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1

Brown, Vanessa, Kerry Key, and Satish Singh. "Seismically regularized controlled-source electromagnetic inversion." GEOPHYSICS 77, no. 1 (January 2012): E57—E65. http://dx.doi.org/10.1190/geo2011-0081.1.

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Marine controlled-source electromagnetic (CSEM) data can be highly sensitive to the presence of resistive hydrocarbon bearing layers in the subsurface. Yet, due to the relatively poor depth resolution of CSEM data and the smoothness constraints imposed by electromagnetic (EM) inversion methods, the resulting resistivity models are often highly smoothed-out, typically underestimating the reservoir resistivity and overestimating its thickness. Conversely, seismic full-waveform inversion (FWI) can accurately recover the depths of seismic velocity changes, yet, is relatively insensitive the presence of hydrocarbons. In spite of their low depth resolution, CSEM data have been shown to be highly sensitive to the resistivity-thickness product of buried resistive layers, suggesting that if the thickness of a target layer can be constrained a priori, very accurate resistivity estimates may be obtained. We developed a method for leveraging the high depth resolution of FWI into a standard CSEM inversion algorithm so that the resulting resistivity models have depth constraints imposed by the seismic structure and consequently may obtain more accurate resistivity estimates. The seismically regularized CSEM inversion that we propose is conceptually similar to minimum-gradient support (MGS) regularization, but it uses regularization weights based on gradients in the seismic velocity model rather than the self-reinforcing model resistivity gradients used in the typical MGS scheme. A suite of synthetic model tests showed how this approach compares with standard smooth and MGS inversions for a range of rock types and hence, levels of correlation between the seismic and resistivity structures, showing that a significantly improved resistivity model can be obtained when the velocity and resistivity profiles are correlated in depth. We also found that this regularization weighting method can be extended to use depth constraints from geophysical data other than seismic velocity models. Tests on a real data example from the Pluto gas field demonstrated how the regularization weights can also be set using a nearby well log, resulting in a more compact estimate of the reservoir resistivity than possible with a standard smooth inversion.
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2

Ermert, L. A., K. Sager, T. Nissen-Meyer, and A. Fichtner. "Multifrequency inversion of global ambient seismic sources." Geophysical Journal International 225, no. 3 (February 6, 2021): 1616–23. http://dx.doi.org/10.1093/gji/ggab050.

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SUMMARY We develop and apply a method to constrain the space- and frequency-dependent location of ambient noise sources. This is based on ambient noise cross-correlation inversion using numerical wavefield simulations, which honour 3-D crustal and mantle structure, ocean loading and finite-frequency effects. In the frequency range from 3 to 20 mHz, our results constrain the global source distribution of the Earth’s hum, averaged over the Southern Hemisphere winter season of 9 yr. During Southern Hemisphere winter, the dominant sources are largely confined to the Southern Hemisphere, the most prominent exception being the Izu-Bonin-Mariana arc, which is the most active source region between 12 and 20 mHz. Generally, strong hum sources seem to be associated with either coastlines or bathymetric highs. In contrast, deep ocean basins are devoid of hum sources. While being based on the relatively small number of STS-1 broad-band stations that have been recording continuously from 2004 to 2013, our results demonstrate the practical feasibility of a frequency-dependent noise source inversion that accounts for the complexities of 3-D wave propagation. It may thereby improve full-waveform ambient noise inversions and our understanding of the physics of noise generation.
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3

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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4

Ermert, Laura, Jonas Igel, Korbinian Sager, Eléonore Stutzmann, Tarje Nissen-Meyer, and Andreas Fichtner. "Introducing noisi: a Python tool for ambient noise cross-correlation modeling and noise source inversion." Solid Earth 11, no. 4 (August 28, 2020): 1597–615. http://dx.doi.org/10.5194/se-11-1597-2020.

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Abstract. We introduce the open-source tool noisi for the forward and inverse modeling of ambient seismic cross-correlations with spatially varying source spectra. It utilizes pre-computed databases of Green's functions to represent seismic wave propagation between ambient seismic sources and seismic receivers, which can be obtained from existing repositories or imported from the output of wave propagation solvers. The tool was built with the aim of studying ambient seismic sources while accounting for realistic wave propagation effects. Furthermore, it may be used to guide the interpretation of ambient seismic auto- and cross-correlations, which have become preeminent seismological observables, in light of nonuniform ambient seismic sources. Written in the Python language, it is accessible for both usage and further development and efficient enough to conduct ambient seismic source inversions for realistic scenarios. Here, we introduce the concept and implementation of the tool, compare its model output to cross-correlations computed with SPECFEM3D_globe, and demonstrate its capabilities on selected use cases: a comparison of observed cross-correlations of the Earth's hum to a forward model based on hum sources from oceanographic models and a synthetic noise source inversion using full waveforms and signal energy asymmetry.
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5

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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6

Xu, Zongbo, T. Dylan Mikesell, Josefine Umlauft, and Gabriel Gribler. "Rayleigh-wave multicomponent crosscorrelation-based source strength distribution inversions. Part 2: a workflow for field seismic data." Geophysical Journal International 222, no. 3 (June 11, 2020): 2084–101. http://dx.doi.org/10.1093/gji/ggaa284.

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SUMMARY Estimation of ambient seismic source distributions (e.g. location and strength) can aid studies of seismic source mechanisms and subsurface structure investigations. One can invert for the ambient seismic (noise) source distribution by applying full-waveform inversion (FWI) theory to seismic (noise) crosscorrelations. This estimation method is especially applicable for seismic recordings without obvious body-wave arrivals. Data pre-processing procedures are needed before the inversion, but some pre-processing procedures commonly used in ambient noise tomography can bias the ambient (noise) source distribution estimation and should not be used in FWI. Taking this into account, we propose a complete workflow from the raw seismic noise recording through pre-processing procedures to the inversion. We present the workflow with a field data example in Hartoušov, Czech Republic, where the seismic sources are CO2 degassing areas at Earth’s surface (i.e. a fumarole or mofette). We discuss factors in the processing and inversion that can bias the estimations, such as inaccurate velocity model, anelasticity and array sensitivity. The proposed workflow can work for multicomponent data across different scales of field data.
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7

Um, Evan Schankee, Michael Commer, and Gregory A. Newman. "A strategy for coupled 3D imaging of large-scale seismic and electromagnetic data sets: Application to subsalt imaging." GEOPHYSICS 79, no. 3 (May 1, 2014): ID1—ID13. http://dx.doi.org/10.1190/geo2013-0053.1.

