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Journal ArticleDOI

2-D multiparameter viscoelastic shallow-seismic full-waveform inversion: reconstruction tests and first field-data application

01 Jul 2020-Geophysical Journal International (Oxford Academic)-Vol. 222, Iss: 1, pp 560-571
TL;DR: In this article, the authors explore the feasibility and performance of multi-parameter viscoelastic 2D FWI in which seismic velocities and attenuation of P- and S-waves, respectively, and mass density are inverted simultaneously.
Abstract: 2D full-waveform inversion (FWI) of shallow-seismic wavefields has recently become a novel way to reconstruct S-wave velocity models of the shallow subsurface with high vertical and lateral resolution. In most applications, seismic wave attenuation is ignored or considered as a passive modelling parameter only. In this study, we explore the feasibility and performance of multi-parameter viscoelastic 2D FWI in which seismic velocities and attenuation of P- and S-waves, respectively, and mass density are inverted simultaneously. Synthetic reconstruction experiments reveal that multiple crosstalks between all viscoelastic material parameters may occur. The reconstruction of S-wave velocity is always robust and of high quality. The parameters P-wave velocity and density exhibit weaker sensitivity and can be reconstructed more reliably by multi-parameter viscoelastic FWI. Anomalies in S-wave attenuation can be recovered but with limited resolution. In a field data application, a small-scale refilled trench is nicely delineated as a low P- and S-wave velocity anomaly. The reconstruction of P-wave velocity is improved by the simultaneous inversion of attenuation. The reconstructed S-wave attenuation reveals higher attenuation in the shallow weathering zone and weaker attenuation below. The variations in the reconstructed P- and S-wave velocity models are consistent with the reflectivity observed in a GPR profile.

Summary (2 min read)

1 INTRODUCTION

  • The reconstruction of near-surface models by using shallow-seismic wavefields plays an important role in geophysical and geotechnical site investigation.
  • With the rapid development of computational power, it has become increasingly popular to use 2D FWI of surface wave to reconstruct near-surface models.
  • Besides the velocity model, seismic attenuation also plays a crucial role in subsurface characterization.
  • Brossier (2011) showed the potential of multi-parameter viscoelastic FWI by using frequency-domain synthetic examples.

2.1 Forward modelling

  • In order to consider the attenuation into time-domain modelling, the generalized standard linear solid (Liu et al. 1976) is widely applied.
  • The parameter α is used to ensure that the waves travel with the model phase velocity at the reference frequency ω0 (Bohlen 2002).
  • (6) Fig. 1 shows the shape of a desired and the simulated Q values by using only one Maxwell body and the corresponding velocities dispersion for both P and S waves.
  • Therefore, the authors only use a single relaxation mechanism in this paper.

2.2 Full waveform inversion

  • The authors use the least-squares l2-error between the true-amplitude (non-normalized) synthetic and observed particle-velocity waveforms as the objective function: Ψ(m) = 1 2 ||dsyn(m)− dobs||2, (7) where dsyn(m) and dobs are the synthetic and observed particle-velocity seismograms, respectively.
  • Adjoint state method provides an efficient way to calculate the gradient of misfit function by cross-correlating the forward (state variables) and backward (adjoint state variables) wavefields.

3 SYNTHETIC EXAMPLES

  • The authors firstly perform two multi-parameter (five-parameters) examples by using a spatially uncorrelated and a spatially correlated model, respectively.
  • Results of viscoelastic and elastic FWIs are also compared.
  • Then the authors further investigate the crosstalk between coupled parameters VS and τS by comparing multi-parameter (two-parameters) viscoelastic and mono-parameter elastic FWI results.

3.1 Multi-parameter examples

  • A triangular lowvalue anomaly is superimposed on each parameter model at different positions (Fig. 2).
  • The 1-D background models are used as the initial models, and the true source wavelet is used during the inversion.

