Automatic Fault Plane Solution for the Provision of Rapid Earthquake Information in South Korea

Abstract

The Korea Meteorological Administration (KMA) provides detailed hypocenter information after the earthquake early warning (EEW) service, due to increased public interest and for the study of fault movements. However, the rapid production of hypocenter information has limitations, including the necessity for the calculation of focal mechanisms, which requires expertise in seismology. Therefore, we developed automatic focal mechanisms (AFMs) based on the time domain moment tensor inversion method. A key feature of AFMs is the automatic collection and reforming of waveform data using information for EEW. Furthermore, we propose an additional module of the iterative inversion by reducing the low variance reduction data. This shows the increased variance reduction value rather than that of the first inversion. The variance reductions for the first inversion results were between 59 and 94%, whilst the results of the second inversion using the additional module were increased to 79–97%. The accuracy of the automatic results was similar to that of the manually determined results and was well adapted to the local earthquakes in and around the Korean Peninsula. The KMA provided the focal mechanisms of local earthquakes that could then be automatically determined using the EEW information within approximately 6–8 min and subsequently reported.

1. Introduction

The most important countermeasure against seismic hazards should be the fast determination of the hypocenter, allowing for a quicker response to the possibility of a disaster. The determination of earthquake source parameters, such as the seismic moment, the focal mechanism, and the depth, can contribute to earthquake hazard responses by quickly characterizing the fault plane [1]. Furthermore, the accurate estimation of hypocenters and fault plane solutions derived from focal mechanisms is useful in improving our understanding of regional tectonics and kinematics [2]. Unfortunately, the direct demand for information on fault motion is low, considering that the majority of people do not have a high level of understanding of this. However, news articles have been made to increase public understanding based on the information of focal mechanisms. Therefore, the Korea Meteorological Administration (KMA) now provides detailed hypocenter information on their webpage after the earthquake early warning (EEW) service. This is a policy that the KMA made to help provide public information.

The focal mechanism or fault plane is calculated using the initial P wave and/or the triaxial component of the waveform. The first representative algorithm is the FOCMAC [3], which is calculated using both the polarity of the initial P wave and the take-off angle. This automatic method is difficult since it requires high accuracy for the initial analysis of the P waves. Additionally, the crustal velocity model also needs to be as accurate as possible to ensure a solved focal mechanism for complex sources [4]. Another potential method is to determine the moment tensor by performing inverse calculations in the time domain. Dreger [5] developed the method TDMT_INV, which could find the depth and moment tensor by comparing the three-component seismic records and theoretical waveforms. The analysis accuracy is dependent on the Green’s function of the seismic observatory.

The initial P-wave approaches [6,7,8,9,10] and the waveform inversion techniques [10,11,12] have both been widely used for the determination of fault movements on the Korean Peninsula. These work to estimate the fault plane solutions of small to moderate earthquake events. However, the initial P-wave approaches can only resolve the faulting type of the initial fault break, which is not necessarily consistent with major faulting [13]. Therefore, the first-motion fault plane solutions can sometimes differ from the moment tensor solutions [14,15]. Moment tensor inversion, based on the complete information of the characteristics of seismic waveforms, can estimate major faulting types better than using an initial P-wave approach. Additionally, moment tensor inversion is less dependent on the seismic network coverage.

In this study, we construct an automatic system based on the moment tensor inversion routine, TDMT_INV, by Dreger [5]. The proposed algorithm is a time domain inversion code, designed to invert regional long-period waveform data and is optimized for the Korean Peninsula. TDMT_INV has been known to constrain focal parameters by using a single station; however, more accurate results can be acquired through the use of multiple stations [12]. Therefore, we develop here a real-time automated moment tensor inversion using TDMT_INV to provide quick source parameters for local and regional earthquakes in the vicinity of the Korean Peninsula. This automated inversion approach is applied to local events with magnitudes greater than 3.5 in order to optimize the control parameters used in the automatic process. After testing, the automatic process using these parameters was successfully implemented at the Korean Meteorological Station (KMA) and used for subsequent local earthquake analysis.

