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This paper describes the methods used to estimate positions, velocities, breaks, and seasonal terms from daily Global Navigation Satellite System (GNSS) measurements. Break detection and outlier removal have been automated so that decades of daily measurements from thousands of stations can be processed in a few hours. New measurements are added, and parameters are updated every week. Model parameters allow separation of interseismic, annual, coseismic, and postseismic signals. Tools available through GeoGateway (http://geo-gateway.org) allow rapid visualization and analysis of these terms for results that can be subsetted in time or space. Results show highly variable and nonlinear motion for GPS stations in southern California. The variable motion is related to seasonal motions, distributed tectonic motion, earthquakes, and postseismic motions that can continue for years. In some areas results suggest that additional processes are responsible for the observed motions. In general, following earthquakes, stations return to their long‐term motions after 2–3 years, though some exceptions occur. The use of the tools shows nonlinear motion in the Salton Trough of southern California related to the 2010 M7.2 El Mayor‐Cucapah earthquake, 2012 Brawley earthquake swarm, and a creep event on the Superstition Hills fault in 2017. Key Points: Positions, velocities, breaks, and seasonal terms for thousands of GNSS stations are updated every weekThese results can be used to study interseismic plate motion, coseismic deformation, postseismic deformation, and seasonal variationsThe use of these tools shows highly variable nonlinear motion of GPS stations in southern California [ABSTRACT FROM AUTHOR]

Following the Mw 6.9 Hawaiian earthquake on 4 May 2018, a remarkable quasiperiodic sequence of collapse events began at Halema'uma'u Crater at the summit of Kīlauea Volcano. The collapse events were associated with the drainage of magma from beneath the summit to the Lower East Rift Zone where fissure eruptions occurred. From 4 June 2018 to 2 August 2018 forty‐seven collapse events Mw 5.3 ± 0.1 occurred with the same temporal pattern of seismicity occurring between sequential pairs of collapse events. This paper focuses on this interevent seismicity pattern. Following a collapse event, there was a relatively quiescent period. This was followed by a sudden increase in seismicity, occurring at a nearly linear rate of 397 ± 96 earthquakes per day. These seismically active periods lasted until the next collapse event occurred. The pattern then repeated itself beginning again with postcollapse quiescence. We provide a statistical summary of this seismicity behavior by isolating the quiescent and active times to look at immediate precollapse and postcollapse activity. In mid‐June there were significant changes in the quiescent time lengths (decreased), the number of earthquakes during the interevent times (increased), and the rates of seismicity during the active times (increased). This type of interevent study could be conducted with other seismically well recorded, sequential caldera collapse events and also with other data types to look for potential physical explanations and an improved understanding of precollapse and postcollapse activity. Key Points: The same pattern of seismically quiescent and active periods occurred between every pair of collapse events at the summitThe active times had linear rates of seismicity, and the quiescent times had fewer earthquakesFollowing a large increase in June 2018, there was a general decrease in the active time seismicity rates until the end of the sequence [ABSTRACT FROM AUTHOR]

