Scattering of seismic waves by three-dimensional large-scale hill topography simulated by a fast parallel IBEM

To solve seismic wave scattering by a large-scale three-dimensional(3-D) hill topography, a fast parallel indirect boundary element method(IBEM) is developed by proposing a new construction method for the wave field, modifying the generalized minimum residual(GMRES) algorithm and constructing an Open MP plus MPI parallel model. The validations of accuracy and efficiency show that this method can solve 3-D seismic response of a large-scale hill topography for broadband waves, and overcome the weakness of large storage and low efficiency of the traditional IBEM. Based on this new algorithm architecture, taking the broadband scattering of plane SV waves by a large-scale Gaussian-shaped hill of thousands-meters height as an example, the influence of several important parameters is investigated, including the incident frequency, the incident angle and the height-width and length-width ratio of the hill. The numerical results illustrate that the amplification effect on the ground motion by a near-hemispherical hill is more significant than the narrow hill. For low-frequency waves, the scattering effect of the higher hill is more pronounced, and there is only a single peak near the top of the hill. However, for high-frequency waves, rapid spatial variation of displacement amplitude appears on the hill surface.

Seismic isolation effect of lined circular tunnels with damping treatments

The Havriliak-Negami model for dynamic viscoelastic material behavior and Biot＇s theory of poroelasticity are employed to develop an exact solution for three-dimensional scattering effect of harmonic plane P-SV waves from a circular cavity lined with a multilayered fluid-filled shell of infinite length containing viscoelastic damping materials and embedded within a fluid-saturated permeable surrounding soil medium. The analytical results are illustrated with numerical examples where the effects of liner/coating structural arrangement, viscoelastic material properties, liner-soil interface bonding condition, seismic excitation frequency, and angle of incidence on the induced dynamic stress concentrations are evaluated and discussed to obtain representative values of the parameters that characterize the system. It is demonstrated that incorporating viscoelastic damping materials with a low shear modulus in the constrained layer configuration is an efficient means of enhancing the overall seismic isolation performance, especially for near-normally incident seismic shear waves where the amplitudes of induced dynamic stresses may be reduced by up to one-third of those without isolation in a relatively wide frequency range. Some additional cases are considered and good agreements with solutions available in the literature are obtained.

Bayesian Markov chain Monte Carlo inversion for anisotropy of PP-and PS-wave in weakly anisotropic and heterogeneous media

A single set of vertically aligned cracks embedded in a purely isotropic background may be con- sidered as a long-wavelength effective transversely iso- tropy （HTI） medium with a horizontal symmetry axis. The crack-induced HTI anisotropy can be characterized by the weakly anisotropic parameters introduced by Thomsen. The seismic scattering theory can be utilized for the inversion for the anisotropic parameters in weakly aniso- tropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derived the linearized PP- and PS-wave reflection coefficients in terms of P- and S-wave impedances, density as well as three anisotropic parameters in HTI media. Then, we proposed a novel Bayesian Mar- kov chain Monte Carlo inversion method of PP- and PS- wave for six elastic and anisotropic parameters directly. Tests on synthetic azimuthal seismic data contaminated by random errors demonstrated that this method appears more accurate, anti-noise and stable owing to the usage of the constrained PS-wave compared with the standards inver- sion scheme taking only the PP-wave into account.

Seismic-Wave Scattering,Imaging,and Inversion

Ru-Shan Wu has made seminal contributions in many research areas in geophysics,such as seismic-wave propagation,scattering,imaging,and inversion.We highlight some of his research in holography imaging,diffraction tomography,seismic-wave scattering and its applications to studying Earth’s heterogeneity,oneway wave propagation and one-return wave modeling,beamlet and dreamlet applications,strong non-linear full-waveform inversion,and direct envelop inversion.

Target-Oriented Inversion of Time-Lapse Seismic Waveform Data

Full waveform inversion of time-lapse seismic data can be used as a means of estimating the reservoir changes due to the production.Since the repeated computa-tions for the monitor surveys lead to a large computational cost,time-lapse full wave-form inversion is still considered to be a challenging task.To address this problem,we present an efficient target-oriented inversion scheme for time-lapse seismic data using an integral equation formulation with Gaussian beam based Green’s function approach.The proposed time-lapse approach allows one to perform a local inversion within a small region of interest(e.g.a reservoir under production)for the monitor survey.We have verified that the T-matrix approach is indeed naturally target-oriented,which was mentioned by Jakobsen and Ursin[24]and allows one to reduce the compu-tational cost of time-lapse inversion by focusing the inversion on the target-area only.This method is based on a new version of the distorted Born iterative T-matrix inverse scattering method.The Gaussian beam and T-matrix are used in this approach to perform the wavefield computation for the time-lapse inversion in the baseline model from the survey surface to the target region.We have provided target-oriented inversion results of the synthetic time-lapse waveform data,which shows that the proposed scheme reduces the computational cost significantly.

Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media

We generalize the existing distorted Born iterative T-matrix(DBIT)method to seismic full-waveform inversion(FWI)based on the scalar wave equation,so that it can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass densities and elastic stiffness tensors.The elastodynamic wave equation for an ar-bitrary anisotropic heterogeneous medium is represented by an integral equation of the Lippmann-Schwinger type,with a 9-dimensional wave state(displacement-strain)vector.We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory.This allows for domain decomposition and novel variational estimates.The tensorial nonlinear inverse scat-tering problem is solved iteratively by using an expression for the Fŕechet derivatives of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green’s functions and wave state vectors that are updated after each iteration.Since the generalized DBIT method is consistent with the Gauss-Newton method,it incorporates approximate Hessian information that is essential for the reduction of multi-parameter cross-talk effects.The DBIT method is implemented efficiently using a variant of the Levenberg-Marquard method,with adaptive selection of the regularization parameter after each iteration.In a series of numerical experiments based on synthetic waveform data for transversely isotropic media with vertical symmetry axes,we obtained a very good match between the true and inverted models when using the traditional Voigt parameterization.This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the use of suitable regularization methods.Since the generalized DBIT method for FWI in anisotropic elastic media is naturally target-oriented,it may be particularly suitable for applications to seismic reservoir characterization and monitoring.However,the theory and method presented here is general.