2. Moment Tensor Inversion Method

Moment tensor analysis involves fitting theoretical waveforms with observed signals and inverting for the moment tensor elements [16]. The applied methodology is based on a simplified general representation of the seismic sources by considering both a spatial and a temporal point source [17]. This method can be summarized by the equation:

(1)$U_n\left(x,t\right)=M_{ij}·G_{ni,j}\left(x,z,t\right)$

where U_n is the observed nth of displacement, G_ni,j is the nth of Green’s function for specific force couple orientations, x is the distance to the source from the seismic station, and z is the depth. We calculated Green’s function, which is the impulse response of the observed seismic data. The empirical Green’s function is obtained between the path- and site-specific effects because these constitute the earth’s response between the source and the receiver [18,19]. Therefore, Green’s function can be used to retrieve earthquake source properties or estimate theoretical waveforms. M_ij is the scalar seismic moment tensor. In addition, the indices i and j refer to geographical directions. The general force couples for a deviatoric moment tensor may be represented by three fundamental faults, namely a vertical strike-slip, a vertical dip-slip, or a 45° dip-slip [20]. Equation (1) can be calculated by assuming the source depth for each inversion using linear least squares. The estimated scalar moment tensor, M_ij, can be decomposed into the scalar seismic moment, a compensated linear vector dipole moment tensor (CLVD), and a double-couple moment tensor (DC) [21]. This decomposition is represented as percent DC (PDC) and CLVD (PCLVD), respectively. A percent isotropic (PISO) is assumed to be zero for this deviatoric application. The strike, rake, and dip of the fault planes can be obtained by DC.

This can then be used to calculate the source depth to find the lowest value of variance reduction (VR), as follows:

(2)$\mathrm{VR}=\left[1-{\displaystyle \sum }_i\raisebox{1ex}{$\sqrt{{\left(ob{s}_i-synt{h}_i\right)}^2}$}\!\left/ \!\raisebox{-1ex}{$\sqrt{ob{s}_i^2}$}\right.\right]\times 100$

where obs and synth are the observed data and the theoretical synthetic waveforms using Green’s function time series, respectively. The VR calculated summation is for all stations and components, although the results of the moment tensor inversion are generally not very sensitive to location errors. It has previously been reported that errors of up to 15 km in epicenters are less important at a distance range of 50–400 km [1,22]. These assumptions are generally reasonable for M_w < 7.5 events since long period waves (>10–20 s) are used in this case [5]. Additionally, it is assumed that the crustal model is sufficiently well known the low-frequency wave propagation. This procedure can also obtain solutions using a minimal number of stations.

Green’s functions of seismic stations in the Korean Peninsula computed in the frequency–wavenumber domain were subsequently stored in the KMA database. The formulation used the three basic focal mechanisms: normal, reverse, and pure strike-slip [23,24], whilst the AK135 velocity model [25] was used to compute Green’s function.

3. Design of Automatic TDMT

The necessary qualities for automatic analysis systems include the ability to be directly controlled without the need for human involvement and the requirement to be quick and reliable and they must be independent of other systems (e.g., earthquake early warnings). Here, the seismic moment tensor inversion was used based on TDMT_INV (time domain moment tensor inversion) and the package developed by Dreger [5].

The observed three-component broadband seismograms in the MiniSEED format were cut into predefined time segments, transformed into the format of the seismic analysis code (SAC), and subsequently converted to ground displacement through the removal of the seismic instrument responses. The converted data were then rotated into a ray coordinate system and filtered in ~0.05–0.1 Hz using a second-order Butterworth bandpass filter. The source time function was assumed to be a Dirac delta function since the events used in this study generally had source durations of 2–3 s (M_L < 6) [5].

To obtain the desired reduction for the moment tensor processing time, we applied three control parameters: epicentral distance range, the number of stations in the quadrants, and the quality factor in the automatic process. The epicentral distance range was tuned based on the epicenter and magnitude in order to then select which seismic station’s data were available. The number of stations in the quadrants prevented the azimuth of the stations from being focused in specific directions. The final parameter, the quality factor, was determined based on the event magnitude, considering that this increases in proportion with the magnitude.

Figure 1 shows a schematic diagram of the design for automatic calculation. After extracting the event information, including origin time, epicenter, and magnitude from the common alerting protocol (CAP), an XML-based data format for exchanging public warnings and emergencies between alerting technologies was transferred via the dissemination system. The automated moment tensor inversion was performed for each source depth between 1 and 35 km, and the best fitting result with the maximum variance reduction was subsequently determined. To increase the accuracy of the first moment tensor inversion result, the second inversion was performed again by reselecting higher variance reduction data with a low limit of VR (>70).