Uninhabited aerial vehicle synthetic aperture radar (UAVSAR) observations 2009–2017 of the Yuha Desert area and Global Positioning System (GPS) time series encompassing the region reveal a northward migrating pattern of deformation following the 4 April 2010 Mw7.2 El Mayor‐Cucapah (EMC) earthquake. The north end of the EMC rupture exhibits an asymmetric pattern of deformation that is substantial and smooth northeast of the rupture and limited but with surface fracturing slip northwest. The earthquake triggered ~1 cm of surface coseismic slip at the Yuha fault, which continued to slip postseismically. 2.5 cm of Yuha fault slip occurred by the time of the 15 June 2010 Mw5.7 Ocotillo aftershock and 5 cm of slip occurred by 2017 following a logarithmic afterslip decay 16‐day timescale. The Ocotillo aftershock triggered 1.4 cm of slip on a northwest trend extending to the Elsinore fault and by 7 years after the EMC earthquake 2.4 cm of slip had accumulated with a distribution following an afterslip function with a 16‐day timescale consistent with other earthquakes and a rate strengthening upper crustal sedimentary layer. GPS data show broad coseismic uplift of the Salton Trough and delayed postseismic motion that may be indicative of fluid migration there and subsidence west of the rupture extension, which continues following the earthquake. The data indicate that the Elsinore, Laguna Salada, and EMC ruptures are part of the same fault system. The results also suggest that north‐south shortening and east‐west extension across the region drove fracture advancing step tectonics north of the EMC earthquake rupture. Plain Language Summary: Airborne radar and Global Positioning System observations of the Yuha Desert and Salton Trough suggest that the 2010 M7.2 El Mayor ‐ Cucapah earthquake rupture, the Laguna Salada fault in Baja California, Mexico, and the Elsinore fault in California are part of the same fault system. The M5.7 Ocotillo aftershock links these faults and is a result of stress propagation from afterslip on the El Mayor ‐ Cucapah rupture. Further east in the Salton Trough fluid migration also contributes to the observed results. Key Points: The Mw5.7 Ocotillo aftershock of the El Mayor‐Cucapah earthquake extended north from a mainshock surface fracture to the Elsinore faultPostseismic slip on the Yuha fault and Ocotillo section and uplift in the Salton Trough continued for several years following the eventSalton Trough spreading causes left slip on the Yuha fault resulting in a left step that links the Laguna Salada and Elsinore faults [ABSTRACT FROM AUTHOR]

Fracking is a popular term referring to hydraulic fracturing when it is used to extract hydrocarbons. We distinguish between low-volume traditional fracking and the high-volume modern fracking used to recover large volumes of hydrocarbons from shales. Shales are fine-grained rocks with low granular permeabilities. During the formation of oil and gas, large fluid pressures are generated. These pressures result in natural fracking, and the resulting fracture permeability allows oil and gas to escape, reducing the fluid pressures. These fractures may subsequently be sealed by mineral deposition, resulting in tight shale formations. The objective of modern fracking is to reopen these fractures and/or create new fractures on a wide range of scales. Modern fracking has had a major impact on the availability of oil and gas globally; however, there are serious environmental objections to modern fracking, which should be weighed carefully against its benefits. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce a framework for developing earthquake forecasts usingVirtual Quake (VQ), the generalized successor to the perhaps better known Virtual California (VC) earthquake simulator. We discuss the basic merits and mechanics of the simulator, and we present several statistics of interest for earthquake forecasting. We also show that, though the system as a whole (in aggregate) behaves quite randomly, (simulated) earthquake sequences limited to specific fault sections exhibit measurable predictability in the form of increasing seismicity precursory to large m>7 earthquakes. In order to quantify this, we develop an alertbased forecasting metric, and show that it exhibits significant information gain compared to random forecasts. We also discuss the long-standing question of activation versus quiescent type earthquake triggering. We show that VQ exhibits both behaviours separately for independent fault sections, some fault sections exhibit activation type triggering, while others are better characterized by quiescent type triggering. We discuss these aspects of VQ specifically with respect to faults in the Salton Basin and near the El Mayor-Cucapah region in southern California, USA and northern Baja California Norte, Mexico. [ABSTRACT FROM AUTHOR]

Abstract: Tectonic motion across the Los Angeles region is distributed across an intricate network of strike‐slip and thrust faults that will be released in destructive earthquakes similar to or larger than the 1933 M6.4 Long Beach and 1994 M6.7 Northridge events. Here we show that Los Angeles regional thrust, strike‐slip, and oblique faults are connected and move concurrently with measurable surface deformation, even in moderate magnitude earthquakes, as part of a fault system that accommodates north‐south shortening and westerly tectonic escape of northern Los Angeles. The 28 March 2014 M5.1 La Habra earthquake occurred on a northeast striking, northwest dipping left‐lateral oblique thrust fault northeast of Los Angeles. We present crustal deformation observation spanning the earthquake showing that concurrent deformation occurred on several structures in the shallow crust. The seismic moment of the earthquake is 82% of the total geodetic moment released. Slip within the unconsolidated upper sedimentary layer may reflect shallow release of accumulated strain on still‐locked deeper structures. A future M6.1–6.3 earthquake would account for the accumulated strain. Such an event could occur on any one or several of these faults, which may not have been identified by geologic surface mapping. [ABSTRACT FROM AUTHOR]

