Stefan Wiemer

Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan

We mapped the minimum magnitude of complete reporting, M c , for Alaska, the western United States, and for the JUNEC earthquake catalog of Japan. Mc was estimated based on its departure from the linear frequency-magnitude relation of the 250 closest earthquakes to grid nodes, spaced 10 km apart. In all catalogs studied, Mc was strongly heterogeneous. In offshore areas the Mc was typically one unit of magnitude higher than onshore. On land also, Mc can vary by one order of magnitude over distance less than 50 km. We recommend that seismicity studies that depend on complete sets of small earthquakes should be limited to areas with similar Mc, or the minimum magnitude for the analysis has to be raised to the highest com- mon value of Mc. We believe that the data quality, as reflected by the Mc level, should be used to define the spatial extent of seismicity studies where Mc plays a role. The method we use calculates the goodness of fit between a power law fit to the data and the observed frequency-magnitude distribution as a function of a lower cutoff of the magnitude data. Mc is defined as the magnitude at which 90% of the data can be modeled by a power law fit. Mc in the 1990s is approximately 1.2 0.4 in most parts of California, 1.8 0.4 in most of Alaska (Aleutians and Panhandle excluded), and at a higher level in the JUNEC catalog for Japan. Various sources, such as ex- plosions and earthquake families beneath volcanoes, can lead to distributions that cannot be fit well by power laws. For the Hokkaido region we demonstrate how neglecting the spatial variability of M c can lead to erroneous assumptions about deviations from self-similarity of earthquake scaling.

Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty

We introduce a new method to determine the magnitude of completeness M c and its uncertainty. Our method models the entire magnitude range (emr method) consisting of the self-similar complete part of the frequency-magnitude distribution and the incomplete portion, thus providing a comprehensive seismicity model. We compare the emr method with three existing techniques, finding that emr shows a superior performance when applied to synthetic test cases or real data from regional and global earthquake catalogues. This method, however, is also the most computationally intensive. Accurate knowledge of M c is essential for many seismicity-based studies, and particularly for mapping out seismicity parameters such as the b -value of the Gutenberg-Richter relationship. By explicitly computing the uncertainties in M c using a bootstrap approach, we show that uncertainties in b -values are larger than traditionally assumed, especially when considering small sample sizes. As examples, we investigated temporal variations of M c for the 1992 Landers aftershock sequence and found that it was underestimated on average by 0.2 with former techniques. Mapping M c on a global scale, M c reveals considerable spatial variations for the Harvard Centroid Moment Tensor (CMT) (5.3 ≤ M c ≤ 6.0) and the International Seismological Centre (isc) catalogue (4.3 ≤ M c ≤ 5.0).

Variations in earthquake-size distribution across different stress regimes

The earthquake size distribution follows, in most instances, a power law, with the slope of this power law, the ‘b value’, commonly used to describe the relative occurrence of large and small events (a high b value indicates a larger proportion of small earthquakes, and vice versa). Statistically significant variations of b values have been measured in laboratory experiments, mines and various tectonic regimes such as subducting slabs, near magma chambers, along fault zones and in aftershock zones. However, it has remained uncertain whether these differences are due to differing stress regimes, as it was questionable that samples in small volumes (such as in laboratory specimens, mines and the shallow Earths crust) are representative of earthquakes in general. Given the lack of physical understanding of these differences, the observation that b values approach the constant 1 if large volumes are sampled was interpreted to indicate that b = 1 is a universal constant for earthquakes in general. Here we show that the b value varies systematically for different styles of faulting. We find that normal faulting events have the highest b values, thrust events the lowest and strike-slip events intermediate values. Given that thrust faults tend to be under higher stress than normal faults we infer that the b value acts as a stress meter that depends inversely on differential stress.

Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times?