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Offshore seismic and electromagnetic (EM) imaging for hydrocarbons can require up to tens of millions of parameters to describe the 3D distribution of complex seabed geology and relevant geophysical attributes. The imaging and data volumes for such problems are enormous. Descent-based methods are the only viable imaging approach, where it is often challenging to manage the convergence of stand-alone seismic and EM inversion experiments. When a joint seismic-EM inversion is implemented, convergence problems with descent-based methods are further aggravated. Moreover, resolution mismatches between seismic and EM pose another challenge for joint inversion. To overcome these problems, we evaluated a coupled seismic-EM inversion workflow and applied it to a set of full-wave-seismic, magnetotelluric (MT) and controlled-source electromagnetic (CSEM) data for subsalt imaging. In our workflow, we address disparate resolution properties between seismic and EM data by implementing the seismic inversion in the Laplace domain, where the wave equation is transformed into a diffusion equation. The resolution of seismic data thus becomes comparable to that of EM data. To mitigate the convergence problems, the full joint seismic-EM inverse problem is split into manageable components: separate seismic and EM inversions and an intermediate step that enforces structural coupling through a cross-gradient-only inversion and resistivity-velocity crossplots. In this workflow, stand-alone seismic and MT inversion are performed first. The cross-gradient-only inversion and the crossplots are used to precondition the resistivity and velocity models for subsequent stand-alone inversions. By repeating the sequence of the stand-alone seismic, MT, and cross-gradient-only inversions along with the crossplots, we introduce the seismic structural information into the resistivity model, and vice versa, significantly improving the salt geometry in both resistivity and velocity images. We conclude that the improved salt geometry can then be used to precondition a starting model for CSEM inversions, yielding significant improvement in the resistivity images of hydrocarbon reservoirs adjacent to the salt.
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8

Song, Chao, Zedong Wu, and Tariq Alkhalifah. "Passive seismic event estimation using multiscattering waveform inversion." GEOPHYSICS 84, no. 3 (May 1, 2019): KS59—KS69. http://dx.doi.org/10.1190/geo2018-0358.1.

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Passive seismic monitoring has become an effective method to understand underground processes. Time-reversal-based methods are often used to locate passive seismic events directly. However, these kinds of methods are strongly dependent on the accuracy of the velocity model. Full-waveform inversion (FWI) has been used on passive seismic data to invert the velocity model and source image, simultaneously. However, waveform inversion of passive seismic data uses mainly the transmission energy, which results in poor illumination and low resolution. We developed a waveform inversion using multiscattered energy for passive seismic to extract more information from the data than conventional FWI. Using transmission wavepath information from single- and double-scattering, computed from a predicted scatterer field acting as secondary sources, our method provides better illumination of the velocity model than conventional FWI. Using a new objective function, we optimized the source image and velocity model, including multiscattered energy, simultaneously. Because we conducted our method in the frequency domain with a complex source function including spatial and wavelet information, we mitigate the uncertainties of the source wavelet and source origin time. Inversion results from the Marmousi model indicate that by taking advantage of multiscattered energy and starting from a reasonably acceptable frequency (a single source at 3 Hz and multiple sources at 5 Hz), our method yields better inverted velocity models and source images compared with conventional FWI.
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9

Reinwald, Michael, Moritz Bernauer, Heiner Igel, and Stefanie Donner. "Improved finite-source inversion through joint measurements of rotational and translational ground motions: a numerical study." Solid Earth 7, no. 5 (October 21, 2016): 1467–77. http://dx.doi.org/10.5194/se-7-1467-2016.

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Abstract. With the prospects of seismic equipment being able to measure rotational ground motions in a wide frequency and amplitude range in the near future, we engage in the question of how this type of ground motion observation can be used to solve the seismic source inverse problem. In this paper, we focus on the question of whether finite-source inversion can benefit from additional observations of rotational motion. Keeping the overall number of traces constant, we compare observations from a surface seismic network with 44 three-component translational sensors (classic seismometers) with those obtained with 22 six-component sensors (with additional three-component rotational motions). Synthetic seismograms are calculated for known finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content to measure how the observations constrain the seismic source properties. We minimize the influence of the source receiver geometry around the fault by statistically analyzing six-component inversions with a random distribution of receivers. Since our previous results are achieved with a regular spacing of the receivers, we try to answer the question of whether the results are dependent on the spatial distribution of the receivers. The results show that with the six-component subnetworks, kinematic source inversions for source properties (such as rupture velocity, rise time, and slip amplitudes) are not only equally successful (even that would be beneficial because of the substantially reduced logistics installing half the sensors) but also statistically inversions for some source properties are almost always improved. This can be attributed to the fact that the (in particular vertical) gradient information is contained in the additional motion components. We compare these effects for strike-slip and normal-faulting type sources and confirm that the increase in inversion quality for kinematic source parameters is even higher for the normal fault. This indicates that the inversion benefits from the additional information provided by the horizontal rotation rates, i.e., information about the vertical displacement gradient.
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10

Stähler, S. C., and K. Sigloch. "Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation." Solid Earth 5, no. 2 (November 17, 2014): 1055–69. http://dx.doi.org/10.5194/se-5-1055-2014.

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Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Seismic source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 source time functions (STFs) by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits propagating these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.
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11

Svarva Helgebostad, Kristian, Martin Landrø, Vetle Vinje, and Carl-Inge Nilsen. "Estimating source signatures from source-over-spread marine seismic data." GEOPHYSICS 83, no. 6 (November 1, 2018): P39—P48. http://dx.doi.org/10.1190/geo2017-0789.1.

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Recent developments in marine seismic acquisition include deploying a source vessel above a towed-streamer spread. We have developed an inversion algorithm to estimate source signatures for such acquisition configurations, by minimizing the difference between the recorded and a modeled direct wave. The forward modeling is based upon a physical modeling of the air bubble created by each air gun in the source array, and a damped Gauss-Newton approach is used for the optimization. Typical inversion parameters are empirical damping factors for the bubble oscillations and firing time delays for each air gun. Variations in streamer depth are taken into account, and a constant sea-surface reflection coefficient is also estimated as a by-product of the inversion. For data acquired in shallow waters, we have developed an extension of the forward modeling to include reflections from the water bottom to stabilize the inversion. The algorithm is tested on synthetic- and field-data examples, and the estimated source signature for the field-data example is used in a designature processing flow.
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12

Krebs, Jerome R., John E. Anderson, David Hinkley, Ramesh Neelamani, Sunwoong Lee, Anatoly Baumstein, and Martin-Daniel Lacasse. "Fast full-wavefield seismic inversion using encoded sources." GEOPHYSICS 74, no. 6 (November 2009): WCC177—WCC188. http://dx.doi.org/10.1190/1.3230502.

