Simulation of Interferometric Seismoelectric Green’s Function Recovery

Abstract

A recent novel technique known as seismic interferometry makes use of seismic ‘noise’ to reconstruct a Green’s function between two receivers by crosscorrelation. This technique can be applied for example in permanent subsurface monitoring using passive seismics or the creation of virtual sources on positions where only recordings were made. The aim of this thesis is to derive and understand equations for seismoelectric interferometry. The first part of this thesis focusses on a the calculation of SH-TE seismoelectrical responses in a 2D horizontally stratified earth. We decompose the two-way wave equation for SH-TE waves into upgoing and downgoing waves which we relate through a reflectivity formulation. The reflectivity formulation is based upon reflection matrices only, even though we can simulate both reflection and transmission experiments. We solve the SH-TE seismoelectric system in a 1D homogeneous world. In the second part of this thesis we derive interferometric Green’s fucntion representations from reciprocity theorems that relate two different states in one domain. Interferometric Green’s function representations express the Green’s function between two receivers as a function of crosscorrelations of responses of sources throughout a domain and on it’s boundary. We cast the seismoelectric system in a general diffusion, flow and wave equation and define a Green’s matrix for all different field and source types. Using this formulation we derive a source-receiver reciprocity relation for the Green’s matrix from the convolution type reciprocity theorem. The correlation type reciprocity theorem for the Green’s matrix is modified using source-receiver reciprocity to obtain the interferometric Green’s function representation. We study the SH-TE seismoelectrical interferometric representation 1D and 2D in homogeneous media. A seismoelectric interferometric representation was written to recover the causal response of the particle velocity at position B due to a electrical current source at position A, as a function of cross correlations of electric field recordings at A and particle velocity recordings at B. Provided there exists a dense coverage of sources in the domain and on it’s boundary, the representation was validated in both 1D and 2D. Approximations to the interferometric representation are investigated by studying the contributions of parts of the domain and boundary integrals. It was found that a dominant spurious event resides in the separate contributions of the domain and boundary integrals, that destructively interferes when both contributions are combined. The role of different source types in the interferometric representation was studied. In a homogeneous medium the measured events have propagated either as an electromagnetic wave or as a shear wave. The dominant contribution to the reconstruction of an electromagnetic event is by electromagnetic sources. Similarly, can the reconstructed shear wave event be attributed mainly due to seismic sources. In a medium with low electromagnetic and shear wave losses we could ignore the domain integral, this will result in amplitude errors and we will suffer from spurious events.