Method for Estimating the Tripartite Array Back-Azimuth Error Caused by the Far-Field Approximation

Abstract

Abstract In recent decades, tripartite arrays (i.e., three-element array) have become an important tool for various seismoacoustic applications, mainly due to their superior back-azimuth estimation. However, the back azimuth is estimated assuming the far-field approximation. Lately, tripartite arrays have been used to monitor microseismicity and aftershocks at distances comparable with the size of the array in which the far-field assumption might not hold. In this work, we determined the validity of the far-field assumption by analyzing the plane-wave errors, that is, the errors of the back azimuth and slowness computations caused by the plane-wave assumption. Computational formulas for estimating the absolute errors, due to the plane-wave assumption, were developed. Several case studies demonstrated that the plane-wave errors are not theoretical issues only and taking them into account can improve the results of field measurements. Proposed practical methods to account for plane-wave errors can improve the performance of arrays aimed to measure low magnitude events such as in induced microseismicity monitoring or on-site inspection.