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Full-wavefield seismic inversion (FWI) estimates a subsurface elastic model by iteratively minimizing the difference between observed and simulated data. This process is extremely computationally intensive, with a cost comparable to at least hundreds of prestack reverse-time depth migrations. When FWI is applied using explicit time-domain or frequency-domain iterative-solver-based methods, the seismic simulations are performed for each seismic-source configuration individually. Therefore, the cost of FWI is proportional to the number of sources. We have found that the cost of FWI for fixed-spread data can be significantly reduced by applying it to data formed by encoding and summing data from individual sources. The encoding step forms a single gather from many input source gathers. This gather represents data that would have been acquired from a spatially distributed set of sources operating simultaneously with different source signatures. The computational cost of FWI using encoded simultaneous-source gathers is reduced by a factor roughly equal to the number of sources. Further, this efficiency is gained without significantly reducing the accuracy of the final inverted model. The efficiency gain depends on subsurface complexity and seismic-acquisition parameters. There is potential for even larger improvements of processing speed.
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13

Lyu, Bin, and Nori Nakata. "Iterative passive-source location estimation and velocity inversion using geometric-mean reverse-time migration and full-waveform inversion." Geophysical Journal International 223, no. 3 (September 9, 2020): 1935–47. http://dx.doi.org/10.1093/gji/ggaa428.

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SUMMARY Passive-seismic provides useful information for reservoir monitoring and structural imaging; for example, the locations of microseismic events are helpful to understand the extension of the hydraulic fracturing. However, passive-seismic imaging still faces some challenges. First, it is not easy to know where the passive-seismic events happened, which is known as passive-source locating. Additionally, the accuracy of the subsurface velocity model will influence the accuracy of the estimated passive-source locations and the quality of the structural imaging obtained from the passive-seismic data. Therefore the velocity inversion using the passive-seismic data is required to provide the velocity with higher accuracy. Focusing on these challenges, we develop an iterative passive-source location estimation and velocity inversion method using geometric-mean reverse-time migration (GmRTM) and full-waveform inversion (FWI). In each iteration, the source location is estimated using a high-resolution GmRTM method, which provides a better focusing of passive-source imaging compared to conventional wavefield scanning method. The passive-source FWI is then followed to optimize the velocity model using the estimated source location provided by GmRTM. The source location estimation and velocity inversion are implemented sequentially. We evaluate this iterative method using the Marmousi model data set. The experiment result and sensitivity analysis indicate that the proposed method is effective to locate the sources and optimize velocity model in the areas with complicated subsurface structures and noisy recordings.
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14

Stähler, S. C., and K. Sigloch. "Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation." Solid Earth Discussions 5, no. 2 (July 23, 2013): 1125–62. http://dx.doi.org/10.5194/sed-5-1125-2013.

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Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves, but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits to propagate these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.
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15

Robinson, Enders A. "Inversion of a seismic transmission response." GEOPHYSICS 66, no. 4 (July 2001): 1235–39. http://dx.doi.org/10.1190/1.1487070.

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Traveling waves are used not only in exploration geophysics but also in other disciplines faced with remote detection problems. A physical system may be described in terms of the input (the source), the medium, and the output (the received signal). The received signal can be made up of either transmitted waves or reflected waves. Two types of inverse problems can be considered, namely, the inverse source problem and the inverse medium problem. In the inverse source problem, the objective is to determine the source. In the inverse medium problem, the objective is to determine the medium. Thus, in terms of this general classification, four types of problems can be encountered, namely, an inverse source problem with transmitted waves, an inverse source problem with reflected waves, an inverse medium problem with transmitted waves, and an inverse medium problem with reflected waves. Let us look at nature. Twinkle, twinkle, little star. The transmission of starlight though the atmosphere makes the star twinkle. A better image of the star can be obtained by solving an inverse source problem using the transmitted starlight. In the typical inverse source problem, the source of energy is remote, the medium transmits the source signal, and the received data are the transmitted waves. Examples are classical earthquake seismology, radio transmission, and passive sonar. Shakespeare said; “For the eye sees not by itself, but by reflection.” Thus the miracle of eyesight solves an inverse medium problem that uses reflected waves. In the typical inverse medium problem, the source of energy is local and often man‐made, the medium reflects the source signal, and the received data are the reflected waves. Examples are reflection seismology, radar, and active sonar. Thus, the two principle types of inverse problems encountered in nature are the inverse source problem with transmitted waves and the inverse medium problem with reflected waves.
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16

Lee, Ki Ha, and Hee Joon Kim. "Source‐independent full‐waveform inversion of seismic data." GEOPHYSICS 68, no. 6 (November 2003): 2010–15. http://dx.doi.org/10.1190/1.1635054.

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A rigorous full‐waveform inversion of seismic data has been a challenging subject, partly because of the lack of precise knowledge of the source. Since currently available approaches involve some form of approximations to the source, inversion results are subject to the quality and choice of the source information used. We propose a new full‐waveform inversion methodology that does not involve source spectrum information. Thus, potential inversion errors from source estimation can be eliminated. A gather of seismic traces is first Fourier transformed into the frequency domain, and a normalized wavefield is obtained for each trace in the frequency domain. Normalization is done with respect to the frequency response of a reference trace selected from the gather, so the complex‐valued normalized wavefield is dimensionless. The source spectrum is eliminated during the normalization procedure. With its source spectrum eliminated, the normalized wavefield lets us construct an inversion algorithm without the source information. The inversion algorithm minimizes misfits between a measured normalized wavefield and a numerically computed normalized wavefield. The proposed approach has been demonstrated successfully using a simple 2D scalar problem.
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17

Han, Bo, Qinglong He, Yong Chen, and Yixin Dou. "Seismic Waveform Inversion Using the Finite-Difference Contrast Source Inversion Method." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/532159.

