showed that the mean square error of the predicted SSC based on the empirical model of ALB depth bias was less than 2.564 mg/L in the experimental area. The proposed method was compared with the waveform decomposition and regression methods. The advantages and limits of the proposed method were analyzed and summarized. The proposed method can effectively retrieve SSC and only requires ALB-derived and sonar-derived water bottom points, eliminating the dependence on the use of green full-waveforms and infrared lasers. This study provides an alternative means of conducting SSC inversion using ALB.
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Warner, Michael, and Lluís Guasch. "Adaptive waveform inversion: Theory." GEOPHYSICS 81, no. 6 (November 2016): R429—R445. http://dx.doi.org/10.1190/geo2015-0387.1.
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Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.
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Barnes, Christophe, and Marwan Charara. "The domain of applicability of acoustic full-waveform inversion for marine seismic data." GEOPHYSICS 74, no. 6 (November 2009): WCC91—WCC103. http://dx.doi.org/10.1190/1.3250269.
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Marine reflection seismic data inversion is a compute-intensive process, especially in three dimensions. Approximations often are made to limit the number of physical parameters we invert for, or to speed up the forward modeling. Because the data often are dominated by unconverted P-waves, one popular approximation is to consider the earth as purely acoustic, i.e., no shear modulus. The material density sometimes is taken as a constant. Nonlinear waveform seismic inversion consists of iteratively minimizing the misfit between the amplitudes of the measured and the modeled data. Approximations, such as assuming an acoustic medium, lead to incorrect modeling of the amplitudes of the seismic waves, especially with respect to amplitude variation with offset (AVO), and therefore have a direct impact on the inversion results. For evaluation purposes, we have performed a series of inversions with different approximations and different constraints whereby the synthetic data set to recover is computed for a 1D elastic medium. A series of numerical experiments, although simple, help to define the applicability domain of the acoustic assumption. Acoustic full-wave inversion is applicable only when the S-wave velocity and the density fields are smooth enough to reduce the AVO effect, or when the near-offset seismograms are inverted with a good starting model. However, in many realistic cases, acoustic approximation penalizes the full-wave inversion of marine reflection seismic data in retrieving the acoustic parameters.
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Vigh, Denes, and E. William Starr. "3D prestack plane-wave, full-waveform inversion." GEOPHYSICS 73, no. 5 (September 2008): VE135—VE144. http://dx.doi.org/10.1190/1.2952623.
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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 are an attractive input to waveform inversion with dramatically reduced computer run times compared to traditional shot-gather approaches. The study was conducted on two synthetic data sets — Marmousi2 and SMAART Pluto 1.5 — and a field data set. The results showed that a velocity field can be reconstructed well using a multiscale time-domain implementation of waveform inversion. Although the time-domain solution does not take advantage of wavenumber redundancy, the method is feasible on current computer architectures for 3D surveys. The inverted velocity volume produces a quality image for exploration geologists by using numerous iterations of waveform inversion.
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Biondi, Biondo, and Ali Almomin. "Simultaneous inversion of full data bandwidth by tomographic full-waveform inversion." GEOPHYSICS 79, no. 3 (May 1, 2014): WA129—WA140. http://dx.doi.org/10.1190/geo2013-0340.1.
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The convergence of full-waveform inversion can be improved by extending the velocity model along either the subsurface-offset axis or the time-lag axis. The extension of the velocity model along the time-lag axis enables us to linearly model large time shifts caused by velocity perturbations. This linear modeling was based on a new linearization of the scalar wave equation in which perturbation of the extended slowness squared was convolved in time with the second time derivative of the background wavefield. The linearization was accurate for reflected events and transmitted events. We determined that it can effectively model conventional reflection data as well as modern long-offset data containing diving waves. It also enabled the simultaneous inversion of reflections and diving waves, even when the starting velocity model was far from being accurate. We solved the optimization problem related to the inversion with a nested algorithm. The inner iterations were based on the proposed linearization and on a mixing of scales between the short- and long-wavelength components of the velocity model. Numerical tests performed on synthetic data modeled on the Marmousi model and on the “Caspian Sea” portion of the well-known BP model demonstrated the global-convergence properties as well as the high-resolution potential of the proposed method.
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Hornby, Brian E. "Tomographic reconstruction of near‐borehole slowness using refracted borehole sonic arrivals." GEOPHYSICS 58, no. 12 (December 1993): 1726–38. http://dx.doi.org/10.1190/1.1443387.
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Two‐dimensional (2-D) reconstructions of the near‐borehole slowness field are computed using arrival times of refracted borehole sonic arrivals. First‐arrival traveltimes, derived from both computer simulations and field data from full‐waveform sonic tools, were inverted for the near‐borehole formation slowness both axially along the borehole and radially away from the borehole. The inversion is nonlinear; the solution is obtained by means of a series of linear inversions followed by provisional ray tracings. Each iteration involves the application of a tomographic reconstruction algorithm similar to those used in seismic crosswell tomography or medical imaging applications. The technique was demonstrated using ray‐theoretic examples to simulate radial variations in slowness. In addition, full‐waveforms were generated using two‐and‐a‐half‐dimensional (2.5-D) FDM computer models. The finite‐difference method (FDM) computer models were used to test the validity of the ray‐theoretic approximation used in the inversion scheme and to simulate the full‐waveform sonic tool response for both radial and axial changes in formation properties. Field data examples highlighted radial changes in formation slowness caused by two separate mechanisms: water take up by swelling shales and the mechanical breakdown of the near‐borehole rock resulting from stress relief caused by the drilling process. Finally, refracted sonic arrivals from near‐borehole bed boundaries were identified in a horizontal well setting. Using refractions arriving beyond the headwave, a 2-D map of formation slowness was computed in the reservoir away from the borehole. Interpretation of the slowness map resulted in an estimation of the stand‐off of the horizontal borehole from the reservoir boundary.
