S22A-01 10:20h
Fault complexity, interaction, and the Gutenberg-Richter relation
Although the Gutenberg-Richter relation is one of the most fundamental observations in earthquake physics, there is still controversy as to whether power-law regional magnitude frequency statistics apply to individual faults. A number of observations suggest that earthquake populations on particular faults are better described by a weakly characteristic model in which a greater number of large events is observed than is expected from the power-law distribution of smaller ones. Such observations are problematical, however, due to the weak statistics of the small number of large events and the effect of box size on the perceived distribution. Here we investigate this problem in a complex fault network model which combines nearest-neighbor stress transfer on individual faults with Coulomb stress transfer between faults. We find that the regional m-f distribution depends on both fault structure and the degree of interaction with more power-law behavior observed with both increased fault complexity and interaction. We further observe that m-f distributions on individual faults can be quite different from the regional m-f distribution. These results have important seismic hazard implications as they suggest that extrapolation of the expected number of large events from the observed population of smaller ones may not be generally appropriate for individual faults, even if the regional m-f distribution is power-law.
S22A-02 INVITED 10:35h
To b or not to b? - Is There Value in b Value Research?
In 1935 Richter proposed measuring the log of amplitude to assess the intrinsic size, or magnitde, of earthquakes; not long after Ishimoto, Iida, and Gutenberg observed that the distribution of log-number vs magnitude had an approximately straight-line form. The slope of this relationship is the b value, or, if scalar moment is used rather than magnitude, the beta value. Subsequently b and beta have been used routinely to describe the size distribution of earthquake groups. There is a truly enormous literature which concerns how to best to measure b and beta and purports to explain their mechanical significance. But, there are problems. First, magnitudes and moments are themselves unreliable; reported values for individual events are highly variable, and systematic errors depend strongly on event size, on the method of measurement, and on geographic region. Second, the log-number/log-moment relationship is seldom really straight, and so its slope depends on the size range chosen. Both these difficulties mean that the true accuracy in measurements of b or beta is seldom better than 0.1 or 0.2, reducing the utility of b and beta for predicting occurrence rates for large events. In general, most investigations overinterpret the significance of b and beta, especially since there is little agreement about what physical processes control the size distribution. Nevertheless, some earthquake populations do exhibit huge differences in the proportions of big and little events, e. g., contrast deep focus earthquakes beneath Tonga, South America, and Spain. Moreover, there is emerging evidence that large differences may occur over distance scales of only a few km. Ongoing research efforts should avoid simply reporting b and beta, and instead should focus on documenting and better understanding the physical reasons for the different proportions of large and small earthquakes.
S22A-03 INVITED 10:50h
Why is Gutenberg-Richter scaling applicable, why are b-values nearly constant?
The near universal applicability of the Gutenberg-Richter (GR) frequency-magnitude scaling of earthquakes is quite remarkable. Even more remarkable is the constancy of the scaling exponent, the b-value (also identified as a fractal dimension D = 2b). Many explanations for this scaling have been given but uncertainties remain. The first question is whether the scaling is applicable to earthquakes on a single fault or to an ensemble of faults. We will argue that the former is the case and it is the fractal distribution of faults that leads to GR scaling. An explanation for the fractal distribution of faults is comminution tectonics. All fractal (power-law) distributions in nature must have upper and lower bounds. The upper and lower bounds on GR scaling will be discussed. The applicability of GR scaling has important implications for probabilistic earthquake hazard assessment. Under many circumstances the probability of large earthquakes can be obtained from the occurrence of smaller earthquakes using GR scaling. The implication of this approach will be discussed. The question of the relationship of characteristic earthquakes to GR scaling will be considered. In terms of statistical physics, the background seismicity associated with GR scaling appears to play the role of thermal fluctuations. A major question is why the background seismicity does not change significantly during the earthquake cycle of characteristic earthquakes.
S22A-04 INVITED 11:05h
What does make the b-value change? The role of the mechanical conditions.
