Toward Reconciling Magnitude Discrepancies Estimated from Paleoearthquake Data: A New Approach for Predicting Earthquake Magnitudes from Fault Segment Lengths

We recognize a discrepancy in magnitudes estimated for several Basin and Range faults in the Intermountain Seismic Belt, U.S.A. For example, magnitudes predicted for the Wasatch (Utah), Lost River (Idaho), and Lemhi (Idaho) faults from fault segment lengths, Lseg, where lengths are defined between geometrical, structural, and/or behavioral discontinuities assumed to persistently arrest rupture, are consistently less than magnitudes calculated from displacements, D, along these same segments. For self-similarity, empirical relationships (e.g. Wells and Coppersmith, 1994) should predict consistent magnitudes (M) using diverse fault dimension values for a given fault (i.e. M ~ Lseg, should equal M ~ D). Typically, the empirical relationships are derived from historical earthquake data and parameter values used as input into these relationships are determined from field investigations of paleoearthquakes. A commonly used assumption - grounded in the characteristic-earthquake model of Schwartz and Coppersmith (1984) - is equating Lseg with surface rupture length, SRL. Many large historical events yielded secondary and/or sympathetic faulting (e.g. 1983 Borah Peak, Idaho earthquake) which are included in the measurement of SRL and used to derive empirical relationships. Therefore, calculating magnitude from the M ~ SRL relationship using Lseg as SRL leads to an underestimation of magnitude and the M ~ Lseg and M ~ D discrepancy. Here, we propose an alternative approach to earthquake magnitude estimation involving a relationship between moment magnitude, Mw, and length, where length is Lseg instead of SRL. We analyze seven historical, surface-rupturing, strike-slip and normal faulting earthquakes for which segmentation of the causative fault and displacement data are available and whose rupture included at least one entire fault segment, but not two or more. The preliminary Mw ~ Lseg results are strikingly consistent with Mw ~ D calculations using paleoearthquake data for the Wasatch, Lost River, and Lemhi faults, demonstrating self-similarity and implying that the Mw ~ Lseg relationship should supplant M ~ SRL relationships currently employed in seismic hazard analyses. The relationship will permit reliable use of Lseg data from field investigations and proper use and weighting of multiple-segment-rupture scenarios in seismic hazard analyses, and eliminate the need to reconcile the Mw ~ SRL and Mw ~ D differences in a multiple-parameter relationship for segmented faults.