Seismicity and magnitude distributions are fundamental for seismic hazard analysis. The Mexican subduction margin along the Pacific Coast is one of the most active seismic zones in the world, which makes it an optimal region for observation and experimentation analyses. Some remarkable seismicity features have been observed on a subvolume of this subduction region, suggesting that the observed simplicity of earthquake sources arises from the rupturing of single asperities. This subregion has been named SUB3 in a recent seismotectonic regionalization of Mexico. In this work, we numerically test this hypothesis using the TREMOL (sThochastic Rupture Earthquake MOdeL) v0.1.0 code. As test cases, we choose four of the most significant recent events (6.5

The variation in seismicity distributions for different regions is a key input for probabilistic seismic hazard analysis (PSHA), as well as for other hazard determination approaches. The frequency–magnitude distribution from individual faults determines the specific earthquake rate of a given size at each source point, which has an important influence on the PSHA outcome

Some authors have provided a possible explanation of the physics underlying the earthquake process observed in the transition from a GR-type to characteristic-type behavior. For example,

Studies on the frequency–magnitude distributions of earthquakes in the Pacific subduction regime of Mexico are not extensive. citetsingh1983 reported that the GR relation was not appropriate to model the occurrence of large earthquakes in the Mexican subduction zone. They found that the GR relation in the range

In this context,

Following

Considering the aforementioned observations on the seismicity of the Mexican SUB3 region, the motivation of this work is to present an alternative way to analyze the influence of the asperities on the frequency–magnitude distribution of that region. This study uses the sTochastic Rupture Earthquake MOdeL (TREMOL) scheme

As already mentioned above, we focus in this work on the Guerrero–Oaxaca SUB3 given that this region provides an ideal setting for testing the single-asperity paradigm with the aid of TREMOL. Moreover, the quality of the database allows us to validate our code, giving support to the extension of our numerical experiments to other regions where few earthquakes are registered due to scarce seismic networks. In this sense, our study intends to be useful to generate synthetic seismicities to allow earthquake databases to be completed, in order to carry out more accurate PSHA studies. We also consider that our study could be appropriate to study different configurations of seismic scenarios, such as the occurrence of large past events that lack records, or future events with a significant hazard as in the case of the Guerrero gap.

TREMOL is a numerical method for the simulation of the earthquake rupture process and is able to contemplate different seismic scenarios. In this work TREMOL starts with the occurrence of previous low-magnitude events and culminates with the mainshock. The current TREMOL implementation does not allow a full earthquake cycle to be simulated, because most of the tectonic load is spent during the whole process of the mainshock rupture and foreshocks, and no extra load is added during the simulation

As described by

the effective length

the effective width

the asperity size

the discrete number of cells

In addition, the following TREMOL parameters allow the load and fault strength distributions to be set, in addition to asperity features:

the load conservation parameter

the asperity strength value

the ratio of the asperity area

It is worth mentioning that the strength

The TREMOL workflow is summarized in three main stages: (i) a preprocessing stage where the input parameters are set, (ii) a processing stage that performs the FBM simulation of the whole rupture process, and (iii) a final postprocessing that converts output results into a synthetic seismic catalog.
During processing, TREMOL generates numerous smaller earthquakes until the rupture of the whole asperity area

Moreover, in order to compare the results obtained by the magnitude–area relations we also estimate the magnitude from the moment–magnitude relation given in

TREMOL is capable of estimating the rupture areas assigning physical units to the numerical domain. In this paper, we do not consider slip to compute the magnitude distributions. On the other hand, TREMOL is not able to model the stress drop since the tectonic load is simulated using dimensionless units. We estimate a mean load drop, not related to any physical unit.

To determine the seismicity curve of a given SA region, TREMOL computes, as a part of the postprocessing, the frequency–magnitude distribution associated with this region. In the case of the SUB3 region,

As basic testing data, we use four subduction earthquakes which occurred in the SUB3 region, from the database published by

It is important to emphasize that, according to results in

Data of four large earthquakes occurred in SUB3 and reported by

The SUB3 region is approximately delineated by the polygon shown in Fig.

The following list describes the global TREMOL's procedure carried out in this work.

Using the database “DB-FiniteFault-2018”, we identified all earthquakes with a magnitude greater than or equal to 6.5 and occurred within the SUB3 region after 1988 (Table

We apply TREMOL v0.1.0 to simulate the seismic activity at each SA region. Even though these SA regions are depicted as simple rectangles in Fig.

We finally add the four individual synthetic curves to obtain an aggregated seismicity curve for the study area. This area corresponds to 15 %–20 % of the SUB3 region, approximately. It is worth mentioning that TREMOL 0.1.0 does not model the simultaneous interaction among the four sources, i.e., the Coulomb stress changes from one source to the next are not considered. However, the objective of this exercise is to aggregate the curve as an example of the aggregated seismicity without considering the interaction between sources. Future TREMOL generalizations would include such interactions.

In the upcoming sections, we describe further details of the simulation procedure based on TREMOL, and we base our discussion on comparisons of synthetic results with observed seismicity.

Additional data of the sub-seismic regions: area and aspect ratio.

A TREMOL simulation of each of the four mainshock earthquakes given in Table

Defining the input model parameters required by TREMOL. In addition to values given in Table

As statistical support to our resulting curves, we execute TREMOL v0.1 20 times per SA region listed in Table

For each realization, we also compute the frequency–magnitude distribution of synthetic earthquakes. To do so, we split the magnitude range

Finally, after the four SA simulation sets have been computed, we add their contribution, in the frequency–magnitude range, to the aggregated seismicity curve, considering their mean and standard deviation. This global curve represents the synthetic seismicity of a seismic area about 15 %–20 % of the whole SUB3 region.

