Development of a modified envelope correlation method based on maximum-likelihood method and application to detecting and locating deep tectonic tremors in western Japan

We develop a modified envelope correlation method for locating deep tectonic tremors and apply it to construct a tremor catalog for western Japan. We redefine the envelope cross-correlation method as a maximum-likelihood method by using the cross-correlation functions as objective functions and then weighting components of the data by the inverse of the error variances. This method is also capable of detecting multiple sources that occur almost simultaneously because they appear as local maxima in our analysis. We employ a nonlinear function, the average of the weighted cross-correlation functions (ACC), to locate the deep tectonic tremor hypocenters. Our optimization method is performed in two steps. We first fix the source depth and use a grid search to find the local ACC maxima, which are the potential event locations. We then use each potential event location as an initial value and apply the gradient method to determine its hypocentral location. Several source locations are sometimes determined in a 5-min time window. We also perform a numerical test using synthetic waveforms to validate our tremor hypocenter estimations. We apply our proposed method to continuous seismograms in western Japan for 12.5-year period, with our new approach detecting 35% more tremors than the envelope correlation method with the outlier control owing to the detection of multiple tremors in a single time window and to the improved tremor hypocenter accuracy yielded by the appropriate weighting scheme. We estimate the spatial resolution, which is defined as the epicentral distance between sources that can be distinguished by the location method, to be similar to 100 km.