S11C-0707
Seismicity Patterns in Southern California and Their Physical Origin
We investigate the temporal and spatial clustering of earthquakes in Southern California using the relocated catalog of Lin et al. (2007). We first search for well-defined earthquake sequences in spatio-temporal regions around each event with 2 ≤ M ≤ 6.0. The spatial influence window around an earthquake is a sphere with a radius that scales with the magnitude and hence the rupture length of the event. The temporal window is also magnitude-dependent. For all earthquake sequences that have a sufficiently large number of events, we fit the ETAS model (Ogata, 1988) and estimate the five ETAS parameters using a maximum likelihood procedure. In addition, we determine with a gridding technique, for events with magnitudes above the completeness threshold, the spatial variation of the b-value, the earthquake background rate (Hainzl et al., 2006) and earthquake density. Based on the values of the triggering exponent α of the ETAS model, we try to separate swarm- like seismicity from sequences that have an obvious mainshock. We also investigate if the various estimated seismicity parameters show correlating spatial patterns. Finally, we compare the seismicity patterns with the estimated local temperature, estimated local tectonic strain rates, existence of sedimentary cover and mainshock faulting style, in an attempt to understand the underlying physics of the different seismicity patterns.
S11C-0708
Comparisons between observed properties of aftershock sequences in southern California and predictions of a damage rheology model
Aftershock sequences are commonly observed, but their properties vary from region to region. Ben-Zion and Lyakhovsky (2006) developed a solution for aftershocks decay in a damage rheology model. The solution indicates that the productivity and duration of aftershocks decrease with increasing value of a material parameter R given by the ratio of timescale for brittle deformation to timescale for viscous relaxation. The parameter R is inversely proportional to the degree of seismic-coupling and is expected to increase primarily with increasing temperature, and also with increasing thickness of sedimentary cover. To test these predictions, we use the relocated catalog of Lin et al. (2007) and analyze properties of aftershock sequences in the following five southern California regions. (1-2) The Coso and Imperial Valley areas with high heat flow. (3) The Landers and Hector- Mine region with low heat flow and thin sedimentary cover. (4-5) The San Bernardino Basin and Ventura Basin with low heat flow and thick sedimentary cover. In each region we consider events with magnitudes between 4.0 and 6.0 to be mainshocks. For each mainshock, we consider events to be aftershocks if they occur in the subsequent 50 days, within a circular region that scales with the magnitude of the mainshock and in the magnitude range between that of the mainshock and 2 units lower. This procedure produces 25-178 aftershock sequences in each of the five regions. We stack the aftershock sequences in each region and analyze the properties of the stacked data. The initial results indicate that the productivity and duration of the stacked aftershock sequences in the different regions increase in the following order: Coso, Imperial Valley, San Bernardino Basin and Ventura Basin, and the Landers and Hector-Mine area. These results are compatible with the damage model predictions. We are in the process of performing additional comparisons between the model predictions and observed data. Updated results will be presented in the meeting.
S11C-0709
Modelling of the spatio-temporal distribution of aftershocks based on rate- and state friction law
We model the spatio-temporal distribution of the aftershocks of the 1995 Kobe earthquake based on static stress change (ΔCFF) and rate- and state-dependent constitutive friction law (Dieterich, 1994). In several studies, such a type of approach reproduces the observed spatio-temporal distribution of off-fault aftershocks (e.g., Toda et al., 2003). On the other hand, for on-fault aftershocks, it is thought to be difficult to match the expected spatio- temporal distribution of aftershocks with the observed one. A slip model of mainshocks derived from a waveform inversion is necessary for the calculation of the ΔCFF. Small-scale slip discontinuities are not represented by the smoothed slip model, and the calculated ΔCFF close to the main fault also does not represent small-scale stress discontinuities. In our model, we incorporate ΔCFF caused by each of the aftershocks and the model parameters are estimated by the maximum likelihood method. We adopt a relatively simple slip model for the calculation of ΔCFF caused by the mainshock; nonetheless, the expected spatial distribution of seismicity close to the fault of the mainshock is roughly consistent with the observed one. Concerning the temporal variation of the aftershocks, the decay of the expected seismicity is slower than the observed one. The temporal behavior of Dieterich model is close to power law decay (Omori-Utsu formula) with exponent p=1. This limitation would be affected the inconsistency between expectation and observation of temporal decay in our modelling.
S11C-0710
Dependence of the Omori-Utsu law parameters on mainshock magnitude: observations and modeling
We examine the dependence on m of the p and χ parameters appearing in Omori-Utsu formula λ(t,m)=χ×(t+c)-p relating the rate of aftershocks λ at time t after a mainshock of magnitude m. Observations point out to a significant increase of p with m, along with a scaling relationship of the form χ~ 10α m. We here show that these observations can be explained within the framework of the rate-and-state friction model, when accounting for realistic levels of co-seismic stress heterogeneity on the main fault. We constrain the model parameters in order to recover the trends observed in previous and new analyses of aftershock sequences. Finally, the influence of afterslip on parameters p and χ is studied, to highlight the fact that it can significantly perturb the p(m) and χ(m) relations obtained with the initial afterslip-free model.
