Complexity penalized hydraulic fracture localization and moment tensor estimation under limited model information

TL;DR

This paper introduces a robust micro-seismic localization method that uses group sparse penalization, requiring only a velocity model, and improves moment tensor inversion with regularization techniques, effective even with limited array geometry.

Contribution

The paper presents a novel seismic localization technique based on group sparsity that is robust to focal mechanisms and limited array geometries, requiring only a velocity model.

Findings

The method accurately localizes seismic events on synthetic data.

Tikhonov regularization and truncated SVD improve moment tensor recovery.

Error bounds are provided for localization and tensor estimation.

Abstract

In this paper we present a novel technique for micro-seismic localization using a group sparse penalization that is robust to the focal mechanism of the source and requires only a velocity model of the stratigraphy rather than a full Green's function model of the earth's response. In this technique we construct a set of perfect delta detector responses, one for each detector in the array, to a seismic event at a given location and impose a group sparsity across the array. This scheme is independent of the moment tensor and exploits the time compactness of the incident seismic signal. Furthermore we present a method for improving the inversion of the moment tensor and Green's function when the geometry of seismic array is limited. In particular we demonstrate that both Tikhonov regularization and truncated SVD can improve the recovery of the moment tensor and be robust to noise. We evaluate our algorithm on synthetic data and present error bounds for both estimation of the moment tensor as well as localization. Furthermore we discuss the estimated moment tensor accuracy as a function of both array geometry and fault orientation.