The simplified average crustal model.
Abstract
The 12 November 2017 MW 7.3 Iran earthquake was further studied. By analyzing Rayleigh-wave dispersion data, crustal models in the surrounding of the epicenter were obtained. It was found that there are high-velocity layers over a low-velocity zone. Using the obtained crustal models and a grid search procedure, the initial rupture depth of about 16.4 km and the rupture propagation velocity of about 1.62 km/s were retrieved. The source rupture models were established using the obtained rupture initial depth and the rupture velocity. The key features are as follows: The earthquake occurred on a shallow dip-angle fault, with ruptures spanning high-velocity layers in a depth range of approximately 7–25 km. A noteworthy observation from comparing crustal and rupture models is the existence of a low-velocity zone (layers) beneath the major rupture region (below about 25 km). It was realized that the seismogenic structure of this earthquake showed that high-velocity layers lay a low-velocity zone in the Zagros mountain seismic belt.
Keywords
- 2017 MW 7.3 Iran earthquake
- source rupture model
- seismogenic structure
- Zagros mountain seismic belt
- grid search method
1. Introduction
On 12 November 2017, a significant earthquake with a moment magnitude (
The epicenter of this
This
The United States Geological Survey (USGS) has provided preliminary finite fault results for this earthquake. More than 10 papers have been published on or related to this earthquake (e.g., [2, 5, 6, 7, 8]).
However, given the varied strengths and weaknesses of existing findings, we were motivated to employ a waveform inversion method to retrieve more plausible source rupture models and surface wave dispersion data to retrieve crustal models in the epicentral region. Given the tectonic activity in the region, it is crucial to study this earthquake and the crustal structures in the epicentral region to enhance tectonic research and improve seismic hazard assessment.
In this article, we present the following: (1) introductions to the crustal modeling method, source rupture inversion method, and the grid search method; (2) the average crustal model obtained through the analysis of Rayleigh wave dispersion data in the epicentral region; (3) the initial rupture depths and rupture propagation velocities derived using a grid search procedure; (4) the source rupture models obtained by using shallow-dipping nodal planes and the identification of the active fault associated with the earthquake; and (5) the exploration of the seismogenic structure, which potentially reveals high-velocity crustal layers over a low-velocity zone in the Zagros mountain seismic zone.
2. Method introduction
In this article, three methods were used: crustal model retrieval using Rayleigh-wave dispersion data, source rupture model inversions, and a grip search procedure.
2.1 Crustal velocity modeling method
The crustal velocity model utilized in this study was obtained using a Rayleigh wave dispersion method. The method consists of two steps: (1) measuring the Rayleigh-wave group velocities and (2) modeling Rayleigh-wave dispersion data to extract S-wave velocities.
2.1.1 Measurement of Rayleigh-wave group velocities
Seismograms often exhibit prominent surface wave trains. These surface waves have different frequency components, and waves with different frequencies travel at different speeds, a phenomenon known as dispersion. As these surface waves propagate through the Earth, their amplitudes decay exponentially with depth. As a result, seismograms recorded at surface stations contain valuable information about the Earth’s structure. Rayleigh waves are generated by P and S waves, thus, S-wave velocity structures can be retrieved by analyzing Rayleigh-wave dispersion.
We measured the group velocities for the selected records using the multiple filter technique (MFT) developed by Dziewonski et al. [9]. A computer program developed by Herrmann and Ammon [10], was employed to implement the MFT method. In this technique, the group time for a specific frequency
where
The envelope of the filtering Rayleigh wave record can be computed using the formula proposed by Båth [11]:
where
2.1.2 Modeling Rayleigh wave dispersion data for S-wave velocities
After obtaining Rayleigh-wave dispersion data at a particular seismic station, we can utilize these data to model the S-wave velocities along the path traversed by the Rayleigh waves.
The initial step involves establishing an initial crustal model and then the model is revised by comparing the observed dispersion with the predicted dispersion generated using the crustal model. The inversion is in fact to identify a revised model that best fits the observed data.