S11C-0711
The Initiation of Aftershock Sequences: a New Formulation for the Omori Aftershock Law
We propose that the onset of an aftershock sequence is controlled by a time constant c that is a simple function of the moment of the initiating earthquake (mainshock). Step changes in a physical system, such as the step change in stress that results from an earthquake rupture, generally result in two responses: a long term response and a transient response. This behaviour is seen in aftershock sequences which are usually modelled by the modified Omori law for aftershock rate of occurrence: dN/dt = A (c + t)-p. There are several theoretical and practical difficulties with this formulation. Moreover the mainshock and large aftershocks mask small aftershocks that occur early in the sequence. This has led to the speculation that the ‘c' term obtained by fitting the law to aftershock times is really an artefact of this non- detection. However, we argue that a priori there should be a transient process before the full 1/t or 1/tp aftershock decay is established. We find that a new formulation of the Omori law, dN/dt = Aexp(-t/c)/t fits aftershock data from the southern California catalogue slightly better than the standard law. In this formulation the timescale c is a simple function of seismic moment. The formulation therefore enables the prediction of the evolution of an aftershock sequence once the mainshock moment is known, including the time after which the aftershock rate falls below the background rate. This will have application in aftershock filtering. The formulation also overcomes the practical difficulties that arise if the standard form is used as a probability density function for time-varying hazard models.
S11C-0712
Is Gutenberg-Richter b value uniform in California and are spontaneous earthquakes stationary in California?
The b value in Gutenberg-Richer relationship is very important in seismology because it is critical for both hazard analysis and physical understanding of earthquakes: the small change of the b value can lead a large change in the predicted number of large earthquakes. It is very important and interesting to explore where the b value in California in uniform or not. The maximum likelihood method of Aki (1965) is the most accurate way to calculate b value, but the uncertainty of b value due to the uncertainty of magnitude, the earthquake catalog incompleteness and the magnitude round off errors is hard to calculate. Different regions may have different b value and different uncertainties of b value. We divide California into several regions, calculate possible both a and b value with 95% confidence in different regions using simulated catalogs after adding all kinds of errors and finally test whether the b value in California is uniform or not. There are two types of earthquakes: spontaneous and triggered. The separation of these two types of earthquakes, called declustering, helps us to understand more about both kinds and their relationships. Because spontaneous seismicity responds local plate movement and stress accumulation, it is useful and helpful to study whether spontaneous seismicity in California is stationary or not. We use ETAS model to decluster the catalog and find that the spontaneous seismicity is stationary in southern California after 1940 while it is not stationary in northern California after 1940.
S11C-0713
Pitfalls of Estimating Background Seismicity Rates from Interevent-time Statistics
The background seismicity rate (i.e. rate of mainshocks) is poorly constrained from seismicity counts because current declustering methods used to remove aftershocks rely on subjectively adjusted space-time parameters. Recently, Hainzl et al. (2006) proposed an objective method for estimating the fraction of background earthquakes in a catalog, γ, using the distribution of times between sequential events. This method is based on the assumption that the interevent times follow a gamma distribution, which is only approximate. I test the Hainzl method, and an alternative method using the theoretical interevent-time distribution of the ETAS model (Ogata, 1988). I find that both methods are plagued by a trade-off between γ and the direct Omori decay parameter pD. Hainzl et al. (2006) propose that γ for any dataset can be found from the mean over the variance of the normalized interevent times, plus a small empirical correction. I test this algorithm on 2000 ETAS simulations with varying γ, total number, duration, b-value, c-value and pD. The results of this suite of tests generally validate the method's ability to recover the correct γ. However, the tests also reveal a systematic error in the estimated γ as a function of pD. No other parameters appear to systematically affect the results. The systematic error in γ can be empirically corrected if pD is known. An alternative would be to find γ and pD that fit the theoretical equations for the interevent-time distribution derived from the ETAS model (e.g. Saichev and Sornette, 2007). However, there is a severe trade-off between γ and pD, such that different pairs of parameter values can produce nearly-identical theoretical distributions. Typically, increasing γ trades off with decreasing pD, the same sign as the correction for the Hainzl method. Either method could be used to constrain γ if pD were already accurately estimated. However, pD is not easily measured, as it is not the same as the cumulative Omori p-value measured for an aftershock sequence. Felzer et al. (2003) use forward modeling to identify a preferred pD=1.37 for California, but it is unclear how universal this value is. Therefore, caution must be used when inferring background rates from interevent-time statistics.
S11C-0714
BASS, a scale-invariant, branching aftershock model that separates aftershocks from background seismicity.