Abstract: The physiology and behaviour of captive cuttlefish have been well studied over recent decades and yet very few parallel studies have investigated the movements and behaviour of free-ranging animals. One reason for this gap is that methods for longer term tracking are not well developed for the majority of species, especially those of smaller size. In this study we describe a methodology for the long-term attachment of electronic tags to free-ranging cuttlefish of a broad size range. Five common cuttlefish Sepia officinalis (122–240mm mantle length) were fitted with temperature and depth-logging archival tags attached to the internal cuttlebone of the living animal (tag weight was <1.8% of body weight). Tagged animals recovered rapidly from sedative and surgical procedures and resumed feeding within 24h of tag attachment. Laboratory-kept cuttlefish maintained in a 2-m deep aquarium exhibited diel vertical movements, spending daylight hours close to the bottom and ascending into the water column at night, a behaviour which is consistent with normal diel vertical migration seen in other marine organisms such as zooplankton and fish. That regular feeding and expected patterns of depth use were observed indicates that tag attachment did not impede normal behaviours. Furthermore, tags remained attached to laboratory cuttlefish for up to 5months, from first tagging through to natural mortality, and with the tag remaining attached to the cuttlebone post mortem. We also found that cuttlebones with attached tags remained buoyant at the water's surface post mortem, offering the unique opportunity to recover archival tags from cuttlebones washed ashore. The capacity for long-term attachment to juvenile cuttlefish and recovery following natural mortality identifies the potential of this method for recording near ‘lifetime’ behaviour and movements of cuttlefish in their natural environment. [Copyright &y& Elsevier]

We quantify the seismicity on the island of Taiwan using the frequency–magnitude statistics of earthquakes since 1900. A break in Gutenberg–Richter scaling for large earthquakes in global seismicity has been observed, this break is also observed in our Taiwan study. The seismic data from the Central Weather Bureau Seismic Network are in good agreement with the Gutenberg–Richter relation taking b ≈ 1 when M < 7. For large earthquakes, M ≥ 7, the seismic data fit Gutenberg–Richter scaling with b ≈ 1.5. If the Gutenberg–Richter scaling for M < 7 earthquakes is extrapolated to larger earthquakes, we would expect a M > 8 earthquake in the study region about every 25 yr. However, our analysis shows a lower frequency of occurrence of large earthquakes so that the expected frequency of M > 8 earthquakes is about 200 yr. The level of seismicity for smaller earthquakes on Taiwan is about 12 times greater than in Southern California and the possibility of a M ≈ 9 earthquake north or south of Taiwan cannot be ruled out. In light of the Fukushima, Japan nuclear disaster, we also discuss the implications of our study for the three operating nuclear power plants on the coast of Taiwan. [ABSTRACT FROM AUTHOR]

Abstract: We identify two distinct scaling regimes in the frequency–magnitude distribution of global earthquakes. Specifically, we measure the scaling exponent b =1.0 for “small” earthquakes with 5.5< m <7.6 and b =1.5 for “large” earthquakes with 7.6< m <9.0. This transition at m t =7.6, can be explained by geometric constraints on the rupture. In conjunction with supporting literature, this corroborates theories in favor of fully self-similar and magnitude independent earthquake physics. We also show that the scaling behavior and abrupt transition between the scaling regimes imply that earthquake ruptures have compact shapes and smooth rupture-fronts. [Copyright &y& Elsevier]

We consider implications of the Regional Earthquake Likelihood Models (RELM) test results with regard to earthquake forecasting. Prospective forecasts were solicited for M ⩾ 4.95 earthquakes in California during the period 2006-2010. During this period 31 earthquakes occurred in the test region with M ⩾ 4.95.We consider five forecasts that were submitted for the test. We compare the forecasts utilizing forecast verification methodology developed in the atmospheric sciences, specifically for tornadoes. We utilize a "skill score" based on the forecast scores λfi of occurrence of the test earthquakes. A perfect forecast would have λfi = 1, and a random (no skill) forecast would have λfi = 2.86×10-3. The best forecasts (largest value of λfi) for the 31 earthquakes had values of λfi = 1.24 × 10-1 to λfi = 5.49 × 10-3. The best mean forecast for all earthquakes was λf = 2.84 × 10-2. The best forecasts are about an order of magnitude better than random forecasts. We discuss the earthquakes, the forecasts, and alternative methods of evaluation of the performance of RELM forecasts. We also discuss the relative merits of alarm-based versus probability-based forecasts. [ABSTRACT FROM AUTHOR]

