23.3 HASH

NOTE: internally in SEISAN, the program is called HASH_SEISAN to avoid conflict with bash command hash.

This program [Hardebeck and Shearer, 2002,2003] determines fault plane solutions using P-polarities and amplitude ratios as input, just like the FOCMEC program. The P-amplitude used by the program is the theroretical radial amplitude and that was obtained by reading [Hardebeck and Shearer, 2003] \bgroup\color{black}$ A_P=\sqrt(A_r^2+A_z^2)$\egroup and the S-amplitude \bgroup\color{black}$ A_S=\sqrt(A_{sv}^2+A_{sh}^2)$\egroup where A is amplitude, r is radial (on rotated seismogram) and z is vertical. The S used was the maximum S on any of the rotated components or Z. This was then compared to the theoretical amplitude \bgroup\color{black}$ A_S=\sqrt(A_{sv}^2+A_{sh}^2)$\egroup where sv is SV, and sh is SH. This approximation apparently worked well. The free surface and attenuation correction is not built in, but was replaced by a fixed factor per station, which had to be determined independently. In order to simplify the input, the free surface and attenuation corrected amplitude ratios from FOCMEC are used as input for HASH. The program was modified to use only SH and by using the free surface corrected P on the Z-component, the true P-amplitude is used. Thus only one amplitude ratio is used for each station (SH to P). HASH returns solutions with less than a given number of polarity errors and average amplitude errors less than a given limit. If no solutions are found, error limits are increased and normally many solutions are returned. Using this, an estimate of the best solution is made and likely errors calculated. The advantage with HASH is that it finds one or a few best solutions, while for FOCMEC the user must select one among many. Also HASH will not completely change the solution by one wrong amplitude ratio, since the average of the amplitude errors is used as selection criteria and not a single amplitude. FOCMEC does not give any estimate of the errors in the solution. HASH calculates an estimated error; however that requires an input where each event has been located with e.g. 10 different likely input models and all data is used as input in order to get estimate of fault plane solution uncertainties generated from the model. This was not done in the SEISAN implementation so only the error estimated from the spread in solutions is used. This might lead to smaller error estimates as compared to the original HASH implementation. The SEISAN HASH implementation is a simplified implementation compared to the original HASH with many parameters hardwired, see hash_seisan.for for implementation details and changes. Like FPFIT, the F-fit function is calculated (called weighted fraction of polarity misfits) and similarly the station distribution ratio (see FPFIT). Both values are given in S-file as well as the average amplitude error. For more information, see the HASH manual hash.pdf and FPFIT manual fpfit.pdf in INF. The software is found at http://earthquake.usgs.gov/research/software/index.php. HASH does not estimate errors in strike, dip and rake but errors in fault plane and auxiliary plane (degrees). HASH, like FOCMEC uses the Vp Vs velocity ratio to calculate amplitudes. In versions of SEISAN before 10.6, this was hardwired to 1.74. Now it is read from the input file focmec.dat also used with FOCMEC. This ratio is in turn read from STATION0.HYP.

Peter Voss : Tue Jun 8 13:38:42 UTC 2021