Finite-difference time dispersion transforms for wave propagation

Wang, Meixia; Xu, Sheng

doi:10.1190/geo2015-0059.1

Cited by 52 publications

(21 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This number challenges currently available computational resources and even advanced time stepping schemes (e.g. Bogey & Bailly 2004;Dumbser et al 2007;Wang & Xu 2015).…”

Section: Computabilitymentioning

confidence: 99%

Generalized interferometry – I: theory for interstation correlations

Fichtner¹,

Stehly

Ermert³

et al. 2016

Geophys. J. Int.

View full text Add to dashboard Cite

We develop a general theory for interferometry by correlation that (i) properly accounts for heterogeneously distributed sources of continuous or transient nature, (ii) fully incorporates any type of linear and nonlinear processing, such as one-bit normalization, spectral whitening and phase-weighted stacking, (iii) operates for any type of medium, including 3-D elastic, heterogeneous and attenuating media, (iv) enables the exploitation of complete correlation waveforms, including seemingly unphysical arrivals, and (v) unifies the earthquake-based two-station method and ambient noise correlations. Our central theme is not to equate interferometry with Green function retrieval, and to extract information directly from processed interstation correlations, regardless of their relation to the Green function. We demonstrate that processing transforms the actual wavefield sources and actual wave propagation physics into effective sources and effective wave propagation. This transformation is uniquely determined by the processing applied to the observed data, and can be easily computed. The effective forward model, that links effective sources and propagation to synthetic interstation correlations, may not be perfect. A forward modelling error, induced by processing, describes the extent to which processed correlations can actually be interpreted as proper correlations, that is, as resulting from some effective source and some effective wave propagation. The magnitude of the forward modelling error is controlled by the processing scheme and the temporal variability of the sources. Applying adjoint techniques to the effective forward model, we derive finite-frequency Fréchet kernels for the sources of the wavefield and Earth structure, that should be inverted jointly. The structure kernels depend on the sources of the wavefield and the processing scheme applied to the raw data. Therefore, both must be taken into account correctly in order to make accurate inferences on Earth structure. Not making any restrictive assumptions on the nature of the wavefield sources, our theory can be applied to earthquake and ambient noise data, either separately or combined. This allows us (i) to locate earthquakes using interstation correlations and without knowledge of the origin time, (ii) to unify the earthquake-based two-station method and noise correlations without the need to exclude either of the two data types, and (iii) to eliminate the requirement to remove earthquake signals from noise recordings prior to the computation of correlation functions. In addition to the basic theory for acoustic wavefields, we present numerical examples for 2-D media, an extension to the most general viscoelastic case, and a method for the design of optimal processing schemes that eliminate the forward modelling error completely. This work is intended to provide a comprehensive theoretical foundation of full-waveform interferometry by correlation, and to suggest improvements to current passive monitoring methods.

show abstract

“…This number challenges currently available computational resources and even advanced time stepping schemes (e.g. Bogey & Bailly 2004;Dumbser et al 2007;Wang & Xu 2015).…”

Section: Computabilitymentioning

confidence: 99%

Generalized interferometry – I: theory for interstation correlations

Fichtner¹,

Stehly

Ermert³

et al. 2016

Geophys. J. Int.

View full text Add to dashboard Cite

show abstract

“…Here a 1 ms step length is used for illustration. The dimensionless parameter θ ′ runs from 0.0 to 12000.0 along the abscissa.The dimensionless parameter θ runs from 0.0 to 12000.0 along the ordinate Wang and Xu (2015) and also proposed to perform the dispersion correction by the following procedure on the numerically simulated field,σ (z,t|z s ),…”

Section: Second-order Correction Proceduresmentioning

confidence: 99%

“…Note that if the ratio of the source waveforms in equation 11 is unity, then the transform proposed by Wang and Xu (2015) and is applicable. To achieve a source waveform ratio equal to unity for all frequencies I postulate a source time function for the numerical simulation, S(t), related to the desired source function, S(t), by,…”

Section: Second-order Correction Proceduresmentioning

confidence: 99%

Second-order time integration of the wave equation with dispersion correction procedures

Mittet

2018

SEG Technical Program Expanded Abstracts 2018

View full text Add to dashboard Cite

Second-order time integration of the wave equation is numerically efficient with time steps close to the limit set by the stability criterion. However, the dispersion errors over realistic propagation distances are unacceptable with time steps in this range. A common procedure is to perform a postpropagation correction on the numerically simulated field. The post-propagation correction does not always provide a sufficiently accurate result. The reason is explained as a lacking source correction term. The proper source correction procedure is identified. Dispersion free results, using secondorder time integration of the wave equation, can be achieved by applying a time-domain bivariate pre-propagation filter to all source time functions followed by a time-domain bivariate post-propagation filter to the simulated field at all recording positions. The bivariate pre-propagation filter and the bivariate post-propagation filter are valid for any reasonable simulation time step. The two filters can be calculated once since they are independent of the simulation time step and they can be applied with any modeling scheme that uses second order time integration.

show abstract

“…Stork (2013) demonstrate that the time-dispersion error can be removed by time-varying filters and interpolation after the wave modelling. Based on this idea, Wang and Xu (2015) propose that the forward time dispersion transform (FTDT) can predict the time-dispersion error, and the inverse time dispersion transform (ITDT) can eliminate the time-dispersion error from synthetic traces. Koene et al (2018) mentions that the obtained traces should not only be filtered by the ITDT method as proposed by Wang and Xu (2015), but also the source time function needs to be filtered by the FTDT method before the simulation, which has been validated in the numerical methods including FD, pseudo-spectral (PS) method and SEM.…”

Section: Introductionmentioning

confidence: 99%

Removing the Courant-Friedrichs-Lewy stability criterion of the explicit time-domain very high degree spectral-element method with eigenvalue perturbation

et al. 2021

View full text Add to dashboard Cite

The explicit time-domain spectral-element method (SEM) for synthesizing seismograms hasgained tremendous credibility within the seismological community at all scales. Althoughthe recent introduction of non-periodic homogenization has addressed the spatial meshing difficulty of the mechanical discontinuities, the Courant-Friedrichs-Lewy (CFL) stability criterionstrictly constrains the maximum time step, which still puts a great burden on the numericalsimulation. In the explicit time-domain SEM, the source of instability of using a time stepbeyond the stability criterion is that some unstable eigenvalues of the updated matrix are largerthan what can be accurately simulated. We succeed in removing the CFL stability condition inthe explicit time-domain SEM by combining the forward time dispersion-transform method,the eigenvalue perturbation, and the inverse time dispersion-transform method. Our theoretical analyses and numerical experiments both in the homogeneous, moderate and strong heterogeneous models, show that this combination can precisely simulate waveforms with timesteps dozens of the CFL limit even towards the Nyquist limit especially for the efficient veryhigh degree SEM, which abundantly saves the iteration times without suffering from the time-dispersion error. It demonstrates a potential application prospect in some situations such as thefull waveform inversion which requires multiple numerical simulations for the same model.

show abstract

Finite-difference time dispersion transforms for wave propagation

Cited by 52 publications

References 36 publications

Generalized interferometry – I: theory for interstation correlations

Generalized interferometry – I: theory for interstation correlations

Second-order time integration of the wave equation with dispersion correction procedures

Removing the Courant-Friedrichs-Lewy stability criterion of the explicit time-domain very high degree spectral-element method with eigenvalue perturbation

Contact Info

Product

Resources

About