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This paper extends the finite-difference contrast source inversion method to reconstruct the mass density for two-dimensional elastic wave inversion in the framework of the full-waveform inversion. The contrast source inversion method is a nonlinear iterative method that alternatively reconstructs contrast sources and contrast function. One of the most outstanding advantages of this inversion method is the highly computational efficiency, since it does not need to simulate a full forward problem for each inversion iteration. Another attractive feature of the inversion method is that it is of strong capability in dealing with nonlinear inverse problems in an inhomogeneous background medium, because a finite-difference operator is used to represent the differential operator governing the two-dimensional elastic wave propagation. Additionally, the techniques of a multiplicative regularization and a sequential multifrequency inversion are employed to enhance the quality of reconstructions for this inversion method. Numerical reconstruction results show that the inversion method has an excellent performance for reconstructing the objects embedded inside a homogeneous or an inhomogeneous background medium.
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18

Bunks, Carey, Fatimetou M. Saleck, S. Zaleski, and G. Chavent. "Multiscale seismic waveform inversion." GEOPHYSICS 60, no. 5 (September 1995): 1457–73. http://dx.doi.org/10.1190/1.1443880.

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Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low‐frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.
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Zhang, Yu, and Daoliu Wang. "Traveltime information-based wave-equation inversion." GEOPHYSICS 74, no. 6 (November 2009): WCC27—WCC36. http://dx.doi.org/10.1190/1.3243073.

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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.
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Hu, Wenyi, Aria Abubakar, and Tarek M. Habashy. "Joint electromagnetic and seismic inversion using structural constraints." GEOPHYSICS 74, no. 6 (November 2009): R99—R109. http://dx.doi.org/10.1190/1.3246586.

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We have developed a frequency-domain joint electromagnetic (EM) and seismic inversion algorithm for reservoir evaluation and exploration applications. EM and seismic data are jointly inverted using a cross-gradient constraint that enforces structural similarity between the conductivity image and the compressional wave (P-wave) velocity image. The inversion algorithm is based on a Gauss-Newton optimization approach. Because of the ill-posed nature of the inverse problem, regularization is used to constrain the solution. The multiplicative regularization technique selects the regularization parameters automatically, improving the robustness of the algorithm. A multifrequency data-weighting scheme prevents the high-frequency data from dominating the inversion process. When the joint-inversion algorithm is applied in integrating marine controlled-source electromagnetic data with surface seismic data for subsea reservoir exploration applications and in integrating crosswell EM and sonic data for reservoir monitoring and evaluation applications, results improve significantly over those obtained from separate EM or seismic inversions.
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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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Li, Han, Xu Chang, Jinlai Hao, and Yibo Wang. "The general dislocation source model and its application to microseismic focal mechanism inversion." GEOPHYSICS 86, no. 4 (June 23, 2021): KS79—KS93. http://dx.doi.org/10.1190/geo2020-0844.1.

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Research on the non-double-couple (NDC) components in an earthquake is important for characterizing true source processes. The moment-tensor (MT) source model is commonly used to study NDC earthquakes. However, MT inversions are still challenging when earthquakes have small magnitudes, especially microearthquakes. The general-dislocation (GD) model specifies the focal mechanism as a shear-tensile slip on a fault plane; thus, GD inversion is better constrained than MT inversion. We focus on GD model-based waveform forward modeling and its application to microseismic source inversions. We expand the generalized reflection-transmission matrix method to synthesize waveforms based on the GD model and fully describe a GD source with five parameters: the scalar seismic moment (which defines the magnitude) and the strike, dip, rake, and slope angles (which define the fault geometry). We compare the GD, MT, and double-couple models and introduce the differences in their characterization and wave synthesis theories. We have developed a GD model-based microseismic focal mechanism inversion method that requires calculating only four angles under hybrid constraints. Two sets of solutions correspond to the same seismograms in a GD model-based inversion. These two solutions have the same scalar seismic moment and slope angle but different strike, dip, and rake angles, and we have derived formulas for mapping from one solution to the other. Synthetic and field surface microseismic data sets are used to test our GD model-based modeling and inversion methods. According to our study, the GD model is effective in microseismic focal mechanism inversion. By developing specific wave synthesis and inversion methods for the GD model, we offer a novel perspective to study this model and the NDC mechanisms for hydraulic fracturing-induced microearthquakes.
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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.

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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.
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Poppeliers, Christian, and Leiph Preston. "Combining translational and rotational seismic motions to invert local-scale seismic data for time-variable moment tensors: do rotational motions help for high-frequency seismic data produced by underground explosions?" Geophysical Journal International 230, no. 1 (March 8, 2022): 235–51. http://dx.doi.org/10.1093/gji/ggac068.

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SUMMARY We present an analysis of combining translational and rotational seismic data in an inversion for the time-variable source time functions corresponding to the components of the seismic moment tensor. We conduct a series of numerical experiments where the data are simulated by a combination of an underground explosion and a co-located double couple shear source and recorded on surface-mounted seismometers within 1–2 km of the source. The experiments are designed to mimic explosion seismology experiments, and thus the data are in the 1–10 Hz frequency range and contain very few surface waves. We use a Monte Carlo method to propagate Earth model uncertainty into the estimates of seismic source parameters. In our experiments, we find that the uncertainty of the estimated seismic source parameters increases when we add rotational seismic motions to the inversion when using a constant number of data channels. In this case, the increased degree of uncertainty in the final results is most likely due to the near-surface Earth model uncertainty that we introduce in our simulations. However, for a fixed number of seismic stations, adding rotational seismic motions to the inversion acts to decrease the uncertainty of the estimated seismic source parameters, most likely due to the increase in the number of data channels used in the inversion.
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Day, Steven M., and Keith L. McLaughlin. "Seismic source representations for spall." Bulletin of the Seismological Society of America 81, no. 1 (February 1, 1991): 191–201. http://dx.doi.org/10.1785/bssa0810010191.

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Abstract Spall may be a significant secondary source of seismic waves from underground explosions. The proper representation of spall as a seismic source is important for forward and inverse modeling of explosions for yield estimation and discrimination studies. We present a new derivation of a widely used point force representation for spall, which is based on a horizontal tension crack model. The derivation clarifies the relationship between point force and moment tensor representations of the tension crack. For wavelengths long compared with spall depth, the two representations are equivalent, and the moment tensor time history is proportional to the doubly integrated time history of the point force. Numerical experiments verify that, for regional seismic phases, this equivalence is valid for all frequencies for which the point-source (long wavelength) approximation is valid. Further analysis shows that the moment tensor and point force representations retain their validity for nonplanar spall surfaces, provided that the average dip of the surface is small. The equivalency of the two representations implies that a singular inverse problem will result from attempts to infer simultaneously the spectra of both of these source terms from seismic waveforms. If the spall moment tensor alone is estimated by inversion of waveform data, the inferred numerical values of its components will depend inversely upon the source depth that is assumed in the inversion formalism.
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Wu, Ru-Shan, Jingrui Luo, and Bangyu Wu. "Seismic envelope inversion and modulation signal model." GEOPHYSICS 79, no. 3 (May 1, 2014): WA13—WA24. http://dx.doi.org/10.1190/geo2013-0294.1.