Abstract: Topologically realistic simulations of earthquake faults systems have been constructed to understand the physics of interacting earthquake fault systems. We focus on one of these models, a simulation called Virtual California, that represents a model for the strike-slip fault system in California. In weather forecasting, current and past observations are routinely extrapolated forward to forecast future weather. The question addressed in this paper is whether a similar application of numerical simulations can be used in earthquake forecasting. Present simulation models are discussed and their ability to successfully generate earthquake recurrence statistics is demonstrated. An important question relates to how paleoseismic data can be used to constrain simulations, and whether these constrained simulations provide improved forecasts of future earthquakes. Here, we show first results from a consideration of these issues using a method of “datascoring”. The data are divided into “training intervals” and “testing intervals”. In the training intervals, the time history of paleoseismic data are used to evaluate space–time windows of simulations. Earthquakes following high-scoring space–time windows in the simulations are then used as a basis for developing waiting time statistics and used to forecast data in the testing intervals. In our present method, we focus on the problem of determining the timing of future earthquakes having magnitude m >7. Our preliminary conclusion is that the amount of paleoseismic data currently available does not as yet improve the waiting time statistics to a level significantly beyond a random (temporal) predictor. However, this conclusion is based on a set of studies that are not extensive, so further investigations may well reveal important new avenues. In particular, it may be that the true value of this approach lies in defining the probable spatial locations of future earthquakes, rather than their timing. [Copyright &y& Elsevier]

The last 12 months have provided further evidence of the potential for cascading ecological and socio-political crises that were warned of 12 months ago. Then a consensus statement from the Regional Action on Climate Change Symposium warned: "the Earth's climatic, ecological, and human systems are converging towards a crisis that threatens to engulf global civilization within the lifetimes of children now living." Since then, the consequences of a broad set of extreme climate events (notably droughts, floods, and fires) have been compounded by interaction with impacts from multiple pandemics (including COVID-19 and cholera) and the Russia-Ukraine war. As a result, new connections are becoming visible between climate change and human health, large vulnerable populations are experiencing food crises, climate refugees are on the move, and the risks of water, food, and climate disruption have been visibly converging and compounding. Many vulnerable populations now face serious challenges to adapt. In light of these trends, this year, RACC identifies a range of measures to be taken at global and regional levels to bolster the resilience of these populations in the face of such emerging crises. In particular, at all scales, there is a need for globally available local data, reliable analytic techniques, community capacity to plan adaptation strategies, and the resources (scientific, technical, cultural, and economic) to implement them. To date, the rate of growth of the support for climate change resilience lags behind the rapid growth of cascading and converging risks. As an urgent message to COP27, it is proposed that the time is now right to devote much greater emphasis, global funding, and support to the increasing adaptation needs of vulnerable populations., (© The Author(s) 2022.)

Nowcasting is a term originating from economics, finance, and meteorology. It refers to the process of determining the uncertain state of the economy, markets or the weather at the current time by indirect means. In this paper, we describe a simple two-parameter data analysis that reveals hidden order in otherwise seemingly chaotic earthquake seismicity. One of these parameters relates to a mechanism of seismic quiescence arising from the physics of strain-hardening of the crust prior to major events. We observe an earthquake cycle associated with major earthquakes in California, similar to what has long been postulated. An estimate of the earthquake hazard revealed by this state variable time series can be optimized by the use of machine learning in the form of the Receiver Operating Characteristic skill score. The ROC skill is used here as a loss function in a supervised learning mode. Our analysis is conducted in the region of 5° × 5° in latitude-longitude centered on Los Angeles, a region which we used in previous papers to build similar time series using more involved methods (Rundle & Donnellan, 2020, https://doi.org/10.1029/2020EA001097; Rundle, Donnellan et al., 2021, https://doi.org/10.1029/2021EA001757; Rundle, Stein et al., 2021, https://doi.org/10.1088/1361-6633/abf893). Here we show that not only does the state variable time series have forecast skill, the associated spatial probability densities have skill as well. In addition, use of the standard ROC and Precision (PPV) metrics allow probabilities of current earthquake hazard to be defined in a simple, straightforward, and rigorous way., (© 2022 The Authors. Earth and Space Science published by Wiley Periodicals LLC on behalf of American Geophysical Union.)

