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The occurrence of earthquakes is now understood as brittle shear fracture releasing the elastic potential energy stored in the earth. Since the 1950s, many studies on the energy balance in earthquake faulting have been done, but there seems to be some incoherence among them. The essential reason is because various changes in conceptual framework happened during the last six decades, specifically the introduction of the new paradigm of plate tectonics in the 1960s, the concept of moment tensor as source representation in the 1970s, and the fault constitutive law governing rupture growth in the 1990s. Therefore, it will be worthwhile to reconsider the energetics of earthquake faulting from a current perspective. For this purpose, first of all, we summarize the basic concepts of elastic potential energy and moment tensor and review the general representation of earthquake sources and the origin of background crustal stress to confirm that the effect of earth's self-gravitation is negligible in the energetics of shear faulting. Next, as a starting point for discussion, we directly derive a basic equation of mechanical energy balance in dynamic shear faulting from the equation of motion for an elastic body subjected to tectonic-origin deviatoric stress. Then, we review the widely accepted formula for indirectly evaluating radiated seismic energy from a simplified energy balance equation and compare with the direct evaluation based on the analytical solution of displacement fields for a point dislocation source in order to call attention to inconsistency between them. The inconsistency comes from the omission of the effects of rupture growth rate in the simplified energy balance equation. So, finally, we review the energy balance at the tips of a propagating shear crack, which naturally leads to the introduction of the slip-weakening fault constitutive law as a fundamental equation governing earthquake rupture. Then, we discuss the whole process of earthquake rupture, consisting of initiation, acceleration, steady propagation, deceleration, and termination from the viewpoint of energy balance. [ABSTRACT FROM AUTHOR]

Key points logEs is proportional to 2.0ML for the Shoufeng earthquake sequence in Taiwan. A crossover magnitude detected at ML = 4.0 divides the MW–ML relation into two parts. For ML > 4.0, logM0 ∝ 0.67ML and MW ∝ ML; for ML

Continuous seismic signals are proposed as a useful quantitative information source for the estimation of rockfall properties. However, few studies have examined the characteristics of the seismic signal of fragmentation‐related rockfalls. In this study, a series of laboratory experiments designed with crushable analog blocks freefalling and impacting on a thin horizontal plate under different initial conditions (e.g., block volume, strength and fall height) were conducted. Strong correlations are observed between the rockfall properties and the seismic parameters when considering the rock fragmentation during impact. However, these relationships are observed only when the variation in potential energy spans over one order of magnitude, indicating that the application of seismic signals is limited by rockfall properties. In particular, the seismic energy calculated by the diffuse method is the most stable seismic parameter that is highly correlated with the potential energy of rockfalls. By compiling the available data of the seismic signals of both natural and experimental rockfalls from previous studies and our experiments, we found that the relationship between the seismic energy and the potential energy of rockfalls follows a power law model at all scales. The exponent of the power law function ranges from 1.11 to 1.69. Rock strength can significantly affect the seismic features, which are quantitatively discussed. Rock fragmentation acts as an intermediate variable, which is controlled by rockfall properties and consequently affects the corresponding seismic characteristics. Furthermore, rock fragmentation reduces the efficiency of the conversion of potential energy to seismic energy of rockfalls. Plain Language Summary: Rockfalls are common natural hazards that threaten lives, local communities and infrastructures in mountainous areas. The movement of rockfalls may radiate seismic signals that can be captured by professional equipment. These seismic signals present useful information about the initial condition (e.g., volume, fall height) and movement process of rockfalls, which is important for disaster mitigation. We designed a series of laboratory experiments, modeling the process by which fragmental material freefalls and impacts a horizontal plate (simplified rockfall). By gathering and analyzing the seismic signals, empirical functions between the parameters calculated from seismic signals and fragmental rockfall properties are built. These empirical functions can be used to infer the rockfall properties (potential energy, volume, fall height, etc.) in real time based on the radiated seismic signals. Moreover, we focus on the effects of rock strength and rock fragmentation on the seismic signals. These factors are seldom considered before but are important, as illustrated in our experiments. Our results may help further understand the relationships between rockfall properties and the features of corresponding seismic signals. Key Points: Empirical functions between seismic parameters and fragmental rockfall properties are establishedA qualitative illustration of the variation in seismic characteristics caused by rock fragmentation is presentedThe relationship between the seismic energy and the potential energy of rockfalls follows a power law model at all scales [ABSTRACT FROM AUTHOR]