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We recognized that the envelope fluctuation and decay of seismic records carries ultra low-frequency (ULF, i.e., the frequency below the lowest frequency in the source spectrum) signals that can be used to estimate the long-wavelength velocity structure. We then developed envelope inversion for the recovery of low-wavenumber components of media (smooth background), so that the initial model dependence of waveform inversion can be reduced. We derived the misfit function and the corresponding gradient operator for envelope inversion. To understand the long-wavelength recovery by the envelope inversion, we developed a nonlinear seismic signal model, the modulation signal model, as the basis for retrieving the ULF data and studied the nonlinear scale separation by the envelope operator. To separate the envelope data from the wavefield data (envelope extraction), a demodulation operator (envelope operator) was applied to the waveform data. Numerical tests using synthetic data for the Marmousi model proved the validity and feasibility of the proposed approach. The final results of combined [Formula: see text] (envelope-inversion for smooth background plus waveform-inversion for high-resolution velocity structure) indicated that it can deliver much improved results compared with regular full-waveform inversion (FWI) alone. Furthermore, to test the independence of the envelope to the source frequency band, we used a low-cut source wavelet (cut from 5 Hz below) to generate the synthetic data. The envelope inversion and the combined [Formula: see text] showed no appreciable difference from the full-band source results. The proposed envelope inversion is also an efficient method with very little extra work compared with conventional FWI.
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Fang, Zhilong, Rongrong Wang, and Felix J. Herrmann. "Source estimation for wavefield-reconstruction inversion." GEOPHYSICS 83, no. 4 (July 1, 2018): R345—R359. http://dx.doi.org/10.1190/geo2017-0700.1.

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Source estimation is essential for all wave-equation-based seismic inversions, including full-waveform inversion (FWI) and the recently proposed wavefield-reconstruction inversion (WRI). When the source estimation is inaccurate, errors will propagate into the predicted data and introduce additional data misfit. As a consequence, inversion results that minimize this data misfit may become erroneous. To mitigate the errors introduced by the incorrect and preestimated sources, an embedded procedure that updates sources along with medium parameters is necessary for the inversion. So far, such a procedure is still missing in the context of WRI, a method that is, in many situations, less prone to local minima related to so-called cycle skipping, compared with FWI through exact data fitting. Although WRI indeed helps to mitigate issues related to cycle skipping by extending the search space with wavefields as auxiliary variables, it relies on having access to the correct source functions. To remove the requirement of having the accurate source functions, we have developed a source-estimation technique specifically designed for WRI. To achieve this task, we consider the source functions as unknown variables and arrive at an objective function that depends on the medium parameters, wavefields, and source functions. During each iteration, we apply the so-called variable projection method to simultaneously project out the source functions and wavefields. After the projection, we obtain a reduced objective function that only depends on the medium parameters and invert for the unknown medium parameters by minimizing this reduced objective. Numerical experiments illustrate that this approach can produce accurate estimates of the unknown medium parameters without any prior information of the source functions.
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Oh, Seokmin, Kyubo Noh, Soon Jee Seol, and Joongmoo Byun. "Cooperative deep learning inversion of controlled-source electromagnetic data for salt delineation." GEOPHYSICS 85, no. 4 (June 10, 2020): E121—E137. http://dx.doi.org/10.1190/geo2019-0532.1.

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Various geophysical data types have advantages for exploring the subsurface, and more reliable exploration can be realized through integration of such data. However, the imaging of physical properties based on deep learning (DL) techniques, which has received considerable attention because of its enormous potential, has generally been performed using only a single type of data. We have developed a cooperative inversion method based on supervised DL for salt delineation. Controlled-source electromagnetic (CSEM) data, which can effectively distinguish a salt body with high electrical resistivity from the surrounding medium, are used as data for cooperative inversion, with high-resolution information derived from seismic data used as the constraint. This approach can entrain seismic information into a fully convolutional network designed to invert CSEM data to reconstruct the resistivity distribution. The inversion network is trained using large synthetic data sets, including the seismic information derived from seismic data as well as CSEM data and resistivity models. A cooperative strategy for reasonable entrainment of seismic information into the inversion network is established based on analysis of the network and kernels of the convolutional layers. The performance of the proposed method is demonstrated through experiments on test data generated for resistivity models for complex salt structures. The trained cooperative inversion network shows improved salt delineation results compared to the independent inversion network, irrespective of noise levels added to the test data, due to restriction of the resistivity model to fit seismic information. Moreover, training with noise-added data decreased the effects of noise on prediction results, similar to the case of adversarial training. We develop the possibility of combining geophysical data with a constraint using DL-based techniques.
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Rasanen, Ryan A., and Brett W. Maurer. "Probabilistic seismic source inversion from regional landslide evidence." Landslides 19, no. 2 (November 25, 2021): 407–19. http://dx.doi.org/10.1007/s10346-021-01780-9.

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Zhang, Liangyong, Weiguo Xiao, Xin Li, Xiaolin Hu, Wenjun Yin, Pengyi Li, and Shiying Tang. "Explosion Yield Estimation of Multi-Ground-Medium-Mixed Site." Journal of Physics: Conference Series 2282, no. 1 (June 1, 2022): 012012. http://dx.doi.org/10.1088/1742-6596/2282/1/012012.

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Abstract The seismo-acoustic analysis approach, which is based on the fusion of acoustic and seismic data, is an extremely effective way of monitoring the yield of explosions over a long distance. To address the problem of estimating the explosion yield at a multi-ground-medium-mixed site (abbreviated as mixed site), this article derives the general explosion yield prediction forms of acoustic model and seismic model, establishes the inversion method for explosion source parameters at mixed site by introducing the ground medium amplification factor, analyzes the inversion accuracy by using experimental data, and discusses the amplification effect and the influence of different scaling relationships. The experimental results indicate that the dispersion of the acoustic impulse relative to the overpressure decreases with distance and the linear relationship of acoustic impulse is better on a logarithmic scale, whereas the vertical component of the first peak of the seismic particle velocity and displacement, as well as the radial-vertical-tangent vector sum, exhibit a good linear variation law over a certain range on the logarithmic scale. The results of the source parameter inversion demonstrate that when the amplification factor is introduced, the inversion of the explosion source parameters of the mixed site has a high accuracy for yield estimation; however, when only single hard-rock media is considered, the inversion of the explosion source parameters produces large errors. The results of the amplification effect and scaling relationship analysis indicate that geological amplification has a substantial effect on the explosion source parameter inversion results, and that the data dispersion degrees of Sachs and KG85 scaling relationships are essentially identical.
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Zhang, Liangyong, Weiguo Xiao, Xin Li, Xiaolin Hu, Wenjun Yin, Pengyi Li, and Shiying Tang. "Explosion Yield Estimation of Multi-Ground-Medium-Mixed Site." Journal of Physics: Conference Series 2282, no. 1 (June 1, 2022): 012012. http://dx.doi.org/10.1088/1742-6596/2282/1/012012.