3.2 Crosstalk between coupled velocity and quality factor

  • The authors perform another two synthetic tests to investigate the crosstalk between coupled parameters: VS and τS .
  • The authors use the same 1D background models for velocities and quality factors, but only superimpose a low-VS anomaly and a low-QS (high-τS) anomaly at different positions (first column, Fig. 6).
  • The sources are generated with a delayed Ricker wavelet of 30 Hz.
  • Nevertheless, the reconstructed VS model suffers stronger crosstalk from the τS anomaly compared to the results of viscoelastic FWI.
  • These artefacts behave as vertical-stripped anomalies, which are parallel to the wavefront of Rayleigh-wave.

4 APPLICATION TO FIELD DATA

  • The authors apply the multi-parameter viscoelastic FWI strategy to a shallow seismic field dataset.
  • The authors only use vertical-component data in their example because the horizontal-component data has a relatively low signal-to-noise ratio.
  • The first source position is located between the first and second geophones.
  • It consists of two layers with sharp velocity 2D viscoelastic shallow-seismic FWI 15 contrast at a depth around 6 m which corresponds to the groundwater table (Pasquet et al. 2015; Wittkamp et al. 2019).
  • The multi-parameter inversion results are shown in the 2nd column in Fig.

5 DISCUSSION

  • In the field-data application, the elastic FWIs also nicely reconstruct the S-wave velocity models because the authors adopt good passive Q models in the elastic FWI.
  • Nevertheless, the numerical tests show that, when encountering heterogeneous Q model, multi-parameter viscoelastic FWI can further improve the accuracy of estimated velocity model and is superior to elastic FWI in which attenuation is considered as a passive modelling parameter only.
  • Therefore, it is meaningful to incorporate attenuation into the inversion for reconstructing accurate multi-parameter results to better delineate the subsurface structures and properties, especially when the Q model is highly heterogeneous.
  • Since the authors only use single relaxation mechanism, the estimated Q values might be lower than their true values (Fig. 1).
  • The authors use a preconditioned conjugate gradient algorithm to invert the data, which cannot reduce the parameter trade-off between coupled parameters appropriately.

6 CONCLUSIONS

  • The authors applied 2D multi-parameter viscoelastic full-waveform inversion (FWI) to shallow-seismic surface waves.
  • The authors tested the capability of this method to reconstruct reliable parameters on synthetic datasets with spatially correlated and uncorrelated models.
  • The synthetic results of spatially uncorrelated models showed that shallow-seismic data has the highest sensitivity with respect to VS , then 2D viscoelastic shallow-seismic FWI 19 VP , and relatively low sensitivity to density, QS and QP .
  • The authors compared their viscoelastic FWI result to the results estimated by elastic FWI in which Q models were included but not updated during the inversion.
  • They were contaminated by vertical-striped artefacts, which was mainly caused by the neglecting of heterogeneity in theQmodels.

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2D multi-parameter viscoelastic shallow-
seismic full waveform inversion:
reconstruction tests and first field-data
application
Lingli Gao, Yudi Pan, Thomas Bohlen
CRC Preprint 2020/14, April 2020
KARLSRUHE INSTITUTE OF TECHNOLOGY
KIT The Research University in the Helmholtz Association
www.kit.edu

