Methods for Large Scale Hydraulic Fracture Monitoring

TL;DR

This paper introduces efficient methods for large-scale hydraulic fracture monitoring by estimating micro-seismic event locations and moment tensors using a novel joint-complexity measure and advanced optimization algorithms, enabling robust and assumption-free analysis.

Contribution

The paper presents a new joint-complexity measure based on nuclear norms and a hybrid optimization algorithm for fast, robust seismic source estimation without assuming source signature.

Findings

Effective estimation of seismic moment tensors and locations.

Significant computational savings with the proposed algorithms.

Robust performance over large search volumes.

Abstract

In this paper we propose computationally efficient and robust methods for estimating the moment tensor and location of micro-seismic event(s) for large search volumes. Our contribution is two-fold. First, we propose a novel joint-complexity measure, namely the sum of nuclear norms which while imposing sparsity on the number of fractures (locations) over a large spatial volume, also captures the rank-1 nature of the induced wavefield pattern. This wavefield pattern is modeled as the outer-product of the source signature with the amplitude pattern across the receivers from a seismic source. A rank-1 factorization of the estimated wavefield pattern at each location can therefore be used to estimate the seismic moment tensor using the knowledge of the array geometry. In contrast to existing work this approach allows us to drop any other assumption on the source signature. Second, we exploit the recently proposed first-order incremental projection algorithms for a fast and efficient implementation of the resulting optimization problem and develop a hybrid stochastic & deterministic algorithm which results in significant computational savings.