Since the works of Mogi (1962) and Scholz (1968) on acoustic emission (AE), we know that the Gutenberg Richter empirical law can be observed at the laboratory sample scale. They showed that a significant overlap exists between the definition of AE (usual term at lab scale) and earthquake respectively. This is further reinforced by the evidence for brittle fracture as observed by AE to obey similar statistics (i.e. Gutenberg-Richter law) over source dimensions spanning more than eight orders of magnitude, possibly ranging from the hundred of kilometers of tectonic earthquakes to the dislocation movement smaller than the micron size (Miguel et al, 2001). As the b-value characterizing the earthquakes dynamics displayed regional and temporal departures from its mean value, the need raised for understanding what does make the b-value change. Hence, since Mogi and Scholz, the laboratory results have been often used to better understand the earthquakes dynamics. Mogi showed the role of material heterogeneity on b-value, and Scholz showed that the b-value decreased before the failure and suggest this exponent to be related to the stress. These very first studies open the route for several authors to investigate at the lab the origins of the b-value variations. More recently, numerical simulations allowed reproducing the power-law distribution of damage events and then to investigate more easily what are the parameters controlling the b-value. In this presentation, basing on natural observations at different scale (rock slopes, mines, rock masses, tectonic faults), on laboratory experiments and numerical simulations, we investigate what are the relationships between the b-value and the mechanical condition of the material (stress, confining pressure, state of failure). In particular we show a set of converging observations (lab, crust, simulation) indicating a strong dependence between the brittle-ductile transition and the b-value that allows us to give a mechanical interpretation for certain b-value variations observed in the earth crust.
S22A-05 11:20h
Linking Earthquake Size Distribution to Stress
Stress dependence of the size distribution of acoustic emissions and micro earthquakes has already been established in the laboratory and for mining related events. However, can this dependence be extrapolated to earthquakes in general? This requires that the parameter $b$ in the Gutenberg-Richter relation $\log N = a - bM$ cannot be a constant, even for worldwide samples. We demonstrate that the $b$-value of earthquakes systematically varies for different styles of faulting, classified through their rake angles. Determining $b$-values as function of rake angle, we universally find that normal faulting events have the highest $b$-values ($b \approx 1.1$), thrust events the lowest ($b \approx 0.75$), and strike-slip events show intermediate values ($b \approx 0.95$). These values are the average from the five datasets investigated for our study: Harvard CMT, southern & northern California, NEID Kanto-Tokai, and NEID F-Net, all providing high-quality focal mechanisms. These results require that $b$ depends inversely on differential stress, offering a framework that explains a range of observational data. Furthermore, seismic hazard assessment needs to correctly estimate the critical parameter $b$ to avoid errors.
S22A-06 11:35h
Simultaneous estimation of $b$-values and detection rates of earthquakes for the application to aftershock probability forecasting
Reasenberg and Jones [{\em Science}, 1989, 1994] proposed the aftershock probability forecasting based on the joint distribution [Utsu, {\em J. Fac. Sci. Hokkaido Univ.}, 1970] of the modified Omori formula of aftershock decay and Gutenberg-Richter law of magnitude frequency, where the respective parameters are estimated by the maximum likelihood method [Ogata, {\em J. Phys. Earth}, 1983; Utsu, {\em Geophys Bull. Hokkaido Univ.}, 1965, Aki, {\em Bull. Earthq. Res. Inst.}, 1965]. The public forecast has been implemented by the responsible agencies in California and Japan. However, a considerable difficulty in the above procedure is that, due to the contamination of arriving seismic waves, detection rate of aftershocks is extremely low during a period immediately after the main shock, say, during the first day, when the forecasting is most critical for public in the affected area. Therefore, for the forecasting of a probability during such a period, they adopt a generic model with a set of the standard parameter values in California or Japan. For an effective and realistic estimation, I propose to utilize the statistical model introduced by Ogata and Katsura [{\em Geophys. J. Int.}, 1993] for the simultaneous estimation of the $b$-values of Gutenberg-Richter law together with detection-rate (probability) of earthquakes of each magnitude-band from the provided data of all detected events, where the both parameters are allowed for changing in time. Thus, by using all detected aftershocks from the beginning of the period, we can estimate the underlying modified Omori rate of both detected and undetected events and their $b$-value changes, taking the time-varying missing rates of events into account. The similar computation is applied to the ETAS model for complex aftershock activity or regional seismicity where substantial missing events are expected immediately after a large aftershock or another strong earthquake in the vicinity. Demonstrations of the present procedure will be shown for the recent examples in Japan.
