Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Multiple Scattering Theory for Strong Scattering Heterogeneous Elastic Continua with Triaxial Inhomogeneities: Theoretical Fundamentals and Applications

Version 1 : Received: 14 July 2020 / Approved: 15 July 2020 / Online: 15 July 2020 (09:01:02 CEST)

How to cite: He, H. Multiple Scattering Theory for Strong Scattering Heterogeneous Elastic Continua with Triaxial Inhomogeneities: Theoretical Fundamentals and Applications. Preprints 2020, 2020070323 (doi: 10.20944/preprints202007.0323.v1). He, H. Multiple Scattering Theory for Strong Scattering Heterogeneous Elastic Continua with Triaxial Inhomogeneities: Theoretical Fundamentals and Applications. Preprints 2020, 2020070323 (doi: 10.20944/preprints202007.0323.v1).

Abstract

The geometry of mesoscopic inhomogeneities plays an important role in determining the macroscopic propagation behaviors of elastic waves in a heterogeneous medium. Non-equiaxed inhomogeneities can lead to anisotropic wave velocity and attenuation. Developing an accurate scattering theory to describe the quantitative relation between the microstructure features and wave propagation parameters is of fundamental importance for seismology and ultrasonic nondestructive characterization. This work presents a multiple scattering theory for strongly scattering elastic media with general tri-axial heterogeneities. A closed analytical expression of the shape-dependent singularity of the anisotropic Green’s tensor for the homogeneous reference medium is derived by introducing a proper non-orthogonal ellipsoidal coordinate. Renormalized Dyson’s equation for the coherent wave field is then derived with the help of Feynman’s diagram technique and the first-order-smoothing approximation. The exact dispersion curves and the inverse Q-factors of coherent waves in several representative medium models for the heterogeneous lithosphere are calculated numerically. Numerical results for small-scale heterogeneities with the aspect ratio varying from 1 to 7 show satisfactory agreement with those obtained from real earthquakes. The results for velocity dispersion give rise to a novel explanation to the formation mechanism of different seismic phases. The new model has potential applications in seismology and ultrasonic microstructure characterization.

Subject Areas

scattering; heterogeneity; anisotropy; elastic waves; dispersion; attenuation; Mohorovičić discontinuity

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