Improving Regional Earthquake Locations Using a Modified G Matrix and Fuzzy Logic

A simple procedure is presented to resolve locations of regional earthquakes with poor quality of recorded phases and/or a very large gap in seismograph recording geometry. In solving earthquake locations, we use a modified G matrix containing S - P time intervals and P - P and S - S time differences between stations and a forward method. Unlike the regular G matrix, which consists of three spatial parameters ( x, y, z ) and one timing parameter ( t ), the modified G matrix contains only two spatial parameters ( x, y ) and a fixed depth ( z ). The origin time parameter is eliminated by using only relative time intervals. In the new G matrix, two base equations instead of one are used. The S - P time intervals constrain epicentral distance, and P - P and S - S time differences constrain the distribution of azimuth. In searching for epicenters, we first divide the modified G matrix based on individual time intervals then map deviations between theoretical and observed time intervals into logic space using the fuzzy logic technique. Resolutions of earthquake locations are enhanced in the logic space by applying logic operations among individual G matrices. Final locations are derived by searching for a center of gravity in the output matrix. Test results indicate that this method effectively avoids the local minimum problem encountered by generalized inverse methods when data are recorded by small aperture arrays from earthquakes outside the arrays or when large errors occur in phase readings.