http://www.ism.ac.jp/~ogata/
S22A-07 11:50h
Investigation of Magmatic Processes in the Alaska Subduction Zone Using $b$-Value Imaging and Seismic Body Wave Tomography
We investigate source region and ascend paths of magma in the Alaska subduction zone using two complementary techniques: 1) Imaging the earthquake size-distribution, or $b$-value, of earthquakes in the subducting slab; 2) imaging seismic body wave velocities using seismic tomography. The earthquake size distribution in the Cook inlet region (CIR) and interior Alaska (IAL) is analyzed using cross-sections, each about 250 km in length, 150 km in depth and 100 km in width, using data from the Alaska Earthquake Information Center (AEIC) for the period of 1989.2 to 2002.5. The seismicity above the magnitude of completeness ($M_c$ 2.1-2.4) is sampled in circles of 10 km radius and centered in a 1x1 km-grid. Different earthquake size distributions are found for IAL and CIR. The cross-sections beneath CIR reveals a high $b$-value anomaly ($b >$ 1.4) near the top of the slab in a depth of 80 km to 100 km, which we interpret to be related to the dehydration of the slab. The cross-section beneath IAL, were no volcanoes are present, on the other hand shows a high $b$-value along the entire upper edge of the slab. To test if the process of dehydration also alters seismic wave velocities, we invert a set of about 75000 P and about 25000S arrivals from about 5000 high quality earthquakes to obtain a tomographic image of the three-dimensional (3D) velocity structure for $V_p$ and $V_s$ down to a depth of about 140 km. The data and model setup allows to resolve structures of 20 km minimal length with certainty at depths of 100 km. The 3D seismic body wave velocity fields are also used to relocate the hypocenters and hence provide improved $b$-value imaging. Combined $b$-value and seismic tomography imaging is a promising new approach for improving our understanding of the processes that lead to subduction volcanism.
S22A-08 INVITED 12:05h
A Review of Frequency-Magnitude Relation Studies at Volcanoes
The frequency-magnitude relation is one of the most widely studied topics in seismology. In volcanic areas very high b-values have been observed. Recent studies used dense spatial grids to study b-values at >13 volcanoes. Such studies require a well-distributed group of earthquakes; if the events all occur at one point then no meaningful spatial mapping can be done. All volcanoes studied to date have shown high spatial variability of b, with regions of normal b (1.0) adjacent to regions with anomously high b (up to 3.0). In general b is high at depths of 7-10 km where the earthquakes are adjacent to inferred magma bodies identified by other techniques. However, about half of the studied volcanoes also show significant high b anomalies at depths of 3-4 km. This is the approximate depth at which magma with 4 wt percent gas starts to exsolve the gas, and further, is near the depth at which open cracks may exist in the host rock. The data sets used for these analyses show that the b-value anomalies are long-lived (years to decades) features. This is somewhat in contrast with previous studies of b as a function of time, or rather, the documented spatial variation has created an ambiguity in interpreting whether b varies as a function of space, time, or both. A new result is the elucidation of a common temporal pattern of b for earthquake swarms associated with eruptions and intrusions. The b changes from a normal background value to a short-lived high, then decreases, then increases again to a secondary (generally lower) high with a longer time constant, eventually returning to a low background level. Based on knowledge of b from lab and field studies, these observations suggest that the short-lived high b is probably a result of high thermal gradients that dissipate quickly. The heat may be carried by gases, liquid water, or magma. The longer-lived secondary high b is consistent with an increase in pore pressure, similar to observations at Rangely, Colorado in association with fluid injection in deep wells. This suggests that diffusion is a main controlling factor. Note that b-value anomalies are features of both the earthquakes themselves and the space they occupy. This is in contrast to tomography studies in which the rays from earthquakes pass through the region of interest, but the earthquakes themselves are not required to be within it. The b-value techniques, while powerful, are limited to those regions that produce earthquakes in sufficiently high numbers to perform the analyses.