Southern California Earthquake Catalog Research Articles

Increased earthquake rate prior to mainshocks

According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock—this law has received much less attention due to its large uncertainty. Here, we mainly study the inverse Omori law based on a highly detailed Southern California earthquake catalog, which is complete for magnitudes mc≥1 or even lower. First, we develop a technique to identify mainshocks, foreshocks, and aftershocks. We then find, based on a statistical procedure we developed, that the rate of earthquakes is higher a few days prior to a mainshock. We find that this increase is much smaller for (a) a catalog with a magnitude threshold of mc=2.5 and (b) for the Epidemic-Type Aftershocks Sequence (ETAS) model catalogs, even when used with a small magnitude threshold (i.e., mc=1). We also analyze the rate of aftershocks after mainshocks and find that the Omori-Utsu law does not hold for many individual mainshocks and that it may be valid only statistically when considering many mainshocks together. Yet, the analysis of the ETAS model based on the Omori-Utsu law exhibits similar behavior as that of the real catalogs, indicating the validity of this law.

Heterogeneity of Aftershock Productivity Along the Mainshock Ruptures and Its Advantage in Improving Short‐Term Aftershock Forecast

AbstractThis study introduces an improved hypocentral version of the space‐time Epidemic‐Type Aftershock Sequence (ETAS) model, entitled as the 3D‐finite source (3D‐FS) ETAS model, and applies it to the analysis of the Southern California earthquake catalog. By stochastic reconstruction, we are able to reconstruct the patterns of aftershock productivity density along the mainshock ruptures. Detailed analysis of the productivity patterns reveals that: (1) Directly triggered aftershocks make up 21% to 41% of all earthquakes within the mainshock rupture areas, and show significant spatial heterogeneity and temporal migrations; (2) Major aftershocks tend to locate in low productivity areas, at the edges of clusters formed by small aftershocks; (3) Large slip areas are depleted of aftershocks, over 60% of all productivity distributes in areas with slip less than 0.3 times of the maximum slip, and the trajectory of the productivity pattern on the fault plane demonstrates apparent compensation to coseismic slip. We relate the difference in triggering abilities of four mainshocks to the heat flow in corresponding regions. Simulation results suggest that the 3D‐FS ETAS model has apparent advantages of improving the performance of short‐term aftershock forecast. Moreover, the later aftershocks are more correlated with the locations of subsequent events than earlier aftershocks, suggesting that the migration of aftershocks is important for mitigating aftershock hazard.

Nowcasting Earthquakes in Southern California With Machine Learning: Bursts, Swarms, and Aftershocks May Be Related to Levels of Regional Tectonic Stress

AbstractSeismic bursts in Southern California are sequences of small earthquakes strongly clustered in space and time and include seismic swarms and aftershock sequences. A readily observable property of these events, the radius of gyration (RG), allows us to connect the bursts to the temporal occurrence of the largest M ≥ 7 earthquakes in California since 1984. In the Southern California earthquake catalog, we identify hundreds of these potentially coherent space‐time structures in a region defined by a circle of radius 600 km around Los Angeles. We compute RG for each cluster then filter them to identify those bursts with large numbers of events closely clustered in space, which we call “compact” bursts. Our basic assumption is that these compact bursts reflect the dynamics associated with large earthquakes. Once we have filtered the burst catalog, we apply an exponential moving average to construct a time series for the Southern California region. We observe that the RG of these bursts systematically decreases prior to large earthquakes, in a process that we might term “radial localization.” The RG then rapidly increases during an aftershock sequence, and a new cycle of “radial localization” then begins. These time series display cycles of recharge and discharge reminiscent of seismic stress accumulation and release in the elastic rebound process. The complex burst dynamics we observe are evidently a property of the region as a whole, rather than being associated with individual faults. This new method allows us to improve earthquake nowcasting, which is a technique to evaluate the current state of hazard in a seismically active region.