We hypothesize that highly stressed asperities may be defined by mapping anomalously low b values. Along the San Andreas fault near Parkfield the asperity under Middle Mountain, with its b=0.46, can be distinguished from all other parts of the fault surface. Likewise, along the Calaveras fault the northern asperity of the Morgan Hill 1984 (M6.2) rupture can be identified by its low b of 0.5 as a high stress patch along the fault. We add further evidence to the observations that the b value of the frequency-magnitude relationship of earthquakes is inversely proportional to stress by showing that it decreases with depth in the Parkfield segment of the San Andreas and along the Calaveras fault. In both of these areas, b values above and below 5 km depth are ∼1.2 and 0.8, respectively. We propose that probabilistic recurrence times Tr, based on the seismicity parameters a and b, should be calculated from their values within asperities only, instead of from the values of the entire rupture area of the maximum expected earthquake. The strong patches on faults control the time of rupture because they are capable of accumulating larger stresses than the rest of the fault zone, which slips along passively when an asperity breaks. Therefore no information on Tr is contained in the passive fault segments, only in the asperities. At Parkfield the probabilistic estimates of Tr derived from the data in the whole rupture and in the asperity only are 72 (−18/+24) and 23 (−12/+18) years, respectively, compared to the historically observed repeat time of 22 years. At Morgan Hill the Tr estimates are 122 (−46/+76) and 78 (−47/+110) years, respectively, compared to the observed repeat time of 72 years.

Mapping spatial variability of the frequency-magnitude distribution of earthquakes

Publisher Summary This chapter summarizes the new facts surrounding the spatial variability of the b -value—the slope of the frequency-magnitude distribution (FMD) describing the relative size distribution of events—to discuss the new hypotheses that grew from the observations, to report how far the tests of these hypotheses have advanced, and to describe the methods used. In addition, the concepts such as temporal variations, fractal dimension, and the correct estimate of b and its uncertainty are discussed. Spatially mapping b -values has proven to be a rich source of information about the seismotectonics of a region. The ample, high-quality earthquake catalogs collected primarily over the past several years and the availability of increased computing power have enabled researchers to investigate spatial variations in b with an unprecedented level of detail. The discovery of strong differences in b is simply a reflection of the heterogeneity of the Earth that emerges on all scales, once suitable datasets become available. The first step in extracting information from the heterogeneity in the b -value is to determine with what other parameters these variations correlate.

Spatial variability of seismicity parameters in aftershock zones

The spatial variability of the b value of the frequency-magnitude relationship and the decay rate of aftershocks as described by the p value of the modified Omori law is investigated. By using dense spatial grids we map out the distribution of b and p values within the Landers, Northridge, Morgan Hill, and Kobe aftershock sequences. Considerable spatial variability is found, with b values of independent subvolumes ranging from 0.6 to 1.4, and p values ranging from 0.6 to 1.8. These systematic and statistically highly significant differences argue that it is an oversimplification to assign one single p and b value to an aftershock sequence that extends up to 100 km. The spatial distribution of these two parameters is compared with the slip distribution during the mainshock, suggesting that the areas of largest slip release correlate with high b value regions. We hypothesize that the frictional heat created during the event may influence the p value distribution within an aftershock zone, while applied shear stress, crack density and pore pressure govern the frequency-magnitude distribution. By investigating the frequency-magnitude distribution separately for preseismic and postseismic periods for the Morgan Hill mainshock, we find that only the volume in the vicinity of the highest slip release shows a significant increase in the b value, which decays to premainshock values within a year. Surrounding areas of the aftershock zone show an approximately constant b value with time. Because the aftershock hazard after a mainshock depends strongly on both the b and p value, we propose that aftershock hazard assessment can be improved by taking into account the spatial distribution of the parameters.