Our models and understanding of the dynamics of earthquake rupture are based largely on estimates of earthquake source parameters, such as stress drop and radiated seismic energy. Unfortunately, the measurements, especially those of small and moderate-sized earthquakes (magnitude less than about 5 or 6), are not well resolved, containing significant random and potentially systematic uncertainties. The aim of this review is to provide a context in which to understand the challenges involved in estimating these measurements, and to assess the quality and reliability of reported measurements of earthquake source parameters. I also discuss some of the ways progress is being made towards more reliable parameter measurements. At present, whether the earthquake source is entirely self-similar, or not, and which factors and processes control the physics of the rupture remains, at least in the author's opinion, largely unconstrained. Detailed analysis of the best recorded earthquakes, using the increasing quantity and quality of data available, and methods less dependent on simplistic source models is one approach that may help provide better constraints. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'. [ABSTRACT FROM AUTHOR]

Locked segment is the geological structure that governs the generation of tectonic earthquakes. As such， studying the energy conversion and allocation principle during the damage process of locked segment can make enhanced insights into its damage behavior and energy evolution mechanism. Based on the energy conservation principle， the relationship between conversion and allocation of elastic strain energy stored in a locked segment during crack propagation was elucidated， and a formula for calculating the radiated seismic energy generated from a cracking event in the locked segment was proposed. Hereby， using the brittle failure theory of multiple locked segments of seismogenic faults， the magnitude criterion for identifying a mainshock was derived， the equivalence between the cumulative Benioff strain ratio and the shear strain ratio was demonstrated， and the methods for calculating the source parameters of cracking event in a locked segment were presented. Case studies show that the methods are reliable. The present results have broad application prospects in identification of mainshock， estimation and verification of source parameters. [ABSTRACT FROM AUTHOR]

To provide reliable and quick estimation of magnitude for moderate to large earthquakes at regional distances, two magnitude relations specific to the peninsular shield have been proposed based on long-period magnitude (MA) and energy magnitude (ME), using broadband velocity data of 23 regional events recorded at 18-station seismic network in the state of Telangana and Andhra Pradesh, India. MA is estimated using amplitude of filtered (0.03–0.08 Hz) broadband velocity seismograms, while ME is estimated based on radiated energy using broadband velocity spectra. It is observed that MA for larger events with Mw > 7.2 saturates, whilst ME does not suffer from saturation even for larger events. Thus, it is apparent that these two magnitude relations can provide magnitude estimates without saturation for all moderate to large regional earthquakes, which, in turn, can provide a homogeneous catalogue for moderate to large regional Indian earthquakes. The data transmission from remote stations to the central server at CSIR-National Geophysical Research Institute (NGRI) is quasi-real-time since it is connected by GPRS and VSAT. Using the proposed region specific magnitude relationships it becomes possible to estimate reliable magnitudes for moderate to large regional Indian earthquakes (Mw ≤ 7.2) within 30 min of the occurrence of an event. [ABSTRACT FROM AUTHOR]

We present a detailed historical review of early attempts to quantify seismic sources through a measure of the energy radiated into seismic waves, in connection with the parallel development of the concept of magnitude. In particular, we explore the derivation of the widely quoted "Gutenberg–Richter energy–magnitude relationship" 1 log 10 E = 1.5 M s + 11.8 (E in ergs), and especially the origin of the value 1.5 for the slope. By examining all of the relevant papers by Gutenberg and Richter, we note that estimates of this slope kept decreasing for more than 20 years before Gutenberg's sudden death, and that the value 1.5 was obtained through the complex computation of an estimate of the energy flux above the hypocenter, based on a number of assumptions and models lacking robustness in the context of modern seismological theory. We emphasize that the scaling laws underlying this derivation, as well as previous relations with generally higher values of the slope, suffer violations by several classes of earthquakes, and we stress the significant scientific value of reporting radiated seismic energy independently of seismic moment (or of reporting several types of magnitude), in order to fully document the rich diversity of seismic sources. [ABSTRACT FROM AUTHOR]