In our inversion process, we assumed that
The partial derivatives
where
If we let
After solving this equation, we obtained a set of corrections to the
As for the theoretical background and the technique of Rayleigh wave dispersion inversion, except for the above introduction, the pioneering work by Haskell [16], Dorman [17], and Dorman and Ewing [18] provide valuable references.
2.2 The source rupture modeling method
The procedure used to establish an earthquake rupture model is described below. One of the two nodal planes is used as the earthquake rupture plane, and a Cartesian coordinate system is set up on this plane. Usually, the x-axis is along the strike direction, and the y-axis is along the dipping direction. The selected rupture plane is divided into many small rectangles where the length of each small rectangle along the
Once a nodal plane is selected as the rupture plane, it is divided into
Assuming that on a sub-fault
where
The Eq. (6) was solved using the nonnegative least squares (NNLS) method [20]. To ensure stability in the slip solution, a smoothness constraint was imposed on the spatial distribution of the total slips using a Laplacian differential operator [21]). To calculate the time delay
2.3 Grid search method
A Grid Search is an optimization algorithm commonly used in various research fields. It is beneficial for selecting the best parameter values to optimize a model or solve a problem. The Grid Search helps identify the optimal parameter values that yield the best results by systematically evaluating the model’s performance across all possible parameter combinations.
Grid searches are particularly effective when the parameter space is not too large or when the relationship between the parameters and the model’s performance is poorly understood. However, they can be computationally expensive when dealing with many parameters or when the parameter space is extensive.
Let a model parameter vector
The problem with this method is that the number of evaluations increases exponentially as
3. Data for the source rupture inversions and the Rayleigh-wave dispersion inversion
The data used for the source rupture inversions are P-wave segments in the teleseismic waveform vertical records. These records contain valuable information about the earthquake source. The waveform records were downloaded from the Incorporated Research Institutions for Seismology (IRIS) database. Specifically, records within an epicentral distance of 30°–90° surrounding the epicenter were selected for analysis. Only the high-quality P-wave segments were considered in the analysis to ensure high signal-to-noise ratios. The selected records underwent an instrument response correction to account for the recording instrument’s characteristics. Additionally, a band-pass filter with frequencies ranging from 0.01 to 0.1 Hz (equivalent to periods of 10–100 s) was applied to the records. The resulting dataset used for the source rupture inversion comprised 52 records.
The digital waveform records generated by moderate earthquakes around the
4. Crustal velocity models in the M W 7.3 epicentral region
The P-wave segments generated by a crustal earthquake, recorded at a teleseismic station, contain the direct P wave radiated from the earthquake source, the reflected wave pP, and the S-wave converted P wave sP. To generate Green’s functions at teleseismic stations, an earth model is required. In our study, we formed an earth model by replacing the crustal part in the preliminary reference Earth model (PREM; [23]) with the crustal model obtained from Rayleigh-wave dispersion data.
At some stations, the Rayleigh waves generated by moderate earthquakes were strong enough to measure surface wave dispersion data. We retrieved waveform records from IRIS and selected 15 clean Rayleigh wave vertical records. Figure 1 shows the 15 Rayleigh wave travel paths, connecting the four stations and the nine epicenters of the selected moderate earthquakes. These travel paths pass through the epicenter region of the
Once a group dispersion curve of a waveform record was measured at a given station, it is used to determine an average 1-D S-wave velocity model along the source station path. The P-wave velocity and density are obtained by converting the S-wave velocity model using a Poisson ratio (Vp/Vs = 1.732) and the Nafe-Drake relation [24].