Participating universities
Funded by
ISSN 2365-662X
2

submitted to Geophys. J. Int.
2D multi-parameter viscoelastic shallow-seismic full
waveform inversion: reconstruction tests and first field-data
application
Lingli Gao
1,
, Yudi Pan
2,
, and Thomas Bohlen
2
1
Institute of Applied and Numerical Mathematics, Karlsruhe Institute of Technology (KIT), Karlsruhe 76131, Germany
2
Geophysical Institute, Karlsruhe Institute of Technology (KIT), Karlsruhe 76187, Germany
The first two authors contributed equally to this work
SUMMARY
2D full-waveform inversion (FWI) of shallow-seismic wavefields has recently become a
novel way to reconstruct S-wave velocity models of the shallow subsurface with high ver-
tical and lateral resolution. In most applications, seismic wave attenuation is ignored or
considered as a passive modelling parameter only. In this study, we explore the feasibil-
ity and performance of multi-parameter viscoelastic 2D FWI in which seismic velocities
and attenuation of P- and S-waves, respectively, and mass density are inverted simul-
taneously. Synthetic reconstruction experiments reveal that multiple crosstalks between
all viscoelastic material parameters may occur. The reconstruction of S-wave velocity is
always robust and of high quality. The parameters P-wave velocity and density exhibit
weaker sensitivity and can be reconstructed more reliably by multi-parameter viscoelas-
tic FWI. Anomalies in S-wave attenuation can be recovered but with limited resolution.
In a field data application, a small-scale refilled trench is nicely delineated as a low P- and
S-wave velocity anomaly. The reconstruction of P-wave velocity is improved by the si-
multaneous inversion of attenuation. The reconstructed S-wave attenuation reveals higher
attenuation in the shallow weathering zone and weaker attenuation below. The variations

2 L. Gao, Y. Pan, T. Bohlen
in the reconstructed P- and S-wave velocity models are consistent with the reflectivity
observed in a GPR profile.
Key words: Surface waves and free oscillations; Waveform inversion; Seismic attenua-
tion
1 INTRODUCTION
The reconstruction of near-surface models by using shallow-seismic wavefields plays an important
role in geophysical and geotechnical site investigation. Shallow-seismic wavefields are dominated
by surface waves, which makes the inversion of them attractive to reconstruct near-surface models.
The inversion of surface waves is getting increasingly popular due to their high sensitivity to the S-
wave velocity (Socco et al. 2010), which is an important lithological and geotechnical parameter to
characterize the composition and stability of sediments.
Most of the current surface-wave methods are based on the extraction and inversion of surface-
wave dispersion curves (Xia et al. 1999). The dispersion-based surface-wave methods, however, fail
when strong lateral heterogeneity exists, which is regarded as one of their limitations (Pan et al. 2019).
Different approaches are proposed to account for lateral heterogeneity, such as laterally constrained
inversion (Socco et al. 2009), cross-correlation analysis of multichannel data (Hayashi & Suzuki 2004;
Ikeda et al. 2013), and spatial windowing (Bohlen et al. 2004; Bergamo et al. 2012). Another limitation
that current surface-wave methods face is the uncertainty in the correct estimation and identification
of multi-modal dispersion curves (Boaga et al. 2013; Gao et al. 2014, 2016). Full waveform inversion
(FWI) may overcome these limitations and can produce high-resolution multi-parameter models for
complex geologic structures. FWI was first introduced by Tarantola (1984) and Mora (1987) in time
domain with gradient-based inversion. With the rapid development of computational power, it has be-
come increasingly popular to use 2D FWI of surface wave to reconstruct near-surface models. Romd-
hane et al. (2011) and Tran et al. (2013) demonstrated the effectiveness of 2D frequency-domain elas-
tic FWI in reconstructing heterogeneous near-surface model. Groos et al. (2014, 2017) and Pan et al.
(2016, 2018) showed that 2D time-domain elastic FWI could efficiently delineate shallow subsurface
with high resolution. Besides, 3D FWI of the surface wave is also becoming feasible in recent years
(Irnaka et al. 2019; Mirzanejad & Tran 2019). FWI of the surface wave is highly ill-posed and might be
trapped in local minima, especially for the conventional least-squares misfit. One practical way to mit-
igate this problem is to use an initial model built by inverting surface-wave dispersion curves. Besides,
an alternative objective function, such as amplitude-spectrum-based misfit (P
´
erez Solano et al. 2014;

