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Advancing the capabilities of earthquake nowcasting, the real-time forecasting of seismic activities remains a crucial and enduring objective aimed at reducing casualties. This multifaceted challenge has recently gained attention within the deep learning domain, facilitated by the availability of extensive, long-term earthquake datasets. Despite significant advancements, existing literature on earthquake nowcasting lacks comprehensive evaluations of pre-trained foundation models and modern deep learning architectures. These architectures, such as transformers or graph neural networks, uniquely focus on different aspects of data, including spatial relationships, temporal patterns, and multi-scale dependencies. This paper addresses the mentioned gap by analyzing different architectures and introducing two innovation approaches called MultiFoundationQuake and GNNCoder. We formulate earthquake nowcasting as a time series forecasting problem for the next 14 days within 0.1-degree spatial bins in Southern California, spanning from 1986 to 2024. Earthquake time series is forecasted as a function of logarithm energy released by quakes. Our comprehensive evaluation employs several key performance metrics, notably Nash-Sutcliffe Efficiency and Mean Squared Error, over time in each spatial region. The results demonstrate that our introduced models outperform other custom architectures by effectively capturing temporal-spatial relationships inherent in seismic data. The performance of existing foundation models varies significantly based on the pre-training datasets, emphasizing the need for careful dataset selection. However, we introduce a new general approach termed MultiFoundationPattern that combines a bespoke pattern with foundation model results handled as auxiliary streams. In the earthquake case, the resultant MultiFoundationQuake model achieves the best overall performance., Comment: 22 pages, 8 figures, 2 tables

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic (ROC) methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. Here we discuss a new method for earthquake nowcasting that uses an AI-enhanced deep learning model "QuakeGPT" that is based on an attention-based science transformer adapted for time series forecasting. Such dot product attention-based transformers were introduced by Vaswani et al. (2017), and are the basis for the new large language models such as ChatGPT. To use these science transformers, they must first be trained on a large corpus of data. A problem is that the existing history of reliable earthquake catalog data extends back in time only a few decades, which is almost certainly too short to train a model for reliable nowcasting/forecasting. As a result, we turn to earthquake simulations to train the transformer model. Specifically we discuss a simple stochastic earthquake simulation model "ERAS" that has recently been introduced. The ERAS model is similar to the more common "ETAS" models, the difference being that the ERAS model has only 2 novel, adjustable parameters, rather than the 6-8 adjustable parameters that characterize most ETAS models. Using this ERAS model, we then define a transformer model and train it using a long catalog of ERAS simulations, then apply it to an ERAS validation dataset with the transformer model. In this paper, we describe this new method and assess the applicability to observed earthquake catalogs for use in nowcasting/forecasting., Comment: 25 Pages, 10 Figures

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic (ROC) methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using statistical simulations of earthquake catalogs computed using Epidemic Type Aftershock Sequence (ETAS) simulations. ETAS earthquake simulations are currently in widespread use for a variety of tasks, in modeling, analysis and forecasting. After examining several of the standard ETAS models, we propose a version of the ETAS model that conforms to the standard ETAS statistical relations of magnitude-frequency scaling, aftershock scaling, Bath's law, and the productivity relation, but with an additional property. We modify the model to introduce variable non-Poisson aftershock clustering, inasmuch as we test the hypothesis that the information in the catalogs originates from aftershock clustering. We find that significant information in the catalogs arises from the non-Poisson aftershock clustering, implying that the common practice of de-clustering catalogs may remove information that would otherwise be useful in forecasting and nowcasting. We also show that the nowcasting method provides similar results with the the ETAS models as it does with observed seismicity., Comment: 17 pages, 3 figures, 1 table

We extend our previous model, avalanche-burst invasion percolation (AIP) by introducing long-range correlations between sites described by fractional Brownian statistics. In our previous models with independent, random site strengths, we reproduced a unique set of power-laws consistent with some of the b-values observed during induced seismicity. We expand upon this model to produce a family of critical exponents which could be characterized by the local long-range correlations inherent to host sediment. Further, in previous correlated invasion percolation studies, fractal behavior was found in only a subset of the range of Hurst exponent, $H$. We find fractal behavior persists for the entire range of Hurst exponent. Additionally, we show how multiple cluster scaling power laws results from changing the generalized Hurst parameter controlling long-range site correlations, and gives rise to a multifractal system. This emergent multifractal behavior plays a central role in allowing us to extend our model to better account for variations in the observed Gutenber-Richter b-values of induced seismicity., Comment: To be Published in Phys. Rev. E 2024

As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order phase transition mechanics due to the emergent scale invariance at the critical point. However for many systems, notions of phases and critical points are both artifical and cumbersome. We characterize the critical features of the avalanche burst invasion percolation(AIP) model since it exists as hybrid critical system(of which many self-organized critical systems may fall under). We find behavior strongly representative of critical systems, namely, from the presence of a critical Fisher type distribution, $n_s(\tau, \sigma)$, but other essential features absent like an order parameter and to a lesser degree hyperscaling. This suggests that we do not need a full phase transition description in order to observe scale invariant behavior, and provides a pathway for more suitable descriptions, Comment: To be Published in Phys. Rev. E (2023)

Yes. Interval statistics have been used to conclude that major earthquakes are random events in time and cannot be anticipated or predicted. Machine learning is a powerful new technique that enhances our ability to understand the information content of earthquake catalogs. We show that catalogs contain significant information on current hazard and future predictability for large earthquakes., Comment: Preprint, submitted to Earth and Space Science

We review previous approaches to nowcasting earthquakes and introduce new approaches based on deep learning using three distinct models based on recurrent neural networks and transformers. We discuss different choices for observables and measures presenting promising initial results for a region of Southern California from 1950-2020. Earthquake activity is predicted as a function of 0.1-degree spatial bins for time periods varying from two weeks to four years. The overall quality is measured by the Nash Sutcliffe Efficiency comparing the deviation of nowcast and observation with the variance over time in each spatial region. The software is available as open-source together with the preprocessed data from the USGS.