Fifteen crustal velocity models were retrieved around the epicenter of the
∆H | Vp | Vs | density |
---|---|---|---|
8.0 | 5.3075 | 3.0656 | 2.5615 |
6.0 | 5.4695 | 3.1557 | 2.5941 |
3.0 | 5.6423 | 3.2551 | 2.6290 |
6.0 | 5.9186 | 3.4167 | 2.6861 |
3.0 | 5.7640 | 3.3283 | 2.6526 |
10. | 5.4377 | 3.1405 | 2.5877 |
4.0 | 6.4516 | 3.5985 | 2.8356 |
0.0 | 6.8496 | 3.8205 | 2.9480 |
In the table, column ∆H represents the layer thickness (km), Vp represents the P-wave velocity (km/s), Vs represents the S-wave velocity (km/s), and density (g/cm3). They are listed from top to bottom in Figure 2.
5. Source rupture models
In this section, we introduce the source rupture models obtained.
5.1 Selection of the rupture plane from the two nodal planes
Selecting a rupture plane from the two nodal planes is necessary when establishing a source rupture model. Typically, the distribution of aftershocks can be used to determine the rupture plane. In Figure 1, the smaller solid circles within and nearby the beach ball indicated by M7.3 represent the distribution of moderate aftershocks that occurred within 1 month after the main shock. The distribution trend aligns closely to the strike direction (351°) of nodal Plane 1 (the shallow-dipping plane). Thus, nodal Plane 1 was selected as the rupture plane.
5.2 The determination of the initial rupture depth and the rupture velocity
An initial rupture depth and a rupture propagation velocity are required to conduct the source rupture process inversion. A grid search scheme was employed to obtain reasonable values for these parameters. The depth range from 14.0 km to 21.0 km with an increment of 0.5 km was set, whereas the range for rupture velocity was from 1.40 km/s to 1.80 km/s with an increment of 0.05 km/s. At each grid point, the source rupture inversion was performed using the inversion code developed by Kikuchi and Kanamori, provided by Lingling Ye (personal communication). To speed up the calculations of the Green’s functions, we made some revisions to the code. The average variance from all the utilized records in each grid point (each inversion) was recorded. This variance represents the fit between the synthetic seismograms generated by the retrieved rupture model and the observed seismograms. A smaller variance value indicates a better fit. A total of 135 variance values were obtained from 135 grid points.
The contour map (Figure 3) illustrates the variance value changes with respect to the initial rupture depth and the rupture velocity. In the search procedure, the shallow-dipping nodal plane obtained by USGS (strike/351°, dip/16°, and rake/137°) was used. Two minima were found. One is at the rupture velocity of 1.47 km/s and an initial depth of 18.9 km (1.47, 18.9); its variance value is 0.1264. The second minimum is at (1.61, 16.4); its value is 0.1269.
5.3 Retrieving rupture models using the obtained minima
With the initial rupture depths and rupture velocities at the two minima, we retrieved two rupture models for the
Figure 5 compares seismograms at 24 stations, generated using the rupture model in Figure 4(b). The fit between the observed (upper) and synthetic (bottom) traces is generally good. For brevity, the comparison for the remaining 28 stations is not provided; the waveform fit at those stations is similar to those shown in Figure 5. This figure allows for a visual comparison between the observed and synthetic waveforms, highlighting the agreement or discrepancies between the recorded and the simulated waveforms based on the obtained slip distribution. It provides, to some extent, insights into the modeling approach’s accuracy and the simulated waveforms’ fidelity in capturing the actual earthquake’s characteristics.
5.4 Rupture models retrieved using nodal planes obtained by other authors
We also utilized shallow-dipping nodal planes obtained by other authors. First, we show the results in detail using the nodal plane provided by Nissen et al. [2] as the rupture plane; then, list the key results using the nodal planes provided by other authors. The contour map in Figure 6 shows variance value changes obtained using the nodal plane (strike/353.7°, dip/14.3°, rake/136.8°) provided by Nissen et al. [2]. Three minima were found. In the deeper colored region, the rupture velocity range is about 1.45–1.75; the initial depth range is about 15–19 km.