4. Verification and Working of Automatic TDMT

The regional solution was automatically employed to investigate all M_L ≥ 3.5 events in South Korea and has been used for local earthquake analysis. The stability of the automated moment tensor inversion was investigated for implementation in real-time processing. For this, broadband waveforms of 13 events that occurred between 2016 and 2019 were used, with magnitude ranges of M_L 3.5–5.8 being reported by the Korean Meteorological Administration (KMA) (Table 1). Previous studies [5,26] have shown that this inversion method was reliable for local events with magnitudes of 3.5 and over. All of the broadband waveforms used in the inversion analysis were recorded from seismic stations operated by either the KMA or the Korea Institute of Geosciences and Mineral Resources (KIGAM) in real time.

To obtain the maximum reduction variance in the inversion, the epicentral distance range was tested from 50 to 250 km and was found to be reasonable up to 200 km for local events. The number of stations in the quadrants, preventing the azimuth of the stations focusing in specific directions, was dependent on the magnitude; so, the numbers in the case of a magnitude less than 4 and greater than 4 are 6 and 4, respectively. Currently, the accuracy of the focal mechanism depends on the stations. Therefore, the reliability of the station used must be controlled; this is called the quality factor. The quality factor of 4 was enough in the automatic process, despite the magnitude being less than 4.

Fault mechanisms are more accurate when obtained using four-quadrant data. FOMEC requires both tensional and compressional wave information based on the epicenter to the double-couple plane, rendering its analysis difficult in earthquakes outside the seismic network. In addition, a reliable focal mechanism can be obtained if the AFM contains at least one station in every quadrant [27].

In contrast, the AFM calculates tomographic information after selecting stations with high VR using theoretical synthetic waveforms. Compared with the AFM, the tomographic information can be calculated across a wider area with fewer stations. If we increase the number of AFM stations, then data on the high relationship between the theoretical synthetic wave and the observed data will be required. When high VR stations were added to the previous test, there was no significant change in the focal mechanism form. However, increasing the number of stations is difficult when earthquakes occur at sea. Therefore, using at least four stations or more in two quadrants is recommended.

As the first automatic moment tensor inversion results showed lower accuracy compared to the manual analysis, the second inversion was performed again based on selecting high variance reduction of the waveforms used in the first inversion. The low limit of the VR was set as larger than 70 in order to reselect higher variance reduction data and perform the second inversion iteratively. Table 2 shows the comparison between the first and second inversion results, with the accuracy of the second being increased by up to approximately 25% more than that of the first. The variance reductions of the first inversion results were between 59 and 94%, whilst the second inversion using the additional module resulted in an increase of up to 79–97%. Figure 2 shows one example of the first and second inversion results by reselecting waveforms based on the variance reduction (VR) criteria (>70). The VRs of the first and second were 90.6 and 94.0, respectively. In Figure 2, the blue thick lines and the red dashed lines indicate, respectively, the observed and synthetic waveforms of the three rotated components (tangential, radial, and vertical). Here, the waveforms of the stations (i.e., NAWB and CHYB) in the box were not included in the second inversion due to their having VRs below 70 (VRNAWB = 66 and VRNAWB = 62).

Figure 3 shows the fluctuations of variance reduction, the computed fault plane solutions for the source depths between 1 and 35 km, and the finally determined fault plane solutions with a VR = 96.8. The corresponding VRs of the waveforms were between 92 and 98, which showed good inversion results in comparison to the manual analysis. The epicentral distance range of the stations used in the analysis ranged from 112 to 187 km. Table 3 shows the final automatic moment tensor inversion results for 13 local events, which included strike, dip, rake, and their corresponding VRs. The accuracy of the automatic results was comparable with that of the manually determined results for the 13 local earthquakes in Figure 4. The differences in strike, dip, and rake were within 5°, 7°, and 10°, respectively.