The epidemic type aftershock sequence (ETAS) model has been used to distinguish aftershocks (foreshocks) from background seismicity. A fundamental problem with the ETAS model is that the results are sensitive to the selection of the branching ratio. Also, in general, the ETAS model is not scale invariant. In order to overcome these difficulties we have introduced the branching aftershock sequence (BASS) model (GRL, 34, L12303, 2007). The BASS model is fully scale invariant. It is not necessary to specify either a largest earthquake or a smallest earthquake (aftershock). In the BASS model the frequency-magnitude statistics of aftershock sequences are fully specified by their b-value and the modified form of Bath's law. These parameters along with the parameters in the generalized form of Omori's law fully specify the relative roles of foreshocks, main shocks and aftershocks. A test of the model is to predict years in which background seismicity dominates versus years in which aftershock (foreshock) seismicity dominates. Utilizing accepted parameter values this test is successful.
S11C-0715
Using the ETAS model for catalog declustering and seismic background assessment.
The concept of background seismicity is strictly related to the identification of spontaneous and triggered earthquakes. The definition of foreshocks, main shocks and aftershocks is currently based on procedures depending on parameters whose values are notoriously assumed by subjective criteria. We propose a method for recognizing the background and the induced seismicity in statistical way. In fact, rather than aiming to a crude distinction of the events in these two categories, we prefer to assign to each of them a probability of being independent or triggered. This probability comes from an algorithm based on the ETAS model. A certain degree of subjectivity is still present in this procedure, but it is limited by the possibility of adjusting the free parameters of the algorithm by rigorous statistical criteria such as that of the maximum likelihood. The robustness of the method can be shown by comparing the results obtained selecting different time windows from a given catalog. In the application of the method to the seismicity of California, we analyze how the determination of some of the free parameters of the algorithm affects the results. Finally, we show how our statistical declustering algorithm may be used for mapping the background seismicity.
S11C-0716
A study of the unified scaling law of earthquakes in the Taiwan region
A recently proposed unified scaling law merging (1) Omori Law, (2) Gutenberg-Richter law, and (3) geometrical fractal distribution of epicenters, seems to successfully investigate the occurrence of earthquakes from a spatial- temporal perspective. This study plans to verify important questions arising from the definition of the model by doing three experiments. These experiments aim to: 1. understand the feasibility of applying this scaling law to the intrinsic characteristic seismicity in Taiwan, 2. ascertain the difference between aftershocks and main shocks in a unified scaling law by comparing earthquake time sequences with declustered ones, 3. investigate the differences among the scaling relationships obtained from various geological settings in Taiwan. Our results show that Regardless of the size of the cells and the cut-off magnitude, a distinct and unified scaling law is always obtained from the spatial-temporal occurrence of earthquakes in Taiwan. After declustering, the constant part that indicates the characteristic of the aftershock apparently disappears, and the slope of the fast decaying part that corresponds to the main shock remains almost the same. A Poisson distribution tends to be a better description for the main shock sequences. In addition, the scaling laws obtained from four different sub-regions in Taiwan, though being slightly different from each other, show a similar scaling relationship.
S11C-0717
Towards a Logical Distinction Between Swarms and Aftershock Sequences
The distinction between swarms and aftershock sequences has, up to this point, been fairly arbitrary and non- uniform. Typically 0.5 to 1 order of magnitude difference between the mainshock and largest aftershock has been a traditional choice, but there are many exceptions. Seismologists have generally assumed that the mainshock carries most of the energy, but this is only true if it is sufficiently large compared to the size and numbers of aftershocks. Here we present a systematic division based on energy of the aftershock sequence compared to the energy of the largest event of the sequence. It is possible to calculate the amount of aftershock energy assumed to be in the sequence using the b-value of the frequency-magnitude relation with a fixed choice of magnitude separation (M-mainshock minus M-largest aftershock). Assuming that the energy of an aftershock sequence is less than the energy of the mainshock, the b-value at which the aftershock energy exceeds that of the mainshock energy determines the boundary between aftershock sequences and swarms. The amount of energy for various choices of b-value is also calculated using different values of magnitude separation. When the minimum b-value at which the sequence energy exceeds that of the largest event/mainshock is plotted against the magnitude separation, a linear trend emerges. Values plotting above this line represent swarms and values plotting below it represent aftershock sequences. This scheme has the advantage that it represents a physical quantity - energy - rather than only statistical features of earthquake distributions. As such it may be useful to help distinguish swarms from mainshock/aftershock sequences and to better determine the underlying causes of earthquake swarms.
S11C-0718
Change-Point Models for aftershock hazard analysis
The distribution of the magnitude of a sequence of aftershocks, especially, post to a strong mainshock usually depends on the time after the mainshock. Therefore, we propose a left-truncated exponential distribution for the magnitude of such a sequence which contains a change-point model for the scale parameters over time. We then discuss the testing for the change-point model and confidence interval for the change point. The proposed distribution is finally illustrated by using the sequence of aftershocks post to the Landers earthquake.