Interferometric synthetic aperture radar (InSAR) interferograms contain valuable information about the fault systems hidden beneath the surface of the Earth. In a new approach, we aim to fit InSAR ground deformation data using a distribution of multiple seismic point sources whose parameters are found by a genetic algorithm. The resulting source distribution could provide another useful tool in solving the difficult problem of accurately mapping earthquake faults. We apply the algorithm to an ALOS-2 InSAR interferogram and perform a multifractal analysis on the resulting distribution, finding that it exhibits multifractal properties. We report first results and discuss advantages and disadvantages of this approach., Competing Interests: The authors declare no conflicts of interest relevant to this study., (© 2021 The Authors.)

Charles Richter's observation that 'only fools and charlatans predict earthquakes,' reflects the fact that despite more than 100 years of effort, seismologists remain unable to do so with reliable and accurate results. Meaningful prediction involves specifying the location, time, and size of an earthquake before it occurs to greater precision than expected purely by chance from the known statistics of earthquakes in an area. In this context, 'forecasting' implies a prediction with a specification of a probability of the time, location, and magnitude. Two general approaches have been used. In one, the rate of motion accumulating across faults and the amount of slip in past earthquakes is used to infer where and when future earthquakes will occur and the shaking that would be expected. Because the intervals between earthquakes are highly variable, these long-term forecasts are accurate to no better than a hundred years. They are thus valuable for earthquake hazard mitigation, given the long lives of structures, but have clear limitations. The second approach is to identify potentially observable changes in the Earth that precede earthquakes. Various precursors have been suggested, and may have been real in certain cases, but none have yet proved to be a general feature preceding all earthquakes or to stand out convincingly from the normal variability of the Earth's behavior. However, new types of data, models, and computational power may provide avenues for progress using machine learning that were not previously available. At present, it is unclear whether deterministic earthquake prediction is possible. The frustrations of this search have led to the observation that (echoing Yogi Berra) 'it is difficult to predict earthquakes, especially before they happen.' However, because success would be of enormous societal benefit, the search for methods of earthquake prediction and forecasting will likely continue. In this review, we note that the focus is on anticipating the earthquake rupture before it occurs, rather than characterizing it rapidly just after it occurs. The latter is the domain of earthquake early warning, which we do not treat in detail here, although we include a short discussion in the machine learning section at the end., (© 2021 IOP Publishing Ltd.)

Invasion percolation is a model that was originally proposed to describe growing networks of fractures. Here we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic b-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing ("fracking"). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths l. But since the networks are characterized by their large-scale behavior, l≪L, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.

We analyze a new model for growing networks, the constrained Leath invasion percolation model. Cluster dynamics are characterized by bursts in space and time. The model quantitatively reproduces the observed frequency-magnitude scaling of earthquakes in the limit that the occupation probability approaches the critical bond percolation probability in d=2. The model may have application to other systems characterized by burst dynamics.

Seismic nowcasting uses counts of small earthquakes as proxy data to estimate the current dynamical state of an earthquake fault system . The result is an earthquake potential score that characterizes the current state of progress of a defined geographic region through its nominal earthquake "cycle." The count of small earthquakes since the last large earthquake is the natural time that has elapsed since the last large earthquake (Varotsos et al., 2006, https://doi.org/10.1103/PhysRevE.74.021123). In addition to natural time, earthquake sequences can also be analyzed using Shannon information entropy ("information"), an idea that was pioneered by Shannon (1948, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x). As a first step to add seismic information entropy into the nowcasting method, we incorporate magnitude information into the natural time counts by using event self-information. We find in this first application of seismic information entropy that the earthquake potential score values are similar to the values using only natural time. However, other characteristics of earthquake sequences, including the interevent time intervals, or the departure of higher magnitude events from the magnitude-frequency scaling line, may contain additional information.

