Avaliação da inversão de Herglotz-Wiechert utilizando tempos de percurso de ondas P em estações da rede sismográfica brasileira

Abstract

The Herglotz-Wiechert method, developed in 1910 by Gustav Herglotz and Emile Wiechert, is based on the analytical solution of the inversion of seismic travel times to determine variations of seismic velocity with depth. The observational data consist of T-Δ curves, where T is travel time in seconds and Δ is epicentral distance in radians. The only limitation of the method is that it is not applicable to low velocity zones. The goal of this work is to develop a computational code that implements the inversion methodology, and to estimate the performance of the method through the measurement and inversion of P-wave travel times for 11 earthquakes recorded at 81 seismic stations of the Brazilian Seismographic Network (RSB). To code the mathematical equations the python language was utilized, while the travel times and epicentral distances were obtained by picking the P-wave arrival times through the Seismic Analysis Code (SAC). The efficiency of the code was assessed through two numerical tests with synthetic “data”, resulting in inverted v(r) functions that accurately match the ak135 global model utilized to generate the synthetic “dataset”. The results obtained from the inversion of real data showed that, for depths up to 1000 km, the inverted v(r) functions are of excellent quality, while for depths between 1000 and 2000 km they present a dispersion that is larger than expected. Thus, it is possible to conclude that the methodology allows to successfully estimate the variation of P-wave velocity with depth within the continental lithosphere and upper mantle of Brazil.