The present study estimates source parameters and proposes scaling relationships for moderate size earthquakes (mb 3.7-5.8) in seismically active North-East India region. The study is based upon the spectral analysis of high-quality waveforms comprising of P- and S-waves obtained from strong ground motion (SMA) records of 50 earthquakes that has occurred in the region. A two-step procedure is adopted to estimate the earthquake source parameters. It has been observed that the average seismic moment and source radii vary from 1.05 × 1015 to 1.99 × 1017 N-m and 500 to 2000 m, respectively. The average corner frequency ratio [fC(P)/fC(S)] of P-wave and S-wave is found to be 1.2, which shows the shift in the corner frequency. The total estimated energy varies between 9.22 × 1010 and 1.42 × 1014 J, while the average stress drop varies from 1.8 to 29.4 MPa. One of the major outcome of this study is that the stress drop does not vary significantly with the magnitude and self-similarity exist among the earthquakes in North-East India region. The scaling relation between the seismic moment and the corner frequency is Mofc3=1.35×1017N- ms-3. The median stress drop value for NE India region is found to be about 9.2 MPa. The earthquake source parameters and the scaling relations developed in this study will be useful for carrying scenario based seismic hazard analysis studies in the NE India region. [ABSTRACT FROM AUTHOR]

Seismicity induced by the injection of fluid into the fractured ground is one of the most challenging issues facing geothermal and deep wastewater disposal industries. This paper introduces an energy-based numerical methodology to study roles of fluid injection in triggering rupture (seismic slip) along preexisting faults. The methodology is developed in the Universal Distinct Element Code (UDEC) using its quasi-static and dynamic schemes and calculates the total seismic energy radiated by a rupture when more energy is made available in the system than can be stored or consumed. As an example of the application of the developed methodology, we study effects of fluid injection on rupture dynamics by pressurizing a single fault surrounded by impermeable rock, representing a simplified analogy for the injection process in deep wastewater disposal and geothermal activities. We discuss effects of raising the fluid pressure on initiating rupture over well-oriented (or critically loaded) and misoriented faults. Results show that fluid injection can trigger a rupture along both well-oriented and misoriented faults although the notion of seismicity may be observed along the well-oriented fault as early as the beginning of the injection process. The well-oriented fault generates higher seismic energy magnitude as more energy is available for rupture due to the higher peak shear stress and stress drop on the fault. Making simplifying assumptions, this study also found that fluid can be injected under a high-pressure increment before and after the fault initial activation while the radiated seismic energy remains relatively insignificant. However, gradually increasing the fluid pressure at the onset of rupture reduces the radiated seismic energy by 30%. Comparing the seismic moment and radiated seismic energy for each event reveals that while radiated seismic energy varies between different values of pressure increment, the calculated seismic moment stays constant, showing the possible ineffectiveness of the seismic moment in representing the intensity of injection-induced ruptures. [ABSTRACT FROM AUTHOR]

The 10–11 July 2015 partial collapses of the lava dome in the crater of Volcán de Colima, México, were accompanied by a sequence of two-stage multiple PDCs, separated by a 15-h interval, with a total bulk volume of 14.2 × 10 6 m 3 of fragmentary material and runout distances reaching 9.1 and 10.3 km, respectively (Reyes-Dávila et al., 2016). Broad-band seismic signals, associated with the PDCs and recorded at seismic station EZ5 installed at a distance of 4 km from the crater, were used for analysis of the 20-h eruption process. This process included two stages of the multiple PDCs emplacements, two one-hour periods of preliminary events to each of the stages, and the inter-stage period. Analysis of seismic signals allowed us to identify the types of volcanic events composing this eruption episode and estimate their quantitative characteristics and spectral parameters of generated seismic signals. It was shown that the seismic signals produced by PDCs emplacements, recorded during the two stages, were characterized by different characteristics. The second stage PDCs had radiated greater seismic energy than the PDCs emplaced during the first stage. Spectral analysis of the seismic signals, produced by PDCs, indicates a clearly separation in frequency content at 1.95 Hz between the higher-frequency events of the first stage and the lower-frequency events of the second stage of the PDCs emplacements. The obtained difference in the spectral contents of the seismic signals, produced by the movement of two multiple PDCs, may be supposed as a consequence of the proposed relative difference in the volumes of the PDCs of two multiple sequences due to a difference in the level of radiated seismic energy and a change in bottom conditions of the ravines during their passing along the ravines. Results of seismic study were used in discussion of the nature of the two-stage eruptive process. [ABSTRACT FROM AUTHOR]