2D viscoelastic shallow-seismic FWI 3
Masoni et al. 2016), envelope-based misfit (Wu et al. 2014; Yuan et al. 2015), and multi-objective
misfit (Pan et al. 2020), can be used to reduce the nonlinearity of surface-wave FWI.
Besides the velocity model, seismic attenuation also plays a crucial role in subsurface characteri-
zation. It mainly influences the amplitude of the seismic wave and would also influence the phase of
the seismic wave when strong attenuation exists. Considering the attenuation effect in FWI is becom-
ing an important topic. Many studies are focused on the viscoacoustic FWI, in which P-wave velocity
(V
P
) and quality factor (Q) can be inverted recursively or simultaneously (Kamei & Pratt 2013; Mali-
nowski et al. 2011; Virieux & Operto 2009). Brossier (2011) showed the potential of multi-parameter
viscoelastic FWI by using frequency-domain synthetic examples. Bai et al. (2017) showed the recon-
struction of attenuation in anisotropic viscoelastic media. Besides the successful applications of FWI
in exploration seismic that are focusing on the utilizing of body waves, there are a few studies which
investigate the performance of viscoelastic FWI on the shallow-seismic surface wave. Some previous
studies neglected effects of attenuation (Romdhane et al. 2011; Tran et al. 2013; Xing & Mazzotti
2019). Groos et al. (2014) and Mirzanejad & Tran (2019) showed that the effects of anelastic damping
must be considered in the shallow-seismic FWI for better reconstruction of a high-resolution S-wave
velocity model. Groos et al. (2014) proposed a passive-viscoelastic FWI approach in which a fixed
prior estimated Q model is used in the forward solver to account for the viscous effect. The pure
elastic and passive-viscoelastic FWI approaches are generally valid when the attenuation is weak and
the Q model is laterally homogeneous. However, near-surface materials can be highly heterogeneous
and may also exhibit strong spatial variation of strong attenuation. In this case, simply ignoring the
viscous effect might deteriorate the reconstruction of S-wave velocity. Furthermore, the Q model is
an important additional material parameter and can help to discriminate different lithologies and to
improve the petrophysical characterization. This can be of interest in hydrological studies or the esti-
mation of local site amplification due to earthquakes (Xia et al. 2002). Therefore, the reconstruction of
multi-parameter models including both velocity and Q models using shallow-seismic surface waves is
of great interest.
Solving the viscoelastic wave equation in the time domain usually requires additional memory
equations (Carcione et al. 1988; Robertsson et al. 1994; Bohlen 2002). Because the viscoelastic wave
equation is not self-adjoint, an adjoint state equation which differs from the viscoelastic wave equation
needs to be solved in viscoelastic FWI (Yang et al. 2016; Fabien-Ouellet et al. 2017).
In this paper, we study the performance of 2D multi-parameter viscoelastic FWI applied to shallow
seismic wavefields. General theories of the forward simulation and FWI workflow are given in the first
section. Synthetic reconstruction tests for spatially correlated and uncorrelated models are performed
to investigate the validity of multi-parameter viscoelastic FWI as well as to study the crosstalk between

Citations
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Journal ArticleDOI
TL;DR: In this paper, a random-objective waveform inversion (ROWI) algorithm is proposed to estimate the Pareto optimality of all solutions explicitly, which is based on the stochastic gradient descent optimization algorithm.
Abstract: Robustness and uncertainty estimation are two challenging topics in full-waveform inversion (FWI). To overcome these challenges, we present the methodology of random-objective waveform inversion (ROWI), which adopts a multi-objective framework and a preconditioned stochastic gradient descent optimization algorithm. The use of one shot per iteration avoids using redundant data and reduces the computational cost. The Pareto solutions represent a group of most likely solutions and their differences quantifies the model uncertainty associated with the trade-off between conflicting objective functions. Due to the high dimensionality in the data and model spaces, it is prohibitively expensive to check the Pareto optimality of all solutions explicitly. Thus, we decompose the original multi-objective function into shot-related subproblems and use the Pareto solutions of the subproblems for trade-off analysis. We apply ROWI to a field multi-component shallow-seismic data set acquired in Rheinstetten, Germany. The 3D near-surface model is successfully reconstructed by ROWI and the main target, a refilled trench, is delineated. We compare the results estimated by ROWI and a conventional least squares FWI to prove the high efficiency of ROWI. We run six ROWI tests on the field data with different solution paths to prove the robustness of ROWI against the random solution path. The validity of the reconstructed model is verified by multiple 2D ground-penetrating radar profiles. We estimate 246 Pareto solutions of multi-objective subproblems for trade-off analysis. Another four ROWI tests starting from different poor initial models are performed, whose results prove the relatively high robustness of ROWI against the initial model.