Real-time forecasts of tomorrow's earthquakes in California

Despite a lack of reliable deterministic earthquake precursors, seismologists have significant predictive information about earthquake activity from an increasingly accurate understanding of the clustering properties of earthquakes. In the past 15 years, time-dependent earthquake probabilities based on a generic short-term clustering model have been made publicly available in near-real time during major earthquake sequences. These forecasts describe the probability and number of events that are, on average, likely to occur following a mainshock of a given magnitude, but are not tailored to the particular sequence at hand and contain no information about the likely locations of the aftershocks. Our model builds upon the basic principles of this generic forecast model in two ways: it recasts the forecast in terms of the probability of strong ground shaking, and it combines an existing time-independent earthquake occurrence model based on fault data and historical earthquakes with increasingly complex models describing the local time-dependent earthquake clustering. The result is a time-dependent map showing the probability of strong shaking anywhere in California within the next 24 hours. The seismic hazard modelling approach we describe provides a better understanding of time-dependent earthquake hazard, and increases its usefulness for the public, emergency planners and the media.

Variations in the frequency‐magnitude distribution with depth in two volcanic areas: Mount St. Helens, Washington, and Mt. Spurr, Alaska

The frequency-magnitude distribution of earthquakes, characterized using the b-value, is examined as a function of space beneath Mount St. Helens (1988–1996), and Mt. Spurr (1991–1995). At Mount St. Helens, two volumes of anomalously high b (b > 1.3) can be observed at depths of 2.6–3.6 km below the crater floor and below 6.4 km. These anomalies coincide with (1) the depth of vesiculation of ascending magma, and (2) the suggested location of a magma chamber at Mount St. Helens. Study of Mt. Spurr reveals an area of high b-value (b ≥ 1.3) at a depth of about 2.3–4.5 km below the crater floor of the active vent Crater Peak. We propose that the higher material heterogeneity in the vicinity of a magma chamber or conduit due to vesiculation of the ascending magma is the main cause of the increased b-value at shallow depths. Alternatively, interaction of magma with groundwater may have increased pore pressure and lowered the effective stress. The deeper anomaly at Mount St. Helens is likely caused by high thermal stress gradients in the vicinity of the magma chamber. Our results indicate that detailed mapping of the frequency-magnitude distribution can be used as a tool to trace vesiculation and locate active magma chambers.

Mapping the B‐value anomaly at 100 km depth in the Alaska and New Zealand Subduction Zones

A positive anomaly in the frequency-magnitude distribution (b-value) is detected at approximately 90–100 km depth in two subduction zones. The b-value in this anomalous zone is 40% higher than in adjacent volumes. We use regional catalogs with a magnitude of completeness of 2.6 (Central Alaska and Cook Inlet), 2.0 (Shumagin Islands), and 3.5 (New Zealand). To resolve the b-value as a function of space in more detail, we project all earthquakes onto planes perpendicular to the strike of the slab. These cross-section views of the b-value distribution locate the high b-value anomalies at a depth of 90–100 km, on the upper surface of the Wadati-Benioff Zone. At these depths, slab dehydration may increase pore pressure, thus lowering the effective stress and increasing the b-value. Increased pore pressure would also lower the liquidus in the overlying asthenosphere, giving rise to the volcanism that occurs directly above this zone.

Mapping active magma chambers by b values beneath the off-Ito volcano, Japan

The b value of the frequency-magnitude relation, and thus the mean magnitude, in the off-Ito volcanic area is not uniform based on detailed b value tomography using about 10,000 events in an area of 10 km radius and in the upper 15 km of the crust. A high b value anomaly (b=15) below 7 km depth and with a radius of about 2 km, located below the coast southeast of Ito, contrasts with lower values of typically b=0.7 north of it and at shallower depths. On the basis of surface deformations, a tensile crack dislocation source was located above 7 km depth. Thus we surmise that the magma chamber in the off-Ito area was located below 7 km depth. The correlation of a high b value anomaly with this model supports our hypothesis that active magma chambers may be mapped by high b value anomalies. The magma body may be described as consisting of two parts: a lower, well-established chamber below 11 km depth and a shallower part (11–7 km depth). The b value in the volume surrounding the magma chamber increased from 0.7 during the 1980s to 1.5 during the earthquake swarms of the 1990s. This may reflect a trend of increasing crack density due to the intrusion activity.