A Closed-Form Solution for Earthquake Location in a Homogeneous Half-Space Based on the Bancroft GPS Location Algorithm

The traditional approach to both earthquake and Global Positioning System (GPS) location problems in a homogeneous half-space produces a nonlinear relationship between a set of known positions, seismic stations or GPS satellites, and an unknown point, an earthquake hypocenter or GPS receiver. Linearization, followed by an iterative inversion, is typically used to solve both problems. Although sources and receivers are swapped in the earthquake and GPS location problems, the observation equation is the same for both, due to the principle of reciprocity. Consequently, the mechanical part of the solution of the equations is the same and single-step closed-form solutions for the GPS location problem, such as the Bancroft algorithm, can also be used to solve for earthquake hypocenters in a homogeneous half-space. This article applies the Bancroft algorithm to synthetic and real data for the Charlevoix seismic zone and compares the location of similar to 1200 events estimated with both the Bancroft algorithm and HYPOINVERSE. The Bancroft algorithm shows quantifiable improvements in accuracy compared with traditional methods. We also show how tools commonly used by the GPS community, such as the geometric dilution of precision, can be used to better estimate the precision of the results obtained by a seismic network.