The nearly coincident forms of the relations between seismic moment M0 and the magnitudes ML, MS, and Mw imply a moment magnitude scale M = ⅔ log M0 ‐ 10.7 which is uniformly valid for 3 ≲ ML ≲ 7, 5 ≲ Ms ≲ 7½, and Mw ≳ 7½.

No abstract

The NGA-West2 project is a large multidisciplinary, multi-year research program on the Next Generation Attenuation (NGA) models for shallow crustal earthquakes in active tectonic regions. The research project has been coordinated by the Pacific Earthquake Engineering Research Center (PEER), with extensive technical interactions among many individuals and organizations. NGA-West2 addresses several key issues in ground-motion seismic hazard, including updating the NGA database for a magnitude range of 3.0–7.9; updating NGA ground-motion prediction equations (GMPEs) for the “average” horizontal component; scaling response spectra for damping values other than 5%; quantifying the effects of directivity and directionality for horizontal ground motion; resolving discrepancies between the NGA and the National Earthquake Hazards Reduction Program (NEHRP) site amplification factors; analysis of epistemic uncertainty for NGA GMPEs; and developing GMPEs for vertical ground motion. This paper presents an overview of the NGA-West2 research program and its subprojects.

From a casual observation that the form of degraded fault scarps resembles the error function, this investigation proceeds through an elementary diffusion equation representation of landform evolution to the application of the resulting equations to the modern topography of scarplike landforms. The morphologic observations can be analyzed either in the form of one or more cross-strike elevation profiles or in the form of the slope-offset plot, a point plot of maximum scarp slope versus scarp offset. Working with either or both of these data representations for nine geologic structures, which range in age from 3 to 400 ka B.P. and in offset from 1 to 50 m, we apply analytical solutions for the vertical initial value scarp, the vertical continuous offset scarp, and the finite slope, initial value scarp. The model calculations are intrinsically ambiguous, yielding as the final answer only the product •ct (in the case of the initial value problem) or the product •cA-• (in the case of the repeated faulting problem); here t is the age of a single scarp-forming event, 2A is the vertical slip rate, and •c is the "mass diffusivity." A single profile across three sea cliffs along the Santa Cruz, California, coast is analyzed as three separate initial value problems. A reasonably constrained age for the sea cliff standing above the Highway 1 platform returns •c = 11 GKG (1 GKG = 1 m2/ka). With this •c, we can date the two older sea cliffs. In fact, we do the converse: age estimates for these two older sea cliffs based on a uniform fate of uplift both yield the same •c as for th• lower sea cliff. We treat a single profile of the Raymond fault in Pasadena/San Marino in terms of the repeated faulting problem; for it ihe uplift rate of R. Crook and others yields •c = 16 GKG. The very substantial preexisting offset across the Raymond fault must have been buried/leveled some 230 ka B.P., when the modern topography began to form. Our analysis of the Lake Bonneville shoreline scarps reveals a dependence 'of •ct on 2a, suggestive of nonlinear modification processes. This appearance is treated with the finite slope initial value scarp model to determine •c = 1.1 GKG for the Lake Bonneville shoreline scarps. The suggestion of M. N. Machette that approximately 100,000-year-old, meter-high s•arps are "unobservable" in weakly consolidated alluvial terranes of the Basin and Range and Rio Grande Rift Valley Provinces can be formulated as •c • 1 GKG. The coincidence between this inequality find the Lake Bonneville shoreline •c is striking, and it suggests that the value of •c = 1 GKG may be generaily applicable, a s a good first approximation, to the modification of alluvial terranes within the semiarid regions of the western United States. The Lake Bonneville shoreline •c is the basis for dating four sets of fault scarps in west-central Utah. The Drum Mountains fault scarps can be modeled in several different circumstances, but the most likely interpretation is that these fault scarps formed as the result of a single episode of normal faul...

The source characteristics of southern California earthquakes with local magnitudes ML between 2 and 7 have been estimated from the gross spectral properties of the locally recorded S waves written on broad band torsion seismograph systems that have operated in California since 1932. The seismic moments M0 are consistent with the magnitude‐moment relation obtained by M. Wyss and J. N. Brune from surface wave amplitudes, although a single straight line given by log M0 = 1.5 ML + 16.0 fits the data equally well. Source dimensions 2r vary from about 0.6 to 25 km, and stress drops Δσ lie between 0.3 and 200 bars. Neither parameter is a well‐defined function of magnitude, although source size roughly increases with increasing ML. A theoretical relation between ML and source parameters is developed by using Brune's source model and the displacement response of the Wood‐Anderson seismograph. The result is ML = log M0 − 32 log r − 17.8, where 3 < ML < 7, M0 is in dynes centimeters, and r is in kilometers. The ML may be accurately obtained by this equation, and the result is used to construct the following relations: log M0 = 2.0 ML + 14.2 − log Δσ, where Δσ is in bars, and log 2r = ⅔ ML + 2.9 − ⅔ log Δσ. Single‐valued relations are not expected unless Δσ is constant. However, all available data are bracketed by these equations if stress drops vary over the range observed in this study. Radiated energies computed by spectrum integration agree with a theoretical result, log Es = 2.0 ML + 8.1, where Es is in ergs. Both are consistent with B. Gutenberg and C. F. Richter's energy‐magnitude relation above ML = 4.5 but depart considerably from their result at lower magnitudes. The apparent stress parameter can provide source information that is independent of stress drop only if the high‐frequency spectral falloff is a well‐determined source property, which is unlikely for most of the data examined in this and other recent spectrum studies. Regional differences in source dimensions and stress drops within the southern California area are suggested by the spectral observations. However, the pattern is complex, and there are significant variations in these source parameters within any one region. Close‐in seismic measurements are needed to substantiate the suggested regional differences, and determination of fault zone properties at depth is required to more fully understand the regional and local variations in seismic source parameters suggested by this study.