Discrimination of fault planes from auxiliary planes based on simultaneous determination of stress tensor and a large number of fault plane solutions

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It is well known that there is a large difference in focal mechanism solutions of events even if they occur within a certain small area. Considering earthquake‐generating stress to be uniform in a studied area, we developed a new method for simultaneously determining the stress tensor and the orientation of fault planes for many events by the use of polarity data of P waves. First, the number of inconsistent stations is calculated for various values of three parameters in the focal mechanism solution, with intervals of 10°. This calculation is made for all the events used. Then, four parameters defining the stress tensor are determined by a grid search using the data calculated above with the assumption that the slip direction in the fault plane should be parallel to the direction where the shear stress on the plane becomes maximum. A numerical test is made by applying the present method to an artificial data set composed of 25 events with 25 × 25 readings. It is found that a stable solution of the stress tensor is determined by the inversion and about 60% of fault planes are distinguished from auxiliary planes. There are no events whose auxiliary planes are incorrectly determined as fault planes. This method is used to estimate the earthquake‐generating stress in the aftershock area of the 1984 western Nagano prefecture earthquake, central Japan. The results obtained show that the maximum principal stress is horizontal in the direction of N80°W‐S80°E. There are strike‐slip events having fault planes almost perpendicular to the fault plane of the main shock.