A standard approach to quantifying the seismic hazard is the relative intensity (RI) method. It is assumed that the rate of seismicity is constant in time and the rate of occurrence of small earthquakes is extrapolated to large earthquakes using Gutenberg-Richter scaling. We introduce nowcasting to extend RI forecasting to time-dependent seismicity, for example, during an aftershock sequence. Nowcasting uses 'natural time'; in seismicity natural time is the event count of small earthquakes. The event count for small earthquakes is extrapolated to larger earthquakes using Gutenberg-Richter scaling. We first review the concepts of natural time and nowcasting and then illustrate seismic nowcasting with three examples. We first consider the aftershock sequence of the 2004 Parkfield earthquake on the San Andreas fault in California. Some earthquakes have higher rates of aftershock activity than other earthquakes of the same magnitude. Our approach allows the determination of the rate in real time during the aftershock sequence. We also consider two examples of induced earthquakes. Large injections of waste water from petroleum extraction have generated high rates of induced seismicity in Oklahoma. The extraction of natural gas from the Groningen gas field in The Netherlands has also generated very damaging earthquakes. In order to reduce the seismic activity, rates of injection and withdrawal have been reduced in these two cases. We show how nowcasting can be used to assess the success of these efforts.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'., (© 2018 The Author(s).)

Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low-permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the gas and oil. In order to model this process, we utilize a loopless nontrapping invasion percolation previously introduced to model optimal polymers in a strongly disordered medium and for determining minimum energy spanning trees on a lattice. We performed numerical simulations on a two-dimensional square lattice and find significant differences from other percolation models. Additionally, we find that the growing fracture network satisfies both Horton-Strahler and Tokunaga network statistics. As with other invasion percolation models, our model displays burst dynamics, in which the cluster extends rapidly into a connected region. We introduce an alternative definition of bursts to be a consecutive series of opened bonds whose strengths are all below a specified value. Using this definition of bursts, we find good agreement with a power-law frequency-area distribution. These results are generally consistent with the observed distribution of microseismicity observed during a high-volume frack.

Many driven threshold systems display a spectrum of avalanche event sizes, often characterized by power-law scaling. An important problem is to compute probabilities of the largest events ("Black Swans"). We develop a data-driven approach to the problem by transforming to the event index frame, and relating this to Shannon information. For earthquakes, we find the 12-month probability for magnitude m>6 earthquakes in California increases from about 30% after the last event, to 40%-50% prior to the next one.

The Regional Earthquake Likelihood Models (RELM) test of earthquake forecasts in California was the first competitive evaluation of forecasts of future earthquake occurrence. Participants submitted expected probabilities of occurrence of M ≥ 4.95 earthquakes in 0.1° × 0.1° cells for the period 1 January 1, 2006, to December 31, 2010. Probabilities were submitted for 7,682 cells in California and adjacent regions. During this period, 31 M ≥ 4.95 earthquakes occurred in the test region. These earthquakes occurred in 22 test cells. This seismic activity was dominated by earthquakes associated with the M = 7.2, April 4, 2010, El Mayor-Cucapah earthquake in northern Mexico. This earthquake occurred in the test region, and 16 of the other 30 earthquakes in the test region could be associated with it. Nine complete forecasts were submitted by six participants. In this paper, we present the forecasts in a way that allows the reader to evaluate which forecast is the most "successful" in terms of the locations of future earthquakes. We conclude that the RELM test was a success and suggest ways in which the results can be used to improve future forecasts.

Observations suggest that contemporary wildfire suppression practices in the United States have contributed to conditions that facilitate large, destructive fires. We introduce a forest-fire model with natural fire resistance that supports this theory. Fire resistance is defined with respect to the size and shape of clusters; the model yields power-law frequency-size distributions of model fires that are consistent with field observations in the United States, Canada, and Australia.

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that the occurrence of major earthquakes in California correlates with time intervals when fluctuations in small earthquakes are suppressed relative to the long term average. We estimate a probability of less than 1% that this coincidence is due to random clustering.

In this work the distribution of interoccurrence times between earthquakes in aftershock sequences is analyzed and a model based on a nonhomogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of interoccurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.