A coupled ETAS-I2GMM point process with applications to seismic fault detection

Epidemic-type aftershock sequence (ETAS) point process is a common model for the occurrence of earthquake events. The ETAS model consists of a stationary background Poisson process modeling spontaneous earthquakes and a triggering kernel representing the space–time-magnitude distribution of aftershocks. Popular nonparametric methods for estimation of the background intensity include histograms and kernel density estimators. While these methods are able to capture local spatial heterogeneity in the intensity of spontaneous events, they do not capture well patterns resulting from fault line structure over larger spatial scales. Here we propose a two-layer infinite Gaussian mixture model for clustering of earthquake events into fault-like groups over intermediate spatial scales. We introduce a Monte Carlo expectation-maximization (EM) algorithm for joint inference of the ETAS-I2GMM model and then apply the model to the Southern California Earthquake Catalog. We illustrate the advantages of the ETAS-I2GMM model in terms of both goodness of fit of the intensity and recovery of fault line clusters in the Community Fault Model 3.0 from earthquake occurrence data.

Simple statistics for complex Earthquake time distributions

Abstract. Here we investigated a statistical feature of earthquake time distributions in the southern California earthquake catalog. As a main data analysis tool, we used a simple statistical approach based on the calculation of integral deviation times (IDT) from the time distribution of regular markers. The research objective is to define whether and when the process of earthquake time distribution approaches to randomness. Effectiveness of the IDT calculation method was tested on the set of simulated color noise data sets with the different extent of regularity, as well as for Poisson process data sets. Standard methods of complex data analysis have also been used, such as power spectrum regression, Lempel and Ziv complexity, and recurrence quantification analysis, as well as multiscale entropy calculations. After testing the IDT calculation method for simulated model data sets, we have analyzed the variation in the extent of regularity in the southern California earthquake catalog. Analysis was carried out for different periods and at different magnitude thresholds. It was found that the extent of the order in earthquake time distributions is fluctuating over the catalog. Particularly, we show that in most cases, the process of earthquake time distributions is less random in periods of strong earthquake occurrence compared to periods with relatively decreased local seismic activity. Also, we noticed that the strongest earthquakes occur in periods when IDT values increase.

An Automatic Phase Picker for Local Earthquakes with Predetermined Locations: Combining a Signal‐to‐Noise Ratio Detector with 1D Velocity Model Inversion

We present a simple method to pick additional P and S phases for local earthquakes with predetermined locations. Different from conventional characteristic function techniques, our method incorporates 1D velocity inversion into phase picking. It first predicts phase arrivals using initial velocity models and available event locations and then applies a detector function to search genuine phase arrivals around the initial predictions. Using the newest searched phase arrivals (picks), the velocity models are updated accordingly and then used to predict more accurate arrival times. Such a procedure can be iterated multiple times, during which both phase picking and velocity model are improved. We perform a synthetic test with a 1D velocity model. The resulting phase picks are consistent with true arrivals, and true velocity models can be well recovered. Another test with real data recorded by the Anza Seismic Network in southern California shows that the resulting velocity models agree with the average Southern California Earthquake Center community models in this region. Out of 23,932 event–station pairs, 23,770 P picks and 21,935 S picks are obtained from this method. After four iterations, 90% of our P picks and 80% of our S picks have differences within 0.15 s from the phase picks of the Southern California Earthquake catalog. Given its simplicity and efficiency and ability to produce robust P and S picks and 1D velocity models, the technique is particularly suitable for a wide range of seismological research in which phase picks at additional stations and/or refined 1D velocity models are needed.

Remarkable changes in the distribution of the order parameter of seismicity before mainshocks

By analyzing in natural time the Southern California Earthquake Catalog (SCEC) during the period 1979–2003, the probability distribution of the order parameter of seismicity is studied. Remarkable changes in the feature of this distribution are identified well before the occurrence of the three major mainshocks reported by SCEC: Landers in 1992, Northridge in 1994 and Hector Mine in 1999. In addition, just before the occurrence of these mainshocks, i.e., for 100 successive events of magnitude M ⩾ 2.0 before each of them, their scaled order parameter probability distributions almost collapse onto a single curve and share over two orders of magnitude a characteristic “exponential tail” reflecting non-Gaussian fluctuations.

Tsallis-Based Nonextensive Analysis of the Southern California Seismicity

Nonextensive statistics has been becoming a very useful tool to describe the complexity of dynamic systems. Recently, analysis of the magnitude distribution of earthquakes has been increasingly used in the context of nonextensivity. In the present paper, the nonextensive analysis of the southern California earthquake catalog was performed. The results show that the nonextensivity parameter q lies in the same range as obtained for other different seismic areas, thus suggesting a sort of universal character in the nonextensive interpretation of seismicity.

