Analysis of the Envelope Waveform of the Initial Part of P-waves and its Application to Quickly Estimating the Epicentral Distance and Magnitude

Abstract

We have found that the envelope waveform of the initial part of P waves changes systematically with magnitude and epicentral distance. In order to represent the envelope waveform quantitatively we introduced a simple function of the form of Bt•exp(-At). Two parameters A and B can easily be determined by the least-squares method. The parameter B defines the slope of the initial part of the P-wave envelope and A is related to the amplitude growth or decay with time. When A is positive, B/(Ae) gives the maximum amplitude where e denotes the base of natural logarithm. This case is typical for small earthquakes, indicating that the initial amplitude increases sharply and decays quickly soon after the P-wave arrival. When A is negative, the amplitude increases exponentially with time. This is a characteristic of large earthquakes. We have found from the analysis of actual seismic data that log B is inversely proportional to the epicentral distance 0 even though the dispersion of data is somewhat large. This relation seems to be independent of earthquake magnitude and thus, by using this relation, we can roughly estimate the epicentral distance immediately after the P-wave arrival. Then, we can estimate the magnitude easily from the formula, similar to the conventional magnitude-amplitude relation, M=a • log Vmax+j • logB +y, where Vmax is the P-wave maximum amplitude within a given short time interval (e.g., 3 seconds) after the P-wave arrival. For M7-and M8-class earthquakes whose rupture duration reaches 10 sec or more, we need to estimate the magnitude repeatedly with time as the amplitude increases. The decrease of the parameter B with distance may be caused by anelasticity of the medium, scattering and geometrical spreading of P waves during propagation.