Isolating Source Information in mb and Ms with Model-Based Corrections: New mb Versus Ms Discriminant Formulations

摘要

Path and signal processing corrections made to amplitudes give magnitudes mb and Ms, that in principle, have only source information. We propose the addition of a model-based magnitude prediction as a correction term, that is, a source correction in addition to path and signal processing corrections under the null (HO) hypothesis that a seismic event is a single- point fully contained explosion. This additional correction removes explosion source information from the Ms versus mb discriminant with the remaining source information represented as a constant. There are effects such as depth, focal mechanism, and local material properties that cannot easily be determined and mathematically included in amplitude corrections. We develop a mathematical model to capture these near source effects as random (unknown) giving an error partition of two sources: model inadequacy and station noise. This mathematical model is the basis for two new Ms versus mb discriminant formulations. Both methods are designed to utilize advances in source physics theory by using new source models to predict (correct) observed surface wave magnitudes. The network average discriminant formulation includes source model error and magnitude correlation in the standard error (SE) of the discriminant, effectively placing a lower bound on the discriminant SE and accounting for scaling between Ms and mb. This new property of the Ms versus mb discriminant correctly reduces the SE only through network averaging of magnitudes. A second discriminant formulation derived from order statistics theory is potentially robust to station coverage for an event by basing discrimination on the maximum observed station Ms value.