The moment tensor inversion module implemented in the KMA analysis system automatically analyzed the M_L 3.9 event on 21 July 2019, and this was compared with the manually inverted results in Figure 5. The fault plane solution automatically determined the strike-slip fault (strike 197/107, dip 86/83, rake −173/−4) with VR = 68.3, and the manual solution indicated a similar strike-slip fault (strike 196/106, dip 85/88, rake −178/−5) with VR = 89.2. Despite the accuracy of the automatic inversion results based on the VR being lower than that of the manually analyzed results, the interpretation of the inverted fault plane solution showed that these were very similar and well adapted to local earthquakes.

Currently, the EEW service in Korea provides cell phone messages to citizens about an incoming earthquake so that they can promptly respond to the danger. The KMA EEW automatically calculates and spreads an earthquake warning message when an earthquake of M_L > 3.5 occurs (or 4.0, if occurring over the sea). The AFM can be used with a magnitude of ≥3.5, rendering it suitable for the notified earthquake analysis. The notified earthquake information service is provided through the KMA website (https://www.weather.go.kr/w/eqk-vol/search/korea.do, accessed on 29 October 2022), which began on 22 July 2019. The earthquake information service report comprises the hypocenter, earthquake magnitude, seismic measurement intensity, waveform, and seismic analysis.

The AFM covers only the notified area and depends on the seismic network distribution. The number of Korean Peninsula seismic stations has rapidly increased since 2016. Figure 6 shows the current status of the observation networks operated by the KMA and KIGAM. There are 301 observatories operating at the KMA and 61 at the KIGAM. The boundary line of the notification area is set based on the operating observations and is indicated using the black line in Figure 6. The KMA has been promoting the expansion and revision of the old stations. In addition, the KMA will be able to add more observatories using other agencies. Therefore, we must estimate Green’s function for the additional stations. These service policies were designed based on the decisions made by the KMA in South Korea, which might differ in other countries.

5. Conclusions

In this study, we developed an automated moment tensor inversion system which applied TDMT_INV to provide the real-time monitoring of earthquake source parameters in and around the Korean Peninsula. This system used continuous broadband waveform data and searched for the best-fitting moment tensor solution in real time. The moment tensor and focal mechanism could be obtained from the predetermined event origin time, location, and magnitude within 10 min of an earthquake occurrence. Quantitative interpretations of the application were not discussed here in detail since TDMT_INV is a widely used application for obtaining fault parameters, and the focus of this paper was on its automatic procedure and stability. This procedure was tested using the 13 small–moderate local earthquakes with local magnitudes greater than or equal to 3.5, which occurred in and around the Korean Peninsula. As previously shown by Dreger [5], this method was reliable for events with local magnitudes (M ≥ 3.5).

To improve the accuracy of the first moment tensor inversion results, a second inversion was performed by reselecting higher variance reduction data with the low limit of VR (>70). The first and second automatic inversion’s VRs were compared, thereby indicating that the performance accuracy iteratively increased for testing local earthquakes. The variance reductions of the first inversion results ranged between 59 and 94%, whilst the second inversion results improved on this, reaching 79–97%. This automated development will be crucial for real-time earthquake monitoring at the local and regional scales. The results obtained in this study were in good agreement with those obtained through the manually inverted solutions, and furthermore, the automated results were relatively stable. As the KMA has the automated inversion process in real time, the provided real-time system can report focal mechanism parameters directly after the event has occurred, which will be important in seismic hazard assessments in the event of a larger earthquake.

Automatic TDMT was applied as a service technology for the KMA, and these results can be found on the KMA website. Currently, the KMA is expanding its observation networks for early earthquake warning (EEW) systems, which consist of sensors both on the ground surface and within boreholes [28,29,30]. Therefore, it is necessary to improve Green’s function, which was influenced by the environmental factors of the Korean Peninsula.

Author Contributions

J.L.: methodology, software, validation, writing; D.K.L.: conceptualization, software, resources; J.-K.A.: conceptualization, formal analysis, writing. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The earthquake record data can be downloaded from https://necis.kma.go.kr (accessed on 29 October 2022), and the algorithm data will be provided upon request.

Acknowledgments

The authors are grateful to the system developer staff of the KMA Earthquake and Volcano Research Division.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Figure 1. Design schematic diagram of automatic TDMT.

Figure 2. The comparison of automatic moment tensor inversion result for the event 201609120: (a) the 1st inversion result with VR = 90.6 (b) the 2nd inversion result with VR = 94.0 by removing two stations’ waveform data with VR less than 70 from the 1st inversion result.