The paper looks first into the history of the derivation of the currently common formulas for calculating seismic moment magnitude M and energy magnitude M into the type of data and relationships available in these years and the parameter assumptions made. The general relationship between M and M is analysed and formulated in physical terms. The original M- and M-defining relationships are then confronted with equivalent relationships derived on the basis of rich modern magnitude data measured according to recently accepted International Association of Seismology and Physics of the Earth's Interior (IASPEI) standards for (a) 20-s surface-wave data and (b) broadband body P wave data as well as M and E data based on digital broadband waveform inversion or integration. The agreement between old and new data and derived relationships is of different quality. The Richter log E- M relationship, which has been instrumental for deriving the current standard M formula, could be very well reproduced with orthogonally regressed M(20) and log E data, provided that the latter were not corrected for source mechanism-dependent radiation. In contrast, the relationships between old and modern m-log E as well as m- M(20) data pairs deviate significantly from the respective Gutenberg and Richter relationships. Also the average E/ M ratio assumed by Kanamori when deriving his M formula differs from those of respective recent data sets. But the various differences between old and new data and data relationships compensate each other partially when deriving related M and M formulas. Therefore, they do not justify the modification of the existing scaling formulas, also for very pragmatic reasons. On the other hand, most striking is the so far not yet considered and by far best correlation that exists between the IASPEI body-wave magnitude standard m(BB) and seismic energy E, both estimated via P wave broadband records. The scatter of the log E- m(BB) data pair plots is only half of that of log E- M(20). This questions the appropriateness of the current exclusive scaling of teleseismic M to the practically monochromatic long-period 20-s surface-wave magnitude M. The potential advantage of a complementary M formula, which scales the currently common teleseismic broadband P wave E data to P wave broadband m(BB), as well as the benefit of fast joint determination and interpretation of M and M in general, is discussed. [ABSTRACT FROM AUTHOR]

We estimate seismological fracture energies from two subsets of events selected from the seismic sequences of L'Aquila (2009), and Northridge (1994): 57 and 16 selected events, respectively, including the main shocks. Following Abercrombie and Rice (Geophys J Int 162: 406-424, ), we postulate that fracture energy (G) represents the post-failure integral of the dynamic weakening curve, which is described by the evolution of shear traction as a function of slip. Following a direct-wave approach, we compute mainshock-/aftershock-source spectral ratios, and analyze them using the approach proposed by Malagnini et al. (Pure Appl. Geophys., this issue, ) to infer corner frequencies and seismic moment. Our estimates of source parameters (including fracture energies) are based on best-fit grid-searches performed over empirical source spectral ratios. We quantify the source scaling of spectra from small and large earthquakes by using the MDAC formulation of W alter and Taylor (A revised Magnitude and Distance Amplitude Correction (MDAC2) procedure for regional seismic discriminants, ). The source parameters presented in this paper must be considered as point-source estimates representing averages calculated over specific ruptured portions of the fault area. In order to constrain the scaling of fracture energy with coseismic slip, we investigate two different slip-weakening functions to model the shear traction as a function of slip: (i) a power law, as suggested by Abercrombie and Rice (Geophys J Int 162: 406-424, ), and (ii) an exponential decay. Our results show that the exponential decay of stress on the fault allows a good fit between measured and predicted fracture energies, both for the main events and for their aftershocks, regardless of the significant differences in the energy budgets between the large (main) and small earthquakes (aftershocks). Using the power-law slip-weakening function would lead us to a very different situation: in our two investigated sequences, if the aftershock scaling is extrapolated to events with large slips, a power law (a la Abercrombie and Rice) would predict unrealistically large stress drops for large, main earthquakes. We conclude that the exponential stress evolution law has the advantage of avoiding unrealistic stress drops and unbounded fracture energies at large slip values, while still describing the abrupt shear-stress degradation observed in high-velocity laboratory experiments (e.g., Di Toro et al., Fault lubrication during earthquakes, Nature ). [ABSTRACT FROM AUTHOR]

