23.3 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]
and the S-amplitude
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
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).