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Manukyan, Edgar, Hansruedi Maurer, and André Nuber. "Improvements to elastic full-waveform inversion using cross-gradient constraints." GEOPHYSICS 83, no. 2 (March 1, 2018): R105—R115. http://dx.doi.org/10.1190/geo2017-0266.1.
Full textAbstract:
Seismic full-waveform inversion (FWI) is potentially a powerful method for obtaining high-resolution subsurface images, but the results are often distorted by nonlinear effects and parameter trade-offs. Such distortions can be particularly severe in the case of multiparameter FWI, such as elastic FWI, in which inversion is performed simultaneously for P- and S-wave velocities and density. The problem can be alleviated by adding constraints in the form of plausible a priori information. A usually well-justified constraint includes the structural similarity of different model parameters; i.e., an anomalous body likely exhibits variations in all elastic properties, although their magnitudes may be different. To consider such types of a priori information, we have developed a structurally constrained elastic FWI, which is based on minimization of the cross products of gradients of different model parameters. Our synthetic 2D experiments show that structurally constrained FWI can significantly improve model reconstruction. It is also demonstrated that our approach still leads to improved results, even when the structural similarity between the individual parameter types is not exactly met. Inversions of field data show that in comparison to conventional FWI, structurally constrained FWI is able to match the field data equally well while requiring less structural complexity of the subsurface.
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Guitton, Antoine, Gboyega Ayeni, and Esteban Díaz. "Constrained full-waveform inversion by model reparameterization." GEOPHYSICS 77, no. 2 (March 2012): R117—R127. http://dx.doi.org/10.1190/geo2011-0196.1.
Full textAbstract:
The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D synthetic and field data examples how preconditioning with nonstationary directional Laplacian filters outperforms traditional waveform inversion when sparse data are inverted and when sharp velocity contrasts are present. Adding geological information with preconditioning could benefit full-waveform inversion of real data whenever irregular geometry, coherent noise and lack of low frequencies are present.
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Eaton, David W., and Farshid Forouhideh. "Solid angles and the impact of receiver-array geometry on microseismic moment-tensor inversion." GEOPHYSICS 76, no. 6 (November 2011): WC77—WC85. http://dx.doi.org/10.1190/geo2011-0077.1.
Full textAbstract:
Seismic moment tensors provide a concise mathematical representation of point sources that can be used to characterize microseismic focal mechanisms. After correction for propagation effects, the six independent components of a moment tensor can be found by least-squares inversion based on P- and/or S-waveform (or spectral) amplitudes observed at different directions from the source. Using synthetic waveform data, we investigated geometrical factors that affect the reliability of such inversions. We demonstrated that the solid angle subtended by the receiver array, as viewed from the source location, plays a fundamental role in the stability of the inversion. In particular, the condition number of the generalized inverse scales approximately inversely with the solid angle, implying that for a solid angle of zero (as is the case for a single vertical borehole) the inversion is ill-conditioned. The presence of random noise alsohas a significant effect on the inversion results; our results showed that the signal-to-noise ratio (S/N) for reliable inversion scales approximately as the square root of the condition number. Taken together with geometrical considerations, we found that a [Formula: see text] is generally needed to obtain reliable inversion results for the full moment tensor under certain microseismic acquisition scenarios that include dual observation wells or surface star pattern. Our numerical tests indicated that least-squares moment-tensor solutions obtained under nonideal conditions are biased toward limited regions of the full parameter space. In particular, random noise introduces a bias toward volumetric source types, whereas ill-conditioned inversions may exhibit bias toward poorly resolved eigenvector(s) of the inversion matrix. Possible strategies to improve the reliability of moment-tensor inversion include ensuring a nonzero solid-angle aperture by using multiple observation wells, and/or incorporating other types of data such as a priori knowledge of fracture orientation.
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Ruan, Youyi, Wenjie Lei, Ryan Modrak, Rıdvan Örsvuran, Ebru Bozdağ, and Jeroen Tromp. "Balancing unevenly distributed data in seismic tomography: a global adjoint tomography example." Geophysical Journal International 219, no. 2 (August 1, 2019): 1225–36. http://dx.doi.org/10.1093/gji/ggz356.
Full textAbstract:
SUMMARY The uneven distribution of earthquakes and stations in seismic tomography leads to slower convergence of nonlinear inversions and spatial bias in inversion results. Including dense regional arrays, such as USArray or Hi-Net, in global tomography causes severe convergence and spatial bias problems, against which conventional pre-conditioning schemes are ineffective. To save computational cost and reduce model bias, we propose a new strategy based on a geographical weighting of sources and receivers. Unlike approaches based on ray density or the Voronoi tessellation, this method scales to large full-waveform inversion problems and avoids instabilities at the edges of dense receiver or source clusters. We validate our strategy using a 2-D global waveform inversion test and show that the new weighting scheme leads to a nearly twofold reduction in model error and much faster convergence relative to a conventionally pre-conditioned inversion. We implement this geographical weighting strategy for global adjoint tomography.