Three rupture models were generated using the above three minima (Figure 7). The upper panel shows the rupture distribution obtained using the nodal plane (strike/353.7°, dip/14.3°, rake/136.8°; Nissen et al. [2]) at the minimum (rupture velocity 1.62 km/s, initial depth 18.2 km). Several rupture patches were obtained. The middle panel shows the rupture distribution using the same nodal plane at the minimum (1.61 km/s, 16.1 km). One larger prolate rupture area, indicated by letter A, was obtained. The bottom panel shows the rupture distribution using the same nodal plane at the minimum (1.60 km/s, 17.2 km). One larger, oval rupture area, indicated by letter A, was obtained. The rupture distributions retrieved using different methods for the same earthquake should be similar. Because the rupture distribution in Panel (b) was similar to those obtained by Nissen et al. [2], so, we preferred to select Figure 7(b).
Other authors have also retrieved rupture planes for the 2017
Authors | data | Strike (°) | Dip (°) | Rake (°) | i.d. | Vr | va | m. s. depth |
---|---|---|---|---|---|---|---|---|
USGS | L. P. | 351.0 | 16.0 | 137.0 | 16.4 | 1.61 | 0.1269 | 14 |
GCMT | L. P. | 351.0 | 11.0 | 140.0 | 16.4 | 1.59 | 0.1153 | 16 |
Nissen et al. [2] | B. W. | 354.0 | 17.0 | 142.0 | 16.3 | 1.65 | 0.1268 | 13 |
Nissen et al. [2] | InSAR | 353.7 | 14.3 | 136.8 | 16.1 | 1.61 | 0.1194 | 14 |
Barhart et al. [4] | InSAR | 351.0 | 15.0 | 128.0 | 16.6 | 1.65 | 0.1258 | 14 |
Vajedian et al. [5] | InSAR | 354.4 | 17.5 | 141.5 | 16.5 | 1.65 | 0.1278 | 14 |
Feng et al. [6] | InSAR | 353.5 | 14.5 | 135.6 | 16.4 | 1.60 | 0.1210 | 14 |
Ding et al. [7] | InSAR | 354.7 | 16.3 | 137.3 | 16.1 | 1.63 | 0.1249 | 14 |
Chen et al. [8] | InSAR | 351.0 | 15.0 | 135.0 | 16.5 | 1.62 | 0.1235 | 14 |
Average | 352.7 | 15.2 | 137.0 | 16.4 | 1.62 | 0.1235 | 14 | |
GCMT | St. NP | 121. | 83. | 82. | 15.4 | 1.62 | 0.1535 | 18 |
In the table, the initial rupture depths (km, i.d.) and the rupture velocities Vr (km/s) were measured on a computer screen. The major slip (m. s.) depth (km) means the centre depth of the major rupture patch, visually estimated. L.P. means long period; B. W. means body waves; St. NP means Steep nodal plane. The other parameters are understandable.
6. A rupture model retrieved using a steep nodal plane as the rupture plane
All the previous models were obtained using shallow-dipping nodal planes as the rupture plane. This section presents the modeling results obtained using the same procedure but with a steep-dipping nodal plane.
Figure 8 displays the contour map depicting the variance values. In the search procedure, the steep-dipping nodal plane by The Global Centroid Moment Tensor (GCMT) (strike/121°, dip/83°, and rake/82°) was used. The small circle represents the obtained minimum variance value (0.1535), occurred at a depth of approximately 15.4 km and a rupture velocity of about 1.62 km/s. Figure 9 illustrates the slip distribution on the steep-dipping nodal plane. Several rupture patches were scattered within a 5–70 km depth range. Figure 10 compares the first 20 observed and synthetic seismograms generated using the rupture model shown in Figure 9. The poorest ratio occurred at station CMLA, with a ratio of 0.52.
