The effects of radiation patterns on magnitude estimates

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Abstract
With a double-couple force system as a model of an earthquake source mechanism, the radiation pattern theory of Ben-Menahem is employed to show that the far-field measurement of its strength can theoretically vary by more than a magnitude unit using either surface waves or body waves depending upon the angles of slip motion and fault dip for a source at a constant depth. The magnitude values determined by surface and body waves do not change linearly in relation to slip and dip angles nor do they change linearly in relation to one another. Random selection of locations within the radiation pattern is used to determine the extent of scatter in magnitude determinations which could be attributed to station distribution relative to the source. The scatter in surface-wave versus body-wave magnitude plots for earthquakes could be severe if only a few stations are used to obtain average magnitude values. A method of obtaining consistent estimates of surface-wave magnitude in practice is discussed.

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