BEM+Born series modeling schemes for wave propagation and their convergence analysis

This paper formulates two different boundary-element＋Born series schemes for wave propagation simulation in multilayered media by incorporating a Born series and boundary integral equations. The first scheme directly decomposes the resulting boundary integral equation matrix into the self-interaction operators associated with each boundary itself and the extrapolation operators expressing cross-interactions between different boundaries in a subregion. For the second scheme, the matrix dimension is firstly reduced to a half by the elimination of the traction field in the equations. The resulting new matrix can also be split into the self-interaction matrices associated each subregion itself and the extrapolation matrices interpreting cross-interactions between different subregions in a whole model. Both the numerical schemes avoid the inversion of the relatively much larger boundary integral equation matrix of a full-waveform BE method and hence save computing time and memory greatly. The two schemes are validated by calculating synthetic seismograms for a homogeneous layered model, compared with the full-waveform BE numerical solution. Numerical experiments indicate that both the BEM＋Born series modeling schemes are valid and effective. The tests also confirm that the second modeling scheme has a faster convergence in comparison with the first one.

Forward Scattering Series for 2-Parameter Acoustic Media:Analysis and Implications to the Inverse Scattering Task Specific Subseries

We study the 2-parameter acoustic Born series for an actual medium with constant velocity and a density distribution.Using a homogeneous background we define a perturbation,the difference between actual and reference medium(we use background and reference as synonyms),which exhibits an anisotropic behavior due to the density distribution.For an actual medium with a constant velocity,the reference velocity can be selected so that the waves in the actual medium travel with the same speed as the waves in the background medium.Scattering theory decomposes the actual wave field into an infinite series where each term contains the perturbation and the propagators in the background medium.Hence,in this formalism,all propagations occur in the background medium and the actual medium is included only through the perturbations which scatter the propagating waves.The density-only perturbation has an isotropic and an anisotropic component.The anisotropic component is dependent on the incident direction of the propagating waves and behaves as a purposeful perturbation in the sense that it annihilates the part of the Born series that acts to correct the time to build the actual wave field,an unnecessary activity when the reference velocity is equal to the one in the actual medium.This means that the forward series is not attempting to correct for an issue that does not exist.We define the purposeful perturbation concept as the intrinsic knowledge of preciselywhat a given term is designed to accomplish.This is a remarkable behavior for a formalism that predicts the scatteredwave fieldwith an infinite series.At each order of approximation the output of the series is consistent with the fact that the time is correct because the velocity is always constant.In the density-only perturbation,the forward series only seeks to predict the correct amplitudes.Finally,we extend the analysis to a wave propagating in a medium where both density and velocity change.By selecting a convenient set of parameters,we find a conceptual framework for the multiparameter Born series.This framework provides an insightful analysis that can be mapped and applied to the concepts and algorithms of the inverse scattering series.