This test demonstrates that the minimum variance value (0.1535) obtained using a steep-dipping nodal plane was notably larger than those obtained using shallow-dipping planes (Table 2). One major rupture patch was as deep as more than 60 km (Figure 9), which is beneath the crust. It is impossible for this
7. The seismogenic structure of the 2017 M W 7.3 Iran earthquake
The 2017
Overall, the modeling results introduced above indicate that the seismogenic structure of the 2017
8. Conclusions
The source rupture models of the 2017
Unlike the common practice that the rupture’s initial depth and the rupture velocity are assumed or by trade-and-errors when the rupture modeling is performed, we used the grid search method to determine the optimal initial depth and rupture velocity. For each nodal plane used as the rupture plane, two or three minima formed by the initial depth and the rupture velocity were found. One minimum was selected by analyzing the shapes of ruptures and comparing the solutions obtained by other authors for the same earthquake. If solutions from other authors for the same earthquake are not available at the moment, we do not have an effective way to select the best minima.
To validate the selection of the shallow-dipping nodal plane as the rupture plane, we tested a steep-dipping nodal plane as the rupture plane. The test revealed that the minimum variance (0.1535) was obviously larger than that (∼ 0.1235) achieved using the shallow-dipping nodal planes. The worst maximum amplitude ratio between observed and synthetic data was 0.52 at station CMLA, a significant deviation from the ideal ratio of 1.0. In contrast, when the shallow nodal plane was employed as the rupture plane, the worst maximum amplitude ratio was 0.64. The rupture distribution associated with the steep-dipping nodal plane also exhibited a scattered pattern ranging from approximately 5–60 km in depth. As a crustal event, the ruptures less likely occurred beneath the crust. Based on the above discussion, it can be concluded that the selection of the shallow nodal plane as the rupture plane was justified. This test also indicates that modeling two nodal planes for the 2017
Barnhart et al. [4] used InSAR observations of both the co-and post-seismic displacement to image the
The compressive force in the epicentral region is in the northeast direction. The epicentral region has a low-velocity zone under a high-velocity zone. This feature was displayed by the crustal models retrieved using the Rayleigh-wave dispersion data (Figure 2). The stress is accumulated in the ‘hard’ layers (high-velocity layers) above the ‘soft’ zone (low-velocity layers). When the accumulated stress is strong enough in the ‘hard’ layers, the crust there had to be broken, leading to the occurrence of this
The features exhibited by Figure 2 were also supported by the Love-wave dispersion inversion. The related article will be published. The factors leading to the uncertainty in the crustal model are multiple. One of them is the uncertainty in the measured dispersion data. It turned out that this uncertainty did not change the crustal features retrieved using the Rayleigh-wave dispersion data [27].
The epicenter of the 2017
Viewing this
Nissen et al. [2] estimated that the rupture velocity of this 2017
The grid search method was used to look for the optimal values of the rupture velocity and the rupture’s initial depth. We found that for each nodal plane used as a rupture plane, two or three minima appeared. It is crucial to consider the unique characteristics of each seismic event. Further investigations into the phenomenon of multiple minima and improved methodologies for rupture plane determination will advance our understanding of earthquake source characterization and hazard assessment.
By source rupture modeling and crustal velocity modeling, the 2017
Acknowledgments
This research was made possible through the support of the Natural Sciences and Engineering Research Council of Canada under the Discovery Grant program. We would like to express our gratitude to editor Walter Salazar for the improvement of this chapter. We would also like to acknowledge the following programs and tools in our data processing and figure preparation: SAC2000, Rdseed, geotool, MATLAB, and Generic Mapping Tools (GMT). Special thanks go to Lingling Ye at the Department of Earth and Planetary Sciences, University of California, Santa Cruz, California, for providing us with a version of the source rupture modeling code. We are sincerely grateful for her assistance.
Data sources
In this study, the seismograms, GCMT, and USGS nodal plane solutions utilized were obtained from the Incorporated Research Institutions for Seismology (IRIS) database, accessed at http://www.iris.edu (last accessed May 29, 2023). Certain information presented in the introduction section was revised based on a web page of the U.S. Geological Survey (https://earthquake.usgs.gov/earthquakes/eventpage/us2000bmcg#executive; last accessed the 31 July 2018).
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