13 citations


Cites background from "2-D multiparameter viscoelastic sha..."

  • ...Arrows highlight the boundaries of the targeted trench, which are picked based on the prior information about the location and shape of the trench (Gao et al., 2020; Pan, Schaneng, Steinweg, & Bohlen, 2018)....

    [...]

Journal ArticleDOI
TL;DR: In this article, a preconditioned truncated Newton method (PTN) was applied to shallow-seismic FWI to simultaneously invert for multiparameters near-surface models (P and S-wave velocities, attenuation of P and S waves, and density).
Abstract: 2D full waveform inversion (FWI) of shallow seismic Rayleigh waves has become a powerful method for reconstructing viscoelastic multiparameter models of shallow subsurface with high resolution. The multiparameter reconstruction in FWI is challenging due to the potential presence of crosstalk between different parameters and the unbalanced sensitivity of Rayleigh-wave data with respect to different parameter classes. Accounting for the inverse Hessian using truncated Newton methods based on second-order adjoint methods provides as an effective tool to mitigate crosstalk caused by the coupling between different parameters. In this study, we apply a preconditioned truncated Newton method (PTN) to shallow-seismic FWI to simultaneously invert for multiparameters near-surface models (P- and S-wave velocities, attenuation of P and S waves, and density). We firstly investigate scattered wavefields caused by these parameters to evaluate the coupling between them. Then we investigate the performance of PTN on shallow-seismic FWI of Rayleigh wave for reconstructing all five parameters simultaneously. The application to spatially correlated and uncorrelated models demonstrate that PTN helps to mitigate the crosstalk and improves the resolution of the multiparameter reconstructions, especially for the weak parameters with small sensitivity such as attenuation and density parameters. The comparison with the classical preconditioned conjugate gradient method highlights the improved performance of PTN and thus the benefit of accounting for the information included in the Hessian.

9 citations

Journal ArticleDOI
TL;DR: In this paper , a multi-parameter inversion in the presence of attenuation is used for the reconstruction of the P- and the S- wave velocities and the density models of a synthetic shallow subsurface structure that contains a dipping high-velocity layer near the surface with varying thicknesses.
Abstract: In the presented study, multi-parameter inversion in the presence of attenuation is used for the reconstruction of the P- and the S- wave velocities and the density models of a synthetic shallow subsurface structure that contains a dipping high-velocity layer near the surface with varying thicknesses. The problem of high-velocity layers also complicates selection of an appropriate initial velocity model. The forward problem is solved with the finite difference, and the inverse problem is solved with the preconditioned conjugate gradient. We used also the adjoint wavefield approach for computing the gradient of the misfit function without explicitly build the sensitivity matrix. The proposed method is capable of either minimizing the least-squares norm of the data misfit or use the Born approximation for estimating partial derivative wavefields. It depends on which characteristics of the recorded data—such as amplitude, phase, logarithm of the complex-valued data, envelope in the misfit, or the linearization procedure of the inverse problem—are used. It showed that by a pseudo-viscoelastic time-domain full-waveform inversion, structures below the high-velocity layer can be imaged. However, by inverting attenuation of P- and S- waves simultaneously with the velocities and mass density, better results would be obtained.

