mwapbavg db [-pf pffile -phase phase]
This program is intended to be run after the multiwavelet array processing program (mwap) to produce an combined, broadband estimate of the timing parameters that mwap estimates. That is, mwap uses multiwavelets to produce narrow band estimates of the slowness vector, time residuals relative to the best fit plane wave, polarization measurements, and relative amplitudes. The parameters most related to time (slowness vector and residuals) are the ones handled by mwapbavg. The reason a special program is required is that the slowness vector and residuals are inseparably linked. Any slowness vector deviation from one band estimate to another produces a planar structure to the residual surface that has to be taken into account to produce an unbiased, broadband estimate.
The mwapbavg program uses the following algorithm to produce a band average:
One should be aware that the arrivals computed by this method are likely to differ from those an analyst would produce. They are more like what one would produce by cross correlation, but it is more complicated because the window used is frequency dependent.
Note this algorith adds new entries for the band averages to the extension tables mwslow and mwtstatic. It also updates arrival as noted above.
-pf allows use of an alternative parameter file to mwapbavg.pf.
-phase allows specification of a phase name other than the default of P.
Accesses the following database tables: arrival, assoc, event, origin, mwslow, mwtstatic. The arrival, mwslow, and mwtstatic tables are updated.
The parameter file used by mwapbavg should, in general, be a copy of the parameter file used by mwap. This is the simplest way to guarantee consistency in parameters required by mwapbavg with those used by mwap. Obviously, many of the parameters used by mwap are not used by mwapbavg, but this is the practical way to run this.
mwap(1)
The averaging algorithm used for the slowness vectors is exact provided the covariance is properly estimated by mwap. In contrast the averaging for residuals is an approximation that may tend to underestimate uncertainties. It neglects covariance between the slowness estimates and residuals. Since we equalize all data to a common slowness vector before averaging this seems correct, but doesn't really correctly account for the true error model which involves coupling between slowness vector errors and residuals. I judged it preferable to give a simple numerical estimate than try to characterize the massive covariance mess of the simultaneous problem.
Note that this program does not use any robust methods under an assumption these were taken care of in mwap. The results may be highly suspect if features like signal-to-noise cutoffs were disabled in mwap.