Parsimonious slope tomography: a variable-projection method for consistent event relocation and subsurface parameters inversion.

Abstract:

Locating seismic events in the subsurface has been of in interest at different scale ranging from microseismics monitoring to global seismology. The problem is far from trivial due to the unknown origin time and subsurface parameters heterogeneity, mainly velocity. Inverting for the location, the velocity and the origin time has been done through different tomographic strategies to overcome the leakage between parameters encountered in relocation strategies based on time-reversal and migration. We present a strategy based on parsimonious slope tomography to invert for all parameters with a proper handling of the hypocenter-velocity coupling.

In brief, the location can be obtained for each event in a given model by a one-to-one mapping of two kinematic attributes (traveltime and slope at the station which is becoming more accessible due to deployment of dense arrays and developments around sparsity-constrained attributes inversion and rotational seismology) to the coordinates of the event. For each station, the position found by migration is kinematically consistent with the given model while the aim is to collapse all the mapped locations at one position by improving the accuracy of the velocity model. We show how, through a variable projection, the optimization problem boils down to a physically consistent form where the location estimation is projected into the subsurface parameter problem. In turn, the latter serves only as a proxy to collapse the positions migrated from each station at the true event position.

We develop our framework using eikonal solvers and the adjoint-state method. The presented approach handles tilted transverse isotropy and can be easily extended to three dimensions by incorporating the backazimuth. We validate our proof of concept on a toy test, we assess the trade-off between the subsurface parameters and the introduced origin time correction parameter. We benchmark our method against the Marmousi model in an exploration experimental setup.