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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'.

Seismic 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. Plain Language Summary: Earthquake nowcasting is a method to evaluate the current state of seismic hazard from large earthquakes. In this paper, we connect the temporal occurrence of the largest and most potentially destructive earthquakes in California since 1984 with a readily observable property of small earthquake seismicity in the region. Our method involves the calculation of the time history of the average radius (horizontal size or extent) of "bursts" of small earthquakes, in the time leading up to and following major earthquakes in the region. We observe that the radius systematically and gradually decreases leading up to major earthquakes, increasing suddenly and discontinuously following the event. This observable pattern resembles the long‐hypothesized cycle of regional tectonic stress buildup and release, or elastic rebound, associated with large destructive earthquakes. We propose that the radius of these bursts might be considered to be a proxy variable for the changing state of regional stress in Southern California. Key Points: A new nowcasting method using earthquake swarms and aftershocks reveals the hazard from large M ≥ 7 earthquakes in Southern CaliforniaMachine learning defines a time series of bursts using an exponential moving average filtered and optimized to reveal temporal structureCycles of recharge and discharge associated with M ≥ 7 earthquakes are revealed, reminiscent of stress accumulation and release [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a branching aftershock sequence (BASS) model for seismicity. We suggest that the BASS model is a preferred alternative to the widely studied epidemic type aftershock sequence (ETAS) model. In the BASS model an initial, or seed, earthquake is specified. The subsequent earthquakes are obtained from the statistical distributions of magnitude, time, and location. The magnitude scaling is based on a combination of the Gutenberg–Richter scaling relation and the modified Båth’s law for the scaling relation of aftershocks relative to the magnitude of the seed earthquake. Omori’s law specifies the distribution of earthquake times, and a modified form of Omori’s law specifies the distribution of earthquake locations. Since the BASS model is specified by the four scaling relations, it is fully self-similar. This is not the case for ETAS. We also give a deterministic version of BASS and show that it satisfies Tokunaga side-branching statistics in a similar way to diffusion-limited aggregation (DLA). [Copyright &y& Elsevier]