This paper describes the use of the idea of natural time to propose a new method for characterizing the seismic risk to the world's major cities at risk of earthquakes. Rather than focus on forecasting, which is the computation of probabilities of future events, we define the term seismic nowcasting, which is the computation of the current state of seismic hazard in a defined geographic region., Comment: 9 Figures, 4 Tables

Injections of large volumes of water into tight shale reservoirs allows the extraction of oil and gas not previously accessible. This large volume "super" fracking induces damage that allows the oil and/or gas to flow to an extraction well. The purpose of this paper is to provide a model for understanding super fracking. We assume that water is injected from a small spherical cavity into a homogeneous elastic medium. The high pressure of the injected water generates hoop stresses that reactivate natural fractures in the tight shales. These fractures migrate outward as water is added creating a spherical shell of damaged rock. The porosity associated with these fractures is equal to the water volume injected. We obtain an analytic expression for this volume. We apply our model to a typical tight shale reservoir and show that the predicted water volumes are in good agreement with the volumes used in super fracking., Comment: 17 pages, 4 figures in International Journal of Damage Mechanics

Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high pressures and an extensive distribution of natural fractures which reduce the pressures. With time these fractures heal, sealing the remaining oil and gas in place. High volume fracking opens the healed fractures allowing the oil and gas to flow the horizontal productions wells. We model the injection process using invasion percolation. We utilize a 2D square lattice of bonds to model the sealed natural fractures. The bonds are assigned random strengths and the fluid, injected at a point, opens the weakest bond adjacent to the growing cluster of opened bonds. Our model exhibits burst dynamics in which the clusters extends rapidly into regions with weak bonds. We associate these bursts with the microseismic activity generated by fracking injections. A principal object of this paper is to study the role of anisotropic stress distributions. Bonds in the $y$-direction are assigned higher random strengths than bonds in the $x$-direction. We illustrate the spatial distribution of clusters and the spatial distribution of bursts (small earthquakes) for several degrees of anisotropy. The results are compared with observed distributions of microseismicity in a fracking injection. Both our bursts and the observed microseismicity satisfy Gutenberg-Richter frequency-size statistics., Comment: 14 pages, 10 figures

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 non-trapping 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 2D 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., Comment: 19 pages, 11 figures, http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.022119

We develop and implement a new type of global earthquake forecast. Our forecast is a perturbation on a smoothed seismicity (Relative Intensity) spatial forecast combined with a temporal time-averaged (Poisson) forecast. A variety of statistical and fault-system models have been discussed for use in computing forecast probabilities. Our paper takes a new approach. The idea is based on the observation that GR statistics characterize seismicity for all space and time. Small magnitude event counts (quake counts) are used as markers for the approach of large events. More specifically, if the GR b-value = 1, then for every 1000 M>3 earthquakes, one expects 1 M>6 earthquake. So if ~1000 M>3 events have occurred in a spatial region since the last M>6 earthquake, another M>6 earthquake should be expected soon. In physics, event count models have been called natural time models, since counts of small events represent a physical or natural time scale characterizing the system dynamics. In a previous paper, we used conditional Weibull statistics to convert event counts into a temporal probability for a given fixed region. In the present paper, we dispense with a fixed region, and develop a method to compute these Natural Time Weibull (NTW) forecasts on a global scale, using an internally consistent method, in regions of arbitrary shape and size. Among the results we find that the Japan region is at serious risk for a major (M>8) earthquake over the next year or two, a result that also follows from considering completeness of the Gutenberg-Richter relation., Comment: 26 pages, 0 figures; To be submitted to Geophysical Journal International

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular-automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.

Earthquake occurrence in nature is thought to result from correlated elastic stresses, leading to clustering in space and time. We show that 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., Comment: 5 pages, 3 figures. Submitted to PRL

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems., Comment: 24 pages 12 figures, revised version for Phys. Rev. E

We present a RELM forecast of future earthquakes in California that is primarily based on the pattern informatics (PI) method. This method identifies regions that have systematic fluctuations in seismicity, and it has been demonstrated to be successful. A PI forecast map originally published on 19 February 2002 for southern California successfully forecast the locations of sixteen of eighteen M>5 earthquakes during the past three years. The method has also been successfully applied to Japan and on a worldwide basis. An alternative approach to earthquake forecasting is the relative intensity (RI) method. The RI forecast map is based on recent levels of seismic activity of small earthquakes. Recent advances in the PI method show considerable improvement, particularly when compared with the RI method using relative operating characteristic (ROC) diagrams for binary forecasts. The RELM application requires a probability for each location for a number of magnitude bins over a five year period. We have therefore constructed a hybrid forecast in which we combine the PI method with the RI method to compute a map of probabilities for events occurring at any location, rather than just the most probable locations. These probabilities are further converted, using Gutenberg-Richter scaling laws, to anticipated rates of future earthquakes that can be evaluated using the RELM test., Comment: 6 pages, 4 figures (color), 1 table

Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to take advantage of the wave-like properties of seismic stresses and utilize the Hilbert transform to create complex eigenvectors out of measured time series. We show that Pattern Informatics analyses using complex eigenvectors create short-term forecast hot-spot maps that differ from hot-spot maps created using only real-valued data and suggest methods of analyzing the differences and calculating the information gain., Comment: 13 pages, 1 figure. Submitted to Tectonophysics on 30 August 2004