Reply to "Comment on 'Changes of Reporting Rates in the Southern California Earthquake Catalog, Introduced by a New Definition of ML' by Thessa Tormann, Stefan Wiemer, and Egill Hauksson" by Duncan Carr Agnew

Monte Carlo magnitude mapping has been proposed as a tool to homogenize earthquake catalogs in time to overcome breaks in homogeneity of reporting. We analyze the uncertainty propagation for the b value due to that transformation and find that the additional error in b is negligibly small in relation to its standard deviation. However, in order to take the arbitrariness out of the proposed simulation, we argue that it has to be repeated a sufficient number of times to be stable, just like any other simulation technique. To illustrate this point, we show the example of cross-sectional mapping of the b value along the San Andreas fault near Parkfield, California.

Comment on "Changes of Reporting Rates in the Southern California Earthquake Catalog, Introduced by a New Definition of ML" by Thessa Tormann, Stefan Wiemer, and Egill Hauksson

Abstract Earthquake catalogs can be inhomogeneous because of changes in the definition of earthquake magnitude. Provided that a sufficient number of events have magnitudes defined in more than one system, it is possible to apply a Monte Carlo method to the observed joint distribution to convert sets of magnitudes from one system to another, improving any statistical analysis of the catalog. I demonstrate the method for the southern California catalog, in which the definition of local magnitude has recently been changed. Monte Carlo magnitude mapping appears to eliminate temporal changes that are otherwise present.

Changes of Reporting Rates in the Southern California Earthquake Catalog, Introduced by a New Definition of ML

Starting January 2008, local magnitudes M_L for southern California are determined by a new calibration that provides various improvements for determining M_L for small earthquakes. Magnitudes for the previous years are being recalculated and the catalog continuously updated, with the first year of overlapping data now being available. Recalibrating a magnitude scale can cause a break in homogeneity of reporting and often produces artifacts in the catalog statistics that can influence a wide range of seismicity studies. To search for such a break, we compare the old M_L and the new M_L catalogs for 2007. We find (1) the two magnitude values differ for 96% of the M_L events, and hand-determined magnitudes are also revised; (2) the magnitude differences are irregular from magnitude increases of up to 1.5 units to reductions by as much as 2.3 units, with an average change of -0.13 units; (3) the number of events above M 1.8 decreases by 32% for the new magnitude scale; (4) the completeness magnitude apparently drops by 0.3 units from 1.6 to 1.3; (5) the b-value reduces by approximately 0.2 units, dropping from 1.16 to 0.95; (6) the new magnitude calibration produces a more stable b-value estimate and can therefore be regarded as the better scaling. We document selected examples of how the change in magnitude calibration may affect seismicity- and hazard-related analyses that are based on the Southern California Seismic Network (SCSN) catalog. Especially the change of the b-value from ~1.1 to ~0.9 has potentially major implications for hazard related applications.

Magnitude‐dependent Omori law: Theory and empirical study

We propose a new physically based “multifractal stress activation” model of earthquake interaction and triggering based on two simple ingredients: (1) a seismic rupture results from activated processes giving an exponential dependence on the local stress and (2) the stress relaxation has a long memory. The combination of these two effects predicts in a rather general way that seismic decay rates after main shocks follow the Omori law ∼1/tpwith exponentsplinearly increasing with the magnitudeMLof the main shock. We carefully test the prediction on the magnitude dependence ofpby a detailed analysis of earthquake sequences in the southern California earthquake catalog. We find power law relaxations of seismic sequences triggered by main shocks with exponentspincreasing with the main shock magnitude by approximately 0.1–0.15 for each magnitude unit increase, fromp(ML= 3) ≈ 0.6 top(ML= 7) ≈ 1.1, in good agreement with the prediction of the multifractal model. The results are robust with respect to different time intervals, magnitude ranges, and declustering methods. When applied to synthetic catalogs generated by the epidemic‐type aftershock sequence (ETAS) model constituting a strong null hypothesis with built‐in magnitude‐independentpvalues, our procedure recovers the correct magnitude‐independentpvalues. Our analysis thus suggests that a new important fact of seismicity has been unearthed. We discuss alternative interpretations of the data and describe other predictions of the model.

Multifractal Scaling of Thermally Activated Rupture Processes

We propose a "multifractal stress activation" model combining thermally activated rupture and long memory stress relaxation, which predicts that seismic decay rates after mainshocks follow the Omori law approximately 1/t(p) with exponents p linearly increasing with the magnitude M(L) of the mainshock. We carefully test this prediction on earthquake sequences in the Southern California earthquake catalog: we find power law relaxations of seismic sequences triggered by mainshocks with exponents p increasing with the mainshock magnitude by approximately 0.1-0.15 for each magnitude unit increase, from p(M(L) = 3) approximately 0.6 to p(M(L) = 7) approximately 1.1, in good agreement with the prediction of the multifractal model.