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Abstract The seismo-acoustic analysis approach, which is based on the fusion of acoustic and seismic data, is an extremely effective way of monitoring the yield of explosions over a long distance. To address the problem of estimating the explosion yield at a multi-ground-medium-mixed site (abbreviated as mixed site), this article derives the general explosion yield prediction forms of acoustic model and seismic model, establishes the inversion method for explosion source parameters at mixed site by introducing the ground medium amplification factor, analyzes the inversion accuracy by using experimental data, and discusses the amplification effect and the influence of different scaling relationships. The experimental results indicate that the dispersion of the acoustic impulse relative to the overpressure decreases with distance and the linear relationship of acoustic impulse is better on a logarithmic scale, whereas the vertical component of the first peak of the seismic particle velocity and displacement, as well as the radial-vertical-tangent vector sum, exhibit a good linear variation law over a certain range on the logarithmic scale. The results of the source parameter inversion demonstrate that when the amplification factor is introduced, the inversion of the explosion source parameters of the mixed site has a high accuracy for yield estimation; however, when only single hard-rock media is considered, the inversion of the explosion source parameters produces large errors. The results of the amplification effect and scaling relationship analysis indicate that geological amplification has a substantial effect on the explosion source parameter inversion results, and that the data dispersion degrees of Sachs and KG85 scaling relationships are essentially identical.
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32

Song, Jiawen, Peiming Li, Zhongping Qian, Mugang Zhang, Pengyuan Sun, Wenchuang Wang, and Yuanming Ma. "Simultaneous vibroseis data separation through sparse inversion." Leading Edge 38, no. 8 (August 2019): 625–29. http://dx.doi.org/10.1190/tle38080625.1.

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Compared with conventional seismic acquisition methods, simultaneous-source acquisition utilizes independent shooting that allows for source interference, which reduces the time and cost of acquisition. However, additional processing is required to separate the interfering sources. Here, we present an inversion-based deblending method, which distinguishes signal from blending noise based on coherency differences in 3D receiver gathers. We first transform the seismic data into the frequency-wavenumber-wavenumber domain and impose a sparse constraint to estimate the coherent signal. We then subtract the estimated signal from the original input to predict the interference noise. Driven by data residuals, the signal is updated iteratively with shrinking thresholds until the signal and noise fully separate. We test our presented method on two 3D field data sets to demonstrate how the method proficiently separates interfering vibroseis sources with high fidelity.
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33

Loewenthal, Dan, and Vladimir Shtivelman. "Source signature estimation using fictitious source and reflector." GEOPHYSICS 54, no. 7 (July 1989): 916–20. http://dx.doi.org/10.1190/1.1442721.

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Source wavelet estimation is an important step in processing and interpreting seismic data. In the context of this work, the term (source wavelet) includes the pure source signature (the source response measured in a homogeneous medium) along with certain model‐related events (such as the ghost and interbed reflections). An estimate of the source wavelet can be used to increase the resolution of seismic data by signature deconvolution, deghosting, and dereverberation. However, pure source signature determination is of particular importance as a first step in direct inversion schemes, as demonstrated by Bube and Burridge (1983) and by Foster and Carrion (1985).
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Wapenaar, Kees, Joost van der Neut, and Jan Thorbecke. "Deblending by direct inversion." GEOPHYSICS 77, no. 3 (May 1, 2012): A9—A12. http://dx.doi.org/10.1190/geo2011-0497.1.

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Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints. We applied the method with numerically modeled data and it suppressed the crosstalk well, when the blended data consisted of responses to adjacent, densely sampled sources.
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35

Minkoff, Susan E., and William W. Symes. "Full waveform inversion of marine reflection data in the plane‐wave domain." GEOPHYSICS 62, no. 2 (March 1997): 540–53. http://dx.doi.org/10.1190/1.1444164.

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Full waveform inversion of a p‐τ marine data set from the Gulf of Mexico provides estimates of the long‐wavelength P‐wave background velocity, anisotropic seismic source, and three high‐frequency elastic parameter reflectivities that explain 70% of the total seismic data and 90% of the data in an interval around the gas sand target. The forward simulator is based on a plane‐wave viscoelastic model for P‐wave propagation and primary reflections in a layered earth. Differential semblance optimization, a variant of output least‐squares inversion, successfully estimates the nonlinear P‐wave background velocity and linear reflectivities. Once an accurate velocity is estimated, output least‐squares inversion reestimates the reflectivities and an anisotropic seismic source simultaneously. The viscoelastic model predicts the amplitude‐versus‐angle trend in the data more accurately than does an elastic model. Simultaneous inversion for reflectivities and source explains substantially more of the actual data than does inversion for reflectivities with fixed source from an air‐gun modeler. The best reflectivity estimates conform to widely accepted lithologic relationships and closely match the filtered well logs.
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Colombo, Daniele, Diego Rovetta, and Ersan Turkoglu. "CSEM-regularized seismic velocity inversion: A multiscale, hierarchical workflow for subsalt imaging." GEOPHYSICS 83, no. 5 (September 1, 2018): B241—B252. http://dx.doi.org/10.1190/geo2017-0454.1.