A forward modeling of P-waves for the 2008 Wenchuan earthquake revealed at least seven sub-events that occurred during faulting with the largest event (i.e., the third sub-event) located at a position ~50 km northeast of the epicenter. Simulations of P-waves showed that it would be more appropriate to model the P-waves using thrust faulting for the first three sub-events and using strike-slip faulting for the last four. In other words, the faulting for the 2008 Wenchuan earthquake was composed substantially of two mechanisms; the former was a thrust faulting and the latter was a strike-slip rupture. The mechanical transition was near the town of Beichuan, ~100 km northeast of the epicenter. Variations in radiated seismic energy (ES) showed the largest ES released from the fourth sub-event. Results also indicated remarkable distinctions between ES and ES0 (called the available energy). On the whole, the total ES, which was higher than ES0 estimated from static stress drop, suggested that the earthquake should be interrupted by a stress model of abrupt-locking. Further, the former thrust faulting released a relatively lower amount of ES than the latter strike-slip event. Orowan’s stress model, i.e., ES ≈ ES0, can specify former thrust ruptures implying a high rupture velocity. Because ES > ES0 for latter strike-slip ruptures, a stress model of abrupt-locking, implying higher dynamic stress drop and lower friction during an earthquake, can account for the feature of the latter ruptures. This might suggest that the 2008 Wenchuan earthquake should have a high rupture velocity, perhaps approaching the crustal S-wave velocity or even higher. [ABSTRACT FROM AUTHOR]

Through a proposed multiple-event analysis of teleseismic P-waves, this study investigated the radiated seismic energy and rupture process of the 2010 JiaSian earthquake. Results showed that the earthquake comprised at least two sub-events. The first sub-event was followed by the second sub-event, ˜1.7 s later. The entire source duration was 5.4 s. Let the two sub-events occur on the same fault plane with a strike of 304° and a dip of 28°; the first sub-event had a relatively smaller seismic moment (M0) and larger radiated seismic energy (Es) than the second sub-event, and this leads to the Es/M0 of the first sub-event larger than that of the second sub-event thus. This feature implies that the first sub-event probably had a higher static stress drop during faulting. The total M0 was estimated to be 2.17 x 1018 Nm, corresponding to Mw = 6.15, and the total Es was ˜2.91 x 1013 Nm, larger than that estimated only from a single source. Subsequently, the Es/M0 was approximately 1.3 x 10-5, lower than ordinary earthquakes. The low static stress drop was probably responsible for the low Es/M0. Overall, the 2010 JiaSian earthquake was characterized by a relatively low ES/M0 and low static stress drop, and then the partial stress drop model would be relatively appropriate to interpret its rupture process. [ABSTRACT FROM AUTHOR]

Abstract: Examination of seismic records during the time interval of the Sago Mine disaster in 2006 revealed a small amplitude signal possibly associated with an event in the mine. Although the epicenter of the signature was located in the vicinity where the explosion occurred, it could not be unequivocally attributed to the explosion. A greater understanding about the seismicity from mine explosions is required in order to properly interpret critical seismic information. A seismic monitoring system located at NIOSH’s Lake Lynn Experimental Mine has monitored 16 experimental methane and coal dust-based explosions. This paper describes the research conducted to quantify a relationship between measured values of radiated seismic energy and peak explosive pressure generated. The radiated seismic energy takes into account seismic signature characteristics such as the frequency content, amplitude, and duration. On the other hand, the size of the explosion is a function of the experimental design, dependent on factors such as the presence of an explosion-containment structure, the mine geometry, and the amount of initial explosive fuel used during the explosion. The seismic signatures from methane and coal dust explosions were analyzed using standard waveform analysis procedures. The procedures used to estimate the radiated seismic energy were conducted using self-produced programs, which are explained in this paper. The radiated seismic energy estimates were considered to be relative values for each experiment. A relationship was derived to correlate the relative radiated seismic energy to the size of the explosion, defined as the peak pressure generated. It was also observed during this study that an explosion-containment structure can act as a major seismic source. Recommendations are made, based upon the findings of this study, for improved collection of seismic data in the future. [Copyright &y& Elsevier]

