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This work addresses the evaluation of the seismic wave field in a graded half-plane with free-surface and/or sub-surface relief subjected to shear horizontally (SH)-polarized wave, radiating from an embedded seismic source. The considered boundary value problem is transformed into a system of boundary integral equations (BIEs) along the boundaries of the free-surface and of any sub-surface relief, using an analytically derived frequency-dependent Green’s function for a quadratically inhomogeneous in depth half-plane. The numerical solution yields synthetic seismic signals at any point of the half-plane in both frequency and time domain following application of Fast Fourier Transform (FFT). Finally, in the companion paper, the verification and numerical simulation studies demonstrate the accuracy and efficiency of the present computational approach. The proposed BIE tool possesses the potential to reveal the sensitivity of the seismic signal to the type and properties of the seismic source, to the existence and type of the material gradient and to the lateral inhomogeneity, due to the free-surface and/or sub-surface relief peculiarities.

journal of theoretical and applied mechanics

Wave Propagation Due to an Embedded Seismic Source in a Graded Half-Plane with Relief Peculiarities Part I: Mechanical Model and Computational Technique