Do earthquakes exhibit self-organized criticality?

If earthquakes are phenomena of self-organized criticality (SOC), statistical characteristics of the earthquake time series should be invariant after the sequence of events in an earthquake catalog are randomly rearranged. In this Letter we argue that earthquakes are unlikely phenomena of SOC because our analysis of the Southern California Earthquake Catalog shows that the first-return-time probability PM(T) is apparently changed after the time series is rearranged. This suggests that the SOC theory should not be used to oppose the efforts of earthquake prediction.

Intermediate-term earthquake prediction using the modified time-to-failure method in southern California

AbstractBased on retrospective modeling of earthquakes from the southern California earthquake catalog, along with previously published evaluations from the New Madrid Seismic Zone, the modified time-to-failure method may be used as an intermediate-term earthquake prediction technique for locating and predicting the size and time of a future mainshock. Modeling previous mainshocks for hypothesis development indicates that the method predicts the actual magnitude of the mainshock to within approximately ±0.5 magnitude units. The error associated with the time-of-failure is approximately ±1.1 years assuming the last precursory event is known. When the last event in the precursory sequence is not known, the predicted magnitude remains similar, but the predicted time will require refinement as additional events are added, with time, to the sequence. The mainshock location can also be identified within a circular region with a radius on the order of tens of kilometers. Criteria are provided for defining acceleration sequences and mainshock locations. The criteria reduce the number of false predictions but also eliminate some mainshocks from our evaluation. Mainshocks as small as magnitude 5.5, occurring between 1980 and 1995, were evaluated from the Southern California earthquake Catalog (SCC). The results were used in association with previous studies to develop a method that can be used for practical (future prediction) applications. The modified time-to-failure method was used to search the SCC for future mainshocks occurring after 17 August 1998. One region satisfied all the criteria and may be modeled by the modified time-to-failure method. The region likely to have a mainshock is a 65-km-radius area centered at 31.43° N, 115.47° W (northern Baja California, Mexico). The predicted magnitude is 6.36, ±0.55, and the predicted time of failure is 1998.565 (7/25/98), ±1.127 years. The addition of future precursory events will allow refinement of the predicted values.

Seismic quiescence before the landers (M = 7.5) and big bear (M = 6.5) 1992 earthquakes

The Landers earthquake of 28 June 1992 was preceded by a seismicity rate decrease of 75% in a volume approximately 11 by 23 by 15 km, located adjacent to and north of the epicenter. This anomaly started, for all magnitude bands, in January 1988, lasting 4.5 yr up to the mainshock. A smaller volume (7 by 14 by 15 km), to the south of the epicenter, showed a seismicity rate decrease of 75% starting in November 1989. The Big Bear earthquake of the same day was preceded by a 100% decrease of the seismicity rate, within a volume of approximately 13 by 22 by 15 km around the hypocenter. This volume contained 192 earthquakes of M ≧ 1.6 during the background period of 9 yr, but none during the 1.6 yr from December 1990 to 27 June 1992. The standard deviate z values characterizing these rate changes are very high, 6.3 and 12.3, respectively, and the anomalies are unique, not surpassed in significance by any other rate decrease in portion of the southern California earthquake catalog examined (117°06′W to 115°40′W and 33°45′N to 35°10′N). No seismicity rate change was found in the vicinity of the M = 6.1 Joshua Tree earthquake of 23 April 1992. Based on magnitude signatures and frequency-magnitude analyses, we conclude that the two quiescence anomalies could not have been due to a shift or a compression of the magnitude scale, and we interpret them as precursor anomalies. This analysis was carried out using the declustered earthquake catalog for the Landers area with corrections of 0.2 and 0.1 (August 1985 and May 1990) for two suspected magnitude shifts. With a new visualization technique we can investigate the stability, and changes, of the seismicity rate as a function of time and space. By mapping z values for rate changes at every time interval, and in volumes centered on a dense grid of points (latitude, longitude), this computer code furnishes an almost continuous sequence of smooth contour maps of the degree of rate changes. Any anomalies, artificial or real, may thus be defined accurately.