Application of Ringdal's Method to Unbiased Measurement of the Ms-mb Relationship
Technical rept. no. 15
TEXAS INSTRUMENTS INC DALLAS EQUIPMENT GROUP
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Ringdals maximum likelihood method of removing magnitude bias was tested by removing the apparent bias of surface wave magnitude estimates. Bias removal was convincingly demonstrated by comparing maximum likelihood estimates of M sub s obtained by a single sensor to those obtained by an array at the Alaskan Long Period Array ALPA site. Since the beamformed array has a lower detection threshold than the single-sensor reference site, it can serve as the standard by which to judge whether positive magnitude bias has been removed from the reference site surface wave magnitude estimates. The results of this test indicate that below the 90 percent detection threshold of the reference site, positive magnitude bias becomes a significant factor in surface wave magnitude estimates. Comparison with beamformed array data indicates that application of Ringdals method accurately removes this bias down to approximately the reference site 25 percent detection threshold. Below this point, the method over-corrects the magnitude estimates, resulting in abnormally low values.
- Seismic Detection and Detectors