Figure 3. The fluctuations of VR against the focal depth for the event 201711151. The blue beach ball indicates the maximum VR = 96.8 at a focal depth of 6 km. (b) The corresponding automatic inverted result from (a).

Figure 4. The comparison of moment tensor inversion results between automatic and manual analysis (a) Automatic analysis results listed in Table 3. (b) Manual analysis results listed in Table 1.

Figure 5. The comparison of moment tensor inversion results between those automatically analyzed in real time (a) and manual analysis (b) for 12 July 2019. M3.9 earthquake that occurred on 12 July 2019.

Figure 6. Observation network in South Korea for earthquake detection. Black line: boundary line of notification for domestic earthquakes; blue triangle: seismic observations from the KMA; green triangle: seismic observations from KIGAM.

Table 1

List of source parameters of the 13 local earthquakes recorded in the Korean Peninsula.

Event ID (yyyymmdd)	Origin Time (UTC)	Lat(°N)	Lon(°E)	Depth(km)	ML	Strike(°)	Dip(°)	Rake(°)
20160705	11:33:03	35.51	129.99	19	5.0	107216	6358	14333
201609120	10:44:32	35.77	129.19	15	5.1	11928	8773	17177
201609121	11:32:54	35.76	129.19	15	5.8	11726	8472	18174
201711150	05:29:31	36.11	129.37	7	5.4	230331	6964	15224
201711151	07:49:30	36.12	129.36	10	4.3	201348	6628	10561
20171116	00:02:42	36.12	129.37	8	3.6	241331	8676	1664
201711190	14:45:47	36.12	129.36	9	3.5	33123	9066	1560
201711191	21:05:15	36.14	129.36	12	3.6	228135	7676	−166−14
20171225	07:19:22	36.11	129.36	10	3.5	49142	8168	15810
201802100	20:03:03	36.08	129.33	14	4.6	18160	5443	11560
201902101	03:53:38	36.16	129.90	21	4.1	33124	8581	1715
20190419	02:16:43	37.88	129.54	32	4.3	344172	4645	8496
20190421	20:45:19	36.86	129.80	21	3.8	1867	4842	8991

Table 2

Comparison of the first and second moment tensor inversion variance reduction (VR).

Event ID (yyyymmdd)	Origin Time (UTC)	1st VR	2nd VR	ΔVR (%)
20160705	11:33:03	87.7	87.7	0.0
201609120	10:44:32	90.6	94.0	3.4
201609121	11:32:54	93.0	93.0	0.0
201711150	05:29:31	94.3	94.3	0.0
201711151	07:49:30	93.9	96.8	2.9
20171116	00:02:42	74.9	89.9	15.0
201711190	14:45:47	82.3	83.6	1.3
201711191	21:05:15	88.1	88.1	0.0
20171225	07:19:22	58.8	84.4	25.6
201802100	20:03:03	93.5	93.5	0.0
201902101	03:53:38	79.4	79.4	0.0
20190419	02:16:43	71.2	84.6	13.4
20190421	20:45:19	92.1	92.1	0.0

Table 3

List of automatic moment tensor inversion results for the 13 events.

Event ID (yyyymmdd)	Origin Time (UTC)	ML	Strike (°)	Dip (°)	Rake (°)	VR (%)
20160705	11:33:03	4.6	107216	6358	14333	87.7
201609120	10:44:32	5.0	11928	8869	21178	94.0
201609121	11:32:54	5.4	11827	8763	28177	93.0
201711150	05:29:31	5.4	225336	6256	14134	94.3
201711151	07:49:30	4.3	200347	6629	10560	96.8
20171116	00:02:42	3.6	241331	8979	1691	89.9
201711190	14:45:47	3.5	33123	9072	1620	83.6
201711191	21:05:15	3.6	229136	7977	−167−11	88.1
20171225	07:19:22	3.6	49142	8368	1578	84.4
201802100	20:03:03	4.5	31146	6350	13436	93.5
201902101	03:53:38	3.8	30121	8681	1714	79.4
20190419	02:16:43	3.9	342178	4744	79101	84.6
20190421	20:45:19	3.8	1876	4644	9189	92.1

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