We derived scaling relationships for different seismic energy metrics for earthquakes around the globe with

The radiated seismic energy (

Choy and Boatwright (1995) reported a focal mechanism dependence of

Other approaches have also been used to calculate seismic energy, such as those based on finite-fault models (Ide, 2002; Venkataraman and Kanamori, 2004b; Senatorski, 2014). Ide (2002) calculated the radiated energy using an expression based on slip and stress on the fault plane. Energy estimates from this method tend to be smaller by about a factor of 3 compared with the integrating far-field waveforms method. Venkataraman and Kanamori (2004b) used a formula for the energy radiated seismically from a finite source as a function of the time-dependent seismic moment

The Kaverina fault classification ternary diagram used to classify focal mechanisms

Hypocenter location and rupture type classification of earthquakes with reported radiated seismic energy (

We retrieved and classified focal mechanism solutions from the Global Centroid Moment Tensor catalog (gCMT) (Dziewonski et al., 1981; Ekström et al., 2012) using a ternary diagram based on the Kaverina et al. (1996) projection. This approximation classifies focal mechanism into seven classes of earthquakes: (1) normal (N), (2) normal–strike-slip (N-SS), (3) strike-slip–normal (SS-N), (4) strike-slip (SS), (5) strike-slip–reverse (SS-R), (6) reverse–strike-slip (R-SS), and (7) reverse (R) (Fig. 1). For implementing fault-plane classification, we used the software FMC developed by Álvarez-Gómez (2019). Additionally, we used radiated seismic energy data and finite-fault models reported by the Incorporated Research Institutions for Seismology (IRIS) and the United States Geological Survey (USGS), respectively. To have homogeneity in the analyzed data, we did not include seismic energy observations and finite-fault models from other sources to avoid bias. IRIS reported automated

In the following, we describe the procedure used to calculate

Senatorski (2014) introduced a method to estimate energy parameters derived from kinematic slip models. In this method, the radiated seismic energy is expressed in terms of slip velocities using an overdamped dynamics approximation (Senatorski, 1994, 1995). The method provides two energy parameters: (1) the overdamped dynamics approximation (

The radiated seismic energy can also be calculated through moment rate functions of finite-fault models (Haskell, 1964; Aki and Richards, 1980; Rudnicki and Freund, 1981; Venkataraman and Kanamori, 2004b). By ignoring the contribution from

Regression results for the radiated seismic energy scaling relationships. The scaling relation is given by

The radiated seismic energy (

The overdamped dynamics approximation of the radiated energy (

The energy obtained from the averaged finite-fault model (

The radiated seismic energy based on moment rate functions (

Comparison between radiated seismic energy based on velocity flux integration (

Comparison between the ratio of radiated seismic energy based on velocity flux integration (

Comparison between the ratio of radiated seismic energy based on velocity flux integration (

Conversion relationships among the different types of energies.

We used different methods to quantify the radiated seismic energy. Table 1 shows the calculated scaling relationships for

The estimated energy-to-moment ratios plotted as a function of the seismic moment for all the rupture types

Energy-to-moment ratios with respect to depth for all rupture types

In terms of the

Estimations of average apparent stress (

Previous studies have provided evidence that mean apparent stress estimates can be obtained using regression models, specifically through the equation

Apparent stress (

Estimations of average apparent stress (

Our results also showed that N and N-SS events exhibit a bimodal distribution of

In this study, we analyzed radiated seismic energy and parameters that measure the amount of energy per unit of the moment, such as the apparent stress and the energy-to-moment ratio (also known as scaled energy or apparent strain), considering their respective particularities. The advantage of using

Furthermore, finite-fault seismic energy estimations are strongly affected by event location, the number of available data, faulting parameterization, and velocity structure. The degree of discrepancy between the finite-fault energy estimates (

Our results agree with previous estimates of

The radiated seismic energy scaled by seismic moment is an essential characterization of earthquake dynamics. The low

Venkataraman and Kanamori (2004a) reported that

Our results support

Nevertheless, other interpretations of the apparent stress variation are related to the mechanical properties of the rock, such as the reduction in rigidity in shallow subduction environments or increment in lithostatic pressure if no change in regional rigidity is assumed (Convers and Newman, 2011). The variation in such estimates concerning expected spatial variations in rigidity is an issue that still needs attention. Choy and Kirby (2004) also suggested that

In terms of the spatial distribution of

In the case of R earthquakes, the highest values of

Finally, when using seismic energy estimates based on finite-fault models (

We studied the radiated seismic energy, energy-to-moment ratio, and apparent stress of different types of faulting. Our data rely on different methodologies employing the velocity flux integration and finite-fault models to determine the seismic energy. The approach based on slip distributions involved the utilization of two techniques: (1) total moment rate functions and (2) overdamped dynamics approximation. We analyzed 3331 energy observations derived from integrating far-field waveforms. On the other hand, we used 231 finite-fault models. For all mechanism types,

In terms of the behavior of the

On the other hand,

All figures were plotted by the Generic Mapping Tools software package (GMT 5) (

Radiated seismic energy data are acquired from the IRIS Data Services Products: EQEnergy (

The supplement related to this article is available online at:

QRP designed the idea, developed the methodology, and performed the preliminary analyses. QRP and FRZ discussed and analyzed the results and wrote the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

Quetzalcoatl Rodríguez-Pérez was supported by the Mexican National Council for Humanities, Science, and Technology (CONAHCYT) Cátedras program (project no. 1126). F. Ramón Zúñiga was partially supported by UNAM-PAPIIT (grant no. IG101823).

This paper was edited by Simone Pilia and reviewed by Rodolfo Console and one anonymous referee.