Magnitude conversion and earthquake recurrence rate models for the central and eastern United States

Development of Seismic Source Characterization (SSC) models, which is an essential part of Probabilistic Seismic Hazard Analyses (PSHA), can help forecast the temporal and spatial distribution of future damaging earthquakes (𝑀_w≥ 5) in seismically active regions. Because it is impossible to associate all earthquakes with known faults, seismic source models for PSHA often include sources of diffuse seismicity in which future earthquake scenarios are not localized on mapped faults. These sources of diffuse seismicity are referred to as area source zones, distributed seismicity zones, or just source zones. During the early years of PSHA studies, it was assumed that earthquakes in seismotectonic zones have (1) uniform spatial distribution, (2) Poisson temporal distribution, and (3) exponential magnitude distribution (NRC, 2012). In seismically active regions (e.g., the Western United States), where active faults are readily identified, models of the spatial distribution of earthquakes include both the fault source geometries and the distributed seismicity (background) source zones. Source characterization of active faults is complemented by paleoseismic studies with estimates of earthquake magnitudes, dates of occurrences, and slip rates, which provide important information for PSHA studies.

In the Central and Eastern United States (CEUS) very few Quaternary-active faults have the requisite information for use in PSHA (i.e., fault geometry and dimensions, event rates or slip rates, etc.), and we lack knowledge about the causative faults for most observed seismicity in the region. As a result, area source zones are frequently used in site-specific PSHA in the CEUS to represent diffuse seismicity that cannot be associated with faults. However, there are examples of active fault sources in the CEUS, such as the Meers fault, the Cheraw fault, and New Madrid region, where individual faults can be characterized.

The source characterization models for background seismicity are based, to a large extent, on an assumption that spatial distribution of historical and recorded seismicity will not change substantially for time periods of interest for PSHA (approximately the next 50-100 years for engineered structures). Furthermore, studies such as those by Kafka (2007, 2009) found a correlation between the locations of small- to moderate-magnitude earthquakes and the locations of large-magnitude earthquakes, indicating that we can, with some level of confidence, use the spatial pattern of smaller earthquakes to forecast the future pattern of damaging earthquakes.

Within background seismicity zones, the earthquake rate forecast is developed using spatial smoothing of the small to moderate magnitude events in earthquake catalogs. Different methodologies are used for this purpose and can predict varying distributions of seismicity rates. This in turn affects the results of a seismic hazard analysis. The U.S. Geological Survey (USGS) and Nuclear Regulatory Commission (NRC) use different methods for computing spatially smoothed seismicity rates in the CEUS; the USGS uses kernel-based spatial smoothing methods in developing the National Seismic Hazard Model (NSHM), and the method adopted in the Central and Eastern United States Seismic Source Characterization (CEUS-SSC) project is used when evaluating seismic hazard for nuclear power plant siting. These methods are described and the impact on seismic hazard are evaluated in this Research Information Letter (RIL).

Another important input to estimating the rate of distributed seismicity is event magnitudes listed in earthquake catalogs. A substantial source of uncertainty in catalogs is the magnitude assigned to a given earthquake. Numerous different magnitude types exist, with each magnitude type computed in a different way. Therefore, for the sake of consistency, both the CEUS-SSC and the USGS NSHM have attempted to assemble a complete catalog with a uniform magnitude determination. To this end, moment magnitude, 𝑀_w, which is a physics-based measurement, has been adopted as the standard. However, 𝑀_w was not computed routinely until the past few decades. To address this issue, the CEUS-SSC conducted extensive analyses to determine conversion equations from which to take a routinely computed network (e.g., 𝑀_L or 𝑚_bLg ) and convert it into 𝑀_w. Another issue with using 𝑀_w is that it becomes increasingly difficult to compute for earthquakes with 𝑀 less than ~4.

This study investigates the effects of moment magnitude estimation and spatial smoothing methods on estimation of the earthquake rate forecast and on seismic hazard. We investigate the validity of the magnitude conversion equations and their associated uncertainties by applying them to a case study for induced earthquakes in southern Kansas and northern Oklahoma, and summarize the use of the decay of the seismic coda to estimate 𝑀_w for small earthquakes (𝑀_w < 4. Furthermore, the study documents a comparison and assessment of background seismicity smoothing methods implemented by the USGS for the NSHM and used by the CEUS-SSC for siting nuclear facilities based on probabilistic seismic hazard estimates from multiple source zones in the CEUS and for multiple sites.