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Seismic imaging in salt geology is complicated by highly contrasted velocity fields and irregular salt geometries, which cause complex seismic wavefield scattering. Although the imaging challenges can be addressed by advanced imaging algorithms, a fundamental problem remains in the determination of robust velocity fields in high-noise conditions. Conventional migration velocity analysis is often ineffective, and even the most advanced methods for depth-domain velocity analysis, such as full-waveform inversion, require starting from a good initial estimate of the velocity model to converge to a correct result. Nonseismic methods, such as electromagnetics, can help guide the generation of robust velocity models to be used for further processing. Using the multiphysics data acquired in the deepwater section of the Red Sea, we apply a controlled-source electromagnetic (CSEM) resistivity-regularized seismic velocity inversion for enhancing the velocity model in a complex area dominated by nappe-style salt tectonics. The integration is achieved by a rigorous approach of multiscaled inversions looping over model dimensions (1D first, followed by 3D), variable offsets and increasing frequencies, data-driven and interpretation-supported approaches, leading to a hierarchical inversion guided by a parameter sensitivity analysis. The final step of the integration consists of the inversion of seismic traveltimes subject to CSEM model constraints in which a common-structure coupling mechanism is used. Minimization is performed over the seismic data residuals and cross-gradient objective functions without inverting for the resistivity model, which is used as a reference for the seismic inversion (hierarchical approach). Results are demonstrated through depth imaging in which the velocity model derived through CSEM-regularized hierarchical inversion outperforms the results of a seismic-only derived velocity model.
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Zhong, Yu, and Yangting Liu. "Source-independent time-domain vector-acoustic full-waveform inversion." GEOPHYSICS 84, no. 4 (July 1, 2019): R489—R505. http://dx.doi.org/10.1190/geo2018-0304.1.

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Dual-sensor seismic acquisition systems that record the pressure and particle velocity allow the recording of the full-vector-acoustic (VA) wavefields. Most previous studies have focused on data-domain processing methods based on VA seismic data; whereas, few studies focused on using full-VA seismic data in full-waveform inversion (FWI). Conventional acoustic FWI only takes advantage of the pressure recordings to estimate the medium’s velocity model. Some artifact events will appear in the adjoint-state wavefields based on the conventional acoustic FWI method. These artifact events further reduce the accuracy of acoustic FWI. To simultaneously use pressure and vertical particle velocity recordings, we introduced a new time-domain VA FWI method. The VA FWI method can take advantage of directivity information contained in the VA seismic data. Thus, the adjoint-state wavefields based on VA FWI are more accurate than those from the conventional acoustic FWI method. In addition, we applied a convolution-based objective function to eliminate the effects of the source wavelet and implement a time-domain multiscale strategy in VA FWI. Synthetic examples are presented to demonstrate that VA FWI can improve the accuracy of acoustic FWI in the presence and absence of a free surface in the acoustic case. In addition, VA FWI does not significantly increase the computation and memory costs, but it has better convergence when compared with conventional acoustic FWI.
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Guo, Zhenwei, Hefeng Dong, and Åge Kristensen. "Image-guided regularization of marine electromagnetic inversion." GEOPHYSICS 82, no. 4 (July 1, 2017): E221—E232. http://dx.doi.org/10.1190/geo2016-0130.1.

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Marine electromagnetic (EM) inverse methods have recently been rapidly developed for offshore exploration. However, inverted resistivity results with low resolution are provided by the EM method. To improve this quality of the results, we have developed an image-guided regularization method for inversion of the marine EM data. The method incorporates seismic constraints into EM inversion. Information is extracted from seismic/geologic images and consists of the metric tensor field and sampling on the geologic structure. In addition to the regularization, geologic horizons picked from the seismic images and samplings on the structure can be used to generate an irregular sparse mesh. Compared with an unstructured regular dense mesh, a coherence-based irregular sparse mesh can reduce computational costs. Furthermore, image-guided regularization represents an improvement compared with traditional regularization that are structurally based on seismic images by following geologic features more closely and handling anomalies better. We have determined that image-guided regularization improves the results of EM inversions with irregular sparse meshes. The image-guided regularized inversion can be applied to marine controlled-source electromagnetic (CSEM) data and magnetotelluric (MT) data, and it can be used for joint inversion of CSEM and MT data. Regarding its application to real data, image-guided inversion was successfully applied to CSEM data on the Troll area, using an anisotropic model.
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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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Mora, Peter. "Inversion = migration + tomography." GEOPHYSICS 54, no. 12 (December 1989): 1575–86. http://dx.doi.org/10.1190/1.1442625.

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Seismic inversion, broadly enough defined, is equivalent to doing migration and reflection tomography simultaneously. Diffraction tomography and inversion work best when sources and receivers surround the region of interest, as in medical imaging applications. Theoretical studies have shown that high vertical wavenumber velocity perturbations are resolved by inverting surface seismic reflection data, but the low vertical wavenumbers must be obtained using a separate step, such as velocity analysis or reflection tomography. I propose that a nonlinear iterative inversion that updates a varying background velocity obtains all wavenumbers that are resolvable separately by migration and tomography. The background velocity must contain reflectors to provide data on both upward and downward transmission paths through the earth and hence the low wavenumbers. By considering the downward transmission paths to be between surface sources and buried image geophones and the upward transmission paths to be between surface geophones and buried image sources, the source and receiver coverage is effectively the same as in medical imaging; although the depth of the image sources and geophones must be determined in the inversion by finding the reflector depths. Synthetic examples verify the theoretical predictions and show that reflector locations and interval velocities can be obtained simultaneously even when there is no prior knowledge of reflector location. However, a good initial “very low‐wavenumber” model is normally required to ensure convergence to the global inverse solution.
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sci, global. "Multi-Frequency Contrast Source Inversion for Reflection Seismic Data." Communications in Computational Physics 28, no. 1 (June 2020): 207–77. http://dx.doi.org/10.4208/cicp.oa-2018-0099.

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42

Minkoff, S. E., and W. W. Symes. "Estimating the energy source and reflectivity by seismic inversion." Inverse Problems 11, no. 2 (April 1, 1995): 383–95. http://dx.doi.org/10.1088/0266-5611/11/2/008.

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43

Kawakatsu, Hitoshi, and Jean-Paul Montagner. "Time-reversal seismic-source imaging and moment-tensor inversion." Geophysical Journal International 175, no. 2 (November 2008): 686–88. http://dx.doi.org/10.1111/j.1365-246x.2008.03926.x.

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44

Long, Quan, Mohammad Motamed, and Raúl Tempone. "Fast Bayesian optimal experimental design for seismic source inversion." Computer Methods in Applied Mechanics and Engineering 291 (July 2015): 123–45. http://dx.doi.org/10.1016/j.cma.2015.03.021.

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45

Chmiel, Małgorzata, Philippe Roux, Marc Wathelet, and Thomas Bardainne. "Phase-velocity inversion from data-based diffraction kernels: seismic Michelson interferometer." Geophysical Journal International 224, no. 2 (October 28, 2020): 1287–300. http://dx.doi.org/10.1093/gji/ggaa512.

