3D virtual seismology

TL;DR

This paper introduces a novel 3D single-sided Green's function representation for virtual seismology, enabling subsurface imaging without boundary receivers, demonstrated through numerical data with improved accuracy over classical methods.

Contribution

The authors develop a 3D single-sided homogeneous Green's function approach that does not require boundary receivers, improving virtual source imaging in seismology.

Findings

Successful retrieval of virtual responses with isotropic and double-couple sources

Application to virtual rupture response with superposed sources

Effective monitoring of wavefield caused by numerical rupture

Abstract

We create virtual sources and receivers in a 3D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at the Earth's surface, a macro velocity model and the Marchenko method. The homogeneous Green's function is a Green's function superposed with its time-reversal. Unlike the classical homogeneous Green's function representation, our approach requires no receivers on an enclosing boundary, however, it does require the source signal to be symmetric in time. We demonstrate that in 3D, the single-sided representation is an improvement over the classical representation by applying the representations to numerical data. We retrieve responses to virtual point sources with an isotropic and with a double-couple radiation pattern and compare the results to a directly modeled reference result. We also demonstrate the application of the single-sided representation for retrieving the response to a virtual rupture that consists of a superposition of double-couple point sources. This is achieved by obtaining the homogeneous Green's function for each source separately, before they are transformed to the causal Green's function, time-shifted and superposed. The single-sided representation is also used to monitor the complete wavefield that is caused by a numerically modeled rupture. However, the source signal of an actual rupture is not symmetric in time and the single-sided represenation can therefore only be used to obtain the causal Green's function. This approach leaves artifacts in the final result, however, these artifacts are limited in space and time.