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References
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Journal ArticleDOI
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
Abstract: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns. The solution is given in n steps. It is shown that this method is a special case of a very general method which also includes Gaussian elimination. These general algorithms are essentially algorithms for finding an n dimensional ellipsoid. Connections are made with the theory of orthogonal polynomials and continued fractions.

7,598 citations

Journal ArticleDOI
TL;DR: In this paper, the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation, which is based on the generalized least squares criterion, and it can handle errors in the data set and a priori information on the model.
Abstract: The nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation. The method is based on the generalized least‐squares criterion, and it can handle errors in the data set and a priori information on the model. Multiply reflected energy is naturally taken into account, as well as refracted energy or surface waves. The inverse problem can be solved using an iterative algorithm which gives, at each iteration, updated values of bulk modulus, density, and time source function. Each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation (backward in time) of the data residuals. The correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models. This shows, in particular, that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data, and commerc...

3,198 citations


"2-D multiparameter viscoelastic sha..." refers methods in this paper

  • ...FWI was first introduced by Tarantola (1984) and Mora (1987) in time domain with gradient-based inversion....

    [...]

Journal ArticleDOI
TL;DR: This review attempts to illuminate the state of the art of FWI by building accurate starting models with automatic procedures and/or recording low frequencies, and improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.
Abstract: Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

2,981 citations


"2-D multiparameter viscoelastic sha..." refers background in this paper

  • ...Many studies are focused on the viscoacoustic FWI, in which P-wave velocity (VP ) and quality factor (Q) can be inverted recursively or simultaneously (Kamei & Pratt 2013; Malinowski et al. 2011; Virieux & Operto 2009)....

    [...]

Journal ArticleDOI
TL;DR: The adjoint-state method as discussed by the authors is a well-known method in the numerical community for computing the gradient of a functional with respect to the model parameters when this functional depends on those model parameters through state variables, which are solutions of the forward problem.
Abstract: SUMMARY Estimating the model parameters from measured data generally consists of minimizing an error functional. A classic technique to solve a minimization problem is to successively determine the minimum of a series of linearized problems. This formulation requires the Frechet derivatives (the Jacobian matrix), which can be expensive to compute. If the minimization is viewed as a non-linear optimization problem, only the gradient of the error functional is needed. This gradient can be computed without the Frechet derivatives. In the 1970s, the adjoint-state method was developed to efficiently compute the gradient. It is now a well-known method in the numerical community for computing the gradient of a functional with respect to the model parameters when this functional depends on those model parameters through state variables, which are solutions of the forward problem. However, this method is less well understood in the geophysical community. The goal of this paper is to review the adjoint-state method. The idea is to define some adjoint-state variables that are solutions of a linear system. The adjoint-state variables are independent of the model parameter perturbations and in a way gather the perturbations with respect to the state variables. The adjoint-state method is efficient because only one extra linear system needs to be solved. Several applications are presented. When applied to the computation of the derivatives of the ray trajectories, the link with the propagator of the perturbed ray equation is established.

1,514 citations


"2-D multiparameter viscoelastic sha..." refers methods in this paper

  • ...Since the viscoelastic wave equation is not self-adjoint, it is difficult to calculate the gradient by using the adjoint state method with the same numerical solver (Plessix, 2006)....

    [...]

Journal ArticleDOI
TL;DR: The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale as mentioned in this paper, where at long scales there are fewer local minima and those that remain are further apart from each other.
Abstract: 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.

1,403 citations

Frequently Asked Questions (2)
Q1. What are the contributions in "2d multi-parameter viscoelastic shallow- seismic full waveform inversion: reconstruction tests and first field-data application" ?

In this paper, a 2D FWI of a surface wave is used to reconstruct a near-surface model of the seafloor. 

Mitigation of crosstalk between coupled parameters needs to be studied in the future.