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SUMMARY We propose a new surface wave tomography approach that benefits from densely sampled active-source arrays and brings together elements from active-source seismic-wave interferometry, full waveform inversion and dense-array processing. In analogy with optical interferometry, seismic Michelson interferometer (SMI) uses seismic interference patterns given by the data-based diffraction kernels in an iterative inversion scheme to image a medium. SMI requires no traveltime measurements and no spatial regularization, and it accounts for bent rays. Furthermore, the method does not need computation of complex synthetic models, as it works as a data-driven inversion technique that makes it computationally very fast. In an automatic way, it provides high-resolution phase-velocity maps and their error estimation. SMI can complete traditional surface wave tomography studies, as its use can be easily extended from land active seismic data to the virtual source gathers of ambient-noise-based studies with dense arrays.
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Kim, Youngseo, Dong-Joo Min, and Changsoo Shin. "Frequency-domain reverse-time migration with source estimation." GEOPHYSICS 76, no. 2 (March 2011): S41—S49. http://dx.doi.org/10.1190/1.3534831.

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Although artificially generated seismic sources such as dynamite, vibroseis, and air guns are used in seismic exploration, it is not easy to exactly recover the source wavelet in field recording or in data processing. For this reason, seismic data processing often assumes that an explosive-source wavelet can be described by a well-known function (e.g., a Ricker wavelet), a near-offset trace, or a deconvolved wavelet. In frequency-domain waveform inversion, it has been proven that a source wavelet can be estimated by an optimization method, and incorporating the source wavelet estimation into an inversion algorithm yields better inversion results. We have developed source wavelet estimation into 2D two-way frequency-domain reverse-time migration. The source wavelet is first estimated independently of reverse-time migration by an optimization method such as the full Newton method. It is then used in reverse-time migration. This source-wavelet-incorporated reverse-time migration algorithm is applied to three model data sets: a simple anticline model, the Institut Français du Petrole (IFP) Marmousi model, and the BP 2004 EAGE model. Numerical examples were used to show that better migration images can be obtained by using an estimated source wavelet than those obtained by using a designatured wavelet without source estimation. To enhance the migrated images, the Laplacian filter is applied and migrated images are scaled using the diagonal of the pseudo-Hessian matrix. It is expected that the source wavelet estimation method can be directly applied to 2D or 3D time-domain two-way reverse-time migration.
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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.

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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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48

Abubakar, Aria, Wenyi Hu, Tarek M. Habashy, and Peter M. van den Berg. "Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data." GEOPHYSICS 74, no. 6 (November 2009): WCC47—WCC58. http://dx.doi.org/10.1190/1.3250203.

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We have applied the finite-difference contrast-source inversion (FDCSI) method to seismic full-waveform inversion problems. The FDCSI method is an iterative nonlinear inversion algorithm. However, unlike the nonlinear conjugate gradient method and the Gauss-Newton method, FDCSI does not solve any full forward problem explicitly in each iterative step of the inversion process. This feature makes the method very efficient in solving large-scale computational problems. It is shown that FDCSI, with a significant lower computation cost, can produce inversion results comparable in quality to those produced by the Gauss-Newton method and better than those produced by the nonlinear conjugate gradient method. Another attractive feature of the FDCSI method is that it is capable of employing an inhomogeneous background medium without any extra or special effort. This feature is useful when dealing with time-lapse inversion problems where the objective is to reconstruct changes between the baseline and the monitor model. By using the baseline model as the background medium in crosswell seismic monitoring problems, high quality time-lapse inversion results are obtained.
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49

Minato, Shohei, Toshifumi Matsuoka, Takeshi Tsuji, Deyan Draganov, Jürg Hunziker, and Kees Wapenaar. "Seismic interferometry using multidimensional deconvolution and crosscorrelation for crosswell seismic reflection data without borehole sources." GEOPHYSICS 76, no. 1 (January 2011): SA19—SA34. http://dx.doi.org/10.1190/1.3511357.

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Abstract:
Crosswell reflection method is a high-resolution seismic imaging method that uses recordings between boreholes. The need for downhole sources is a restrictive factor in its application, for example, to time-lapse surveys. An alternative is to use surface sources in combination with seismic interferometry. Seismic interferometry (SI) could retrieve the reflection response at one of the boreholes as if from a source inside the other borehole. We investigate the applicability of SI for the retrieval of the reflection response between two boreholes using numerically modeled field data. We compare two SI approaches — crosscorrelation (CC) and multidimensional deconvolution (MDD). SI by MDD is less sensitive to underillumination from the source distribution, but requires inversion of the recordings at one of the receiver arrays from all the available sources. We find that the inversion problem is ill-posed, and propose to stabilize it using singular-value decomposition. The results show that the reflections from deep boundaries are retrieved very well using both the CC and MDD methods. Furthermore, the MDD results exhibit more realistic amplitudes than those from the CC method for downgoing reflections from shallow boundaries. We find that the results retrieved from the application of both methods to field data agree well with crosswell seismic-reflection data using borehole sources and with the logged P-wave velocity.
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50

Zhang, Pan, Ru-Shan Wu, and Liguo Han. "Source-independent seismic envelope inversion based on the direct envelope Fréchet derivative." GEOPHYSICS 83, no. 6 (November 1, 2018): R581—R595. http://dx.doi.org/10.1190/geo2017-0360.1.

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Abstract:
Seismic envelope inversion (EI) uses low-frequency envelope data to recover long-wavelength components of the subsurface media. Conventional EI uses the same waveform Fréchet derivative as conventional full-waveform inversion. Due to linearization of the sensitivity operator (Born approximation), neither of these methods can yield good inversion results for media with strong preturbations, such as salt domes, when the source lacks low-frequency information. Because seismic envelope data contain large amount of ultra-low-frequency information and the direct envelope Fréchet derivative maps envelope data perturbation directly to velocity perturbation, the direct envelope inversion (DEI) method (based on the direct envelope Fréchet derivative) can handle such strong nonlinear inversion problems. However, this method is sensitive to source wavelet errors. We developed a source-independent DEI method. To achieve the source-independent objective function, we derive a convolution expression for the envelope data. We derive the gradient of the new objective function by using the direct envelope Fréchet derivative. Numerical tests conducted on a 2D salt model indicate that our method can achieve good reconstruction of salt bodies (strong velocity perturbations) and recover low-velocity background structures (weak velocity perturbations), despite using an inaccurate source wavelet.
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