Observed and TREMOL synthetic frequency–magnitude curves for SA region 1 (Table

As the basis for comparison for TREMOL output, we compiled the distribution of seismicity from a seismic catalog SSN-1988–2018 of 34 716 events that occurred at the SUB3 region from 1988 to 2018 with a minimum magnitude of 1.5

The epicentral latitude and longitude coordinates must be within the study regions, according to Fig.

They should fall within the reference depth which corresponds to the mainshock hypocenter depth. We included all events in a range of 8 km above and below the mainshock depth to account for the uncertainty of this value, which is a well-known limitation on the hypocentral location. Moreover, in the case of the 25 February 1996 earthquake, we considered all events regardless of their depth, because of the lack of data in the reference catalog (SSN-1988–2018).

The occurrence time should fall into the temporal window, from the catalog start date (1 January 1988) to half a year after the corresponding mainshock date.

Observed and TREMOL synthetic frequency–magnitude curves for SA region 2 (Table

The above selection criteria agree with the phenomenology simulated by TREMOL, which aims to model the previous seismic activity up to the mainshock, and in some cases, a few events just after its occurrence since the simulation ends when the area of

Lastly, it is worth mentioning that, when we construct the aggregated curve of the observed seismicity on the four SA regions of Fig.

Observed and TREMOL synthetic frequency–magnitude curves for SA region 3 (Table

We obtained four synthetic curves computed at each SA region according to the four area–magnitude relations (Eqs.

Observed and TREMOL synthetic frequency–magnitude curves for SA region 4 (Table

The SA region 1 has an area of approximately 3207 km

A similar analysis can be done for the other SA regions. According to the results for region 2 in Fig.

Observed and TREMOL synthetic frequency–magnitude curves for the aggregated frequency–magnitude curves computed with the contribution of the four mainshock ruptures. The solid black line is the mean of the synthetic results considering 80 realizations and the broken lines the standard deviation. The blue line is the seismicity curve for the events of Figs.

Magnitude histogram computed from the aggregated synthetic seismicity using the

Results for region 3, depicted in Fig.

Finally, TREMOL's results for region 4 in Fig.

Aiming at approximating the seismicity of nearly 15 %–20 % of the SUB3 region, as mentioned in Sect.

In what follows, we discuss the sensitivity of the model to the aspect ratio

Previous observational and numerical studies have implied a direct relation of the fault aspect ratio over the frequency–magnitude distribution

We define the aspect factor

To perform this study, we chose as reference the fourth SA region because its width–length ratio is close to 1 (1.03), making it a squared source (

Example of two sub-seismic regions with different aspect ratio,

In Fig.

Frequency–magnitude histograms as a function of the ratio size

The aim of this section is to explore the effect of the fault aspect ratio

The behavior of the synthetic seismicity displayed in Fig.

In our results, we observed that the maximum magnitude is approximately 7.4, independent of the aspect ratio. Nevertheless, as is seen in Fig.

The simulated TREMOL seismicity distributions show a high similarity to real seismicity curves associated with the four SUB3 reference mainshocks, for magnitude values of

In three of the study cases the best relationship is the one proposed by

It is worth pointing out the cases including events of magnitude lower than

In summary, we can conclude that the synthetic seismicity distributions agree well with the observations related to the four earthquakes of magnitude

The real and TREMOL frequency–magnitude curves for the SA region 4. The solid black line represents the mean synthetic seismicity curve of 20 realizations considering one single asperity in the domain. The red line corresponds to the mean synthetic seismicity curve of 20 realizations without any single asperity in the domain.

Lastly, TREMOL results in Fig.

The frequency–magnitude distribution has a significant impact on the seismic hazard assessment. Asperities seem to have a direct relation with the occurrence of preferred size events. In this work, we demonstrate the capability of the model employed in TREMOL to generate seismicity distributions similar to those observed in region SUB3 of the subduction regime of Mexico for magnitudes

TREMOL makes it possible to analyze regions where seismic data are too limited. In this sense, it should be highlighted that we use as input data the information of four large earthquakes, but the number of events generated approaches 1000.
Furthermore, we find that our model agrees with the results obtained in other studies that emphasize the importance of the fault aspect ratio

Results further encourage us to continue exploring the capabilities of our model, for future applications of TREMOL for the modeling of seismicity distributions at other subduction zones, such as Chile or Japan. In addition, we continue working on more general rupture models by including tridimensional fault systems, source interactions such as those produced in the doublets phenomena, and a reloading process that allows the generation of the seismic cycle.

The TREMOL code is freely available at GitHub repository (

Data sets are available through

MMV developed TREMOL v0.1.0 code and the methodology used in this paper. MMV, RZ, AAM, OR, QRP, and JP provided guidance and theoretical advice during the study. All the authors contributed to the analysis and interpretation of the results. All the authors contributed to the writing and editing of the paper.

The authors declare that they have no conflict of interest.

We thank the two anonymous reviewers whose comments and suggestions helped improve and clarify this paper. The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under the grant agreement no. 823844, the ChEESE CoE Project. Marisol Monterrubio-Velasco, Otilio Rojas, and Josep de la Puente thank the ChEESE CoE Project. Quetzalcoatl Rodríguez-Pérez was supported by the Mexican National Council for Science and Technology (CONACYT) (Cátedras program – project 1126).

The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under the grant agreement no. 823844, the Center of Excellence for Exascale in Solid Earth (ChEESE CoE Project).

This paper was edited by Thomas Poulet and reviewed by two anonymous referees.