Starting from the classical empirical magnitude-energy relationships, in this article, the derivation of the modern scales for moment magnitude M and energy magnitude M is outlined and critically discussed. The formulas for M and M calculation are presented in a way that reveals, besides the contributions of the physically defined measurement parameters seismic moment M and radiated seismic energy E, the role of the constants in the classical Gutenberg-Richter magnitude-energy relationship. Further, it is shown that M and M are linked via the parameter Θ = log( E/ M), and the formula for M can be written as M = M + (Θ + 4.7)/1.5. This relationship directly links M with M via their common scaling to classical magnitudes and, at the same time, highlights the reason why M and M can significantly differ. In fact, Θ is assumed to be constant when calculating M. However, variations over three to four orders of magnitude in stress drop Δ σ (as well as related variations in rupture velocity V and seismic wave radiation efficiency η) are responsible for the large variability of actual Θ values of earthquakes. As a result, for the same earthquake, M may sometimes differ by more than one magnitude unit from M. Such a difference is highly relevant when assessing the actual damage potential associated with a given earthquake, because it expresses rather different static and dynamic source properties. While M is most appropriate for estimating the earthquake size (i.e., the product of rupture area times average displacement) and thus the potential tsunami hazard posed by strong and great earthquakes in marine environs, M is more suitable than M for assessing the potential hazard of damage due to strong ground shaking, i.e., the earthquake strength. Therefore, whenever possible, these two magnitudes should be both independently determined and jointly considered. Usually, only M is taken as a unified magnitude in many seismological applications (ShakeMap, seismic hazard studies, etc.) since procedures to calculate it are well developed and accepted to be stable with small uncertainty. For many reasons, procedures for E and M calculation are affected by a larger uncertainty and are currently not yet available for all global earthquakes. Thus, despite the physical importance of E in characterizing the seismic source, the use of M has been limited so far to the detriment of quicker and more complete rough estimates of both earthquake size and strength and their causal relationships. Further studies are needed to improve E estimations in order to allow M to be extensively used as an important complement to M in common seismological practice and its applications. [ABSTRACT FROM AUTHOR]

We investigate the fault parameters of the 2005 Miyagi-Oki (Japan) earthquake using duration variations of teleseismic P-waves. The results show that the earthquake has a thrust-type mechanism and a seismic moment of 4.46 x 1019 Nm. Rupture directivity analysis suggests that the earthquake occurred as a result of a bilateral faulting on the fault plane with a strike of 247°, a dip of 17° and a slip of 125°. The optimal rupture azimuth, measured counterclockwise from the strike on the fault plane, is 170° (or 350°). The rupture length and average source duration are estimated to be 73.4 km and 14.5 sec, respectively. Thus the rupture velocity is 2.53 km sec-1 (~0.57 times the value of S-wave velocity), which is lower than the value for other similarly sized earthquakes. This implies that the 2005 Miyagi-Oki earthquake was probably a slow event. Consequently, there may have been less release of high-frequency seismic energy, leading to lower radiated seismic energy and radiation efficiency (~0.32 - 0.48). In other words, relatively larger fracture energy occurred during earthquake faulting in addition to the heat due to friction. The ratio of the static stress drop to the apparent stress (> 2.0) also suggests that the earthquake can be modeled as a frictional overshoot in a stress model, which implies the transformation of a lower percentage of strain energy into seismic-wave energy during the process of earthquake rupturing. [ABSTRACT FROM AUTHOR]