Seismic and electromagnetic controlled‐source interferometry in dissipative media

Abstract

A B S T R A C TSeismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an 'interferometry-bydeconvolution' approach which circumvents this assumption. The proposed method applies not only to seismic waves, but to any type of diffusion and/or wave field in a dissipative medium. This opens the way to applying interferometry to controlledsource electromagnetic (CSEM) data. Interferometry-by-deconvolution replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications. We demonstrate this at the hand of numerically modeled CSEM data.

Three-Dimensional Single-Sided Marchenko Inverse Scattering, Data-Driven Focusing, Green’s Function Retrieval, and their Mutual Relations

“…Using a similar derivation as in Ref. [13], we also obtain Z Applying the reflection response R to both sides of Eq. (7) gives, using Eq.…”

Data-driven inversion of GPR surface reflection data for lossless layered media

“…Notice that for the Green's function z i is the receiver depth level and z r is the source depth level. Now we can interpret equations (3) and (4). Equation (3) says that if we convolve in the time domain the downgoing part of the focusing wavefield with the layered earth reflection response, we obtain the upgoing part of focusing wavefield and the Green's function that corresponds to the upgoing wavefield measured at z i that is generated by a source wavefield at z r .…”

“…Equation (3) says that if we convolve in the time domain the downgoing part of the focusing wavefield with the layered earth reflection response, we obtain the upgoing part of focusing wavefield and the Green's function that corresponds to the upgoing wavefield measured at z i that is generated by a source wavefield at z r . Equation (4) says that if we correlate in the time domain the upgoing part of the focusing wavefield with the layered earth reflection response, we obtain the timereverse of the downgoing part of focusing wavefield minus the Green's function that corresponds to the downgoing wavefield measured at z i that is generated by a source wavefield at z r .…”

“…If these are in the subsurface the reflection response of the medium below the receiver (or source) level can be obtained through multidimensional deconvolution of the upgoing wavefield by the downgoing wavefield at this level [4], [5]. To obtain information below this level, model driven methods are being used to first create reflection images and then medium parameters are estimated from the reflection coefficients.…”

Single-sided Marchenko focusing of compressional and shear waves

“…Its definition depends on the chosen normalization of the down-and upgoing compressional and shear waves P ± and S ± . Choosing powerflux normalization for these waves, matrix L(p,z) is defined as [29][30][31] …”