method for determining this RMS value used by HYPOSAT is extensively documented

Method for determining this rms value used by hyposat

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method for determining this RMS value used by HYPOSAT is extensively documented (Schweitzer, 1997). The method used by the LEVR algorithm is summarized as follows. A. The Point of Closest Approach. Seismic theory for signals with a linear source moving at supersonic speed through the earth implies that the first arrival at a given seismic station will come, to a good approximation, from the Point of Closest Approach (POCA) of the source to the station. The POCA is the intersection of the trajectory with a perpendicular from the station to the line defined by the entry and exit points of the linear source, as diagrammed in Figure 1. The first arrival signal source is offset slightly from this intersection (POCA) by the angle of the MACH cone produced by the supersonic transit. In practice, the effect of the cone angle is negligible at the expected velocities and can be ignored. The galactic viral velocity for trapped materials is about 250 km/s. In cases where the point of closest approach lies outside of the Earth, the first arrival signal source is the closer of the entry or the exit point. Referring to Figure 1, the arrival time at any station is determined as the sum of the source entry time, the time-of-flight from entry to POCA for that station, and the seismic travel time from the POCA to the station. The model assumes a spherical earth. Two additional second order corrections were manually included in the final fitting of the event of November 1993: an elevation correction for the individual seismic stations, and a source correction for signals originating in oceanic rather than continental crust. B. The Test of Hypotheses The test for fit to a linear source consists of constructing a hypothetical source as defined by an entry, exit, and speed. The POCA for each station in the event window is calculated and the POCA-to-station travel times are obtained. A range of speeds from 100 to 800 km/sec in 50 km/sec steps is used to calculate the time-of-flight, and a set of predicted arrival times is determined. Each station is then taken in turn as the reference station, and its arrival time subtracted 11 11
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from the arrival times of all the others to produce an array of travel time differences, t. A similar t array is created for the observed arrivals using the same reference stations, and the two arrays are differenced to produce an array of residuals. Next the residuals are sorted and the lowest N residuals are used to calculate the total RMS error, where N is an input parameter 7. The residual, source geometry, velocity, and reference station are returned for the linear source with the lowest RMS. LEVR repeats this process for all "acceptable" linear sources with entry and exit points located on a global 0.1x0.1 degree grid. (A linear source was not considered "acceptable" for a given geometry for a set of reports if the signal received by a station from its POCA would require passage of the signal through the Earth's core, i.e. if there is core shadowing.)
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