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Article

Moment Magnitude Homogenization Relations in the South Korean Region from 1900 to 2020

Department of Nuclear Power Plant Engineering, KEPCO International Nuclear Graduate School, 658-91 Haemaji-ro, Seosaeng-myeon, Ulju-gun, Ulsan 45014, Korea
*
Author to whom correspondence should be addressed.
Appl. Sci. 2022, 12(14), 7215; https://doi.org/10.3390/app12147215
Submission received: 29 April 2022 / Revised: 4 July 2022 / Accepted: 13 July 2022 / Published: 18 July 2022
(This article belongs to the Section Earth Sciences)

Abstract

:
Utilizing several international and local earthquake catalogs, a set of regression models converting magnitude types typically found in the South Korean region to moment magnitude MW is presented. These linear regressions were performed using ordinary and total least squares techniques. A standard deviation applied to the residuals was used as a metric for ranking the MW regressions. This resulted in MW regressions from MV,JMA, MD,JMA, MS,MOS, and MS,BJI having the lowest standard deviations, while ML,IDC showed the highest standard deviation. Other magnitude types ranked differently depending on regression type. An examination of the residuals showed a linear model was appropriate for most magnitude types, with the exception of ML,KMA and ML,IDC. Residuals suggested a bilinear model worked well for ML,KMA, while ML,IDC showed a monotonic trend.

1. Introduction

After a period of relatively low seismicity, South Korea suddenly experienced two moderate earthquakes, the 16 September 2016 Gyeongju Earthquake and the 15 November 2017 Pohang Earthquake [1,2]. These events ignited multiple discussions on the vulnerability of South Korean infrastructure to seismic events, especially considering that both earthquakes occurred near nuclear power plants. The state-of-practice in evaluating how earthquakes can impact engineered infrastructure is seismic hazard analysis [3,4,5,6,7]. Seismic hazard analyses on major projects are typically conducted using a probabilistic approach, whereby stochastic models are used as components in solving the hazard integral. These models, such as modern ground motion prediction equations and recurrence relationships, are generally calibrated to moment magnitude, MW [8,9,10,11,12]. However, earthquake catalogs used to develop tools for use in probabilistic seismic hazard analysis tend to have earthquakes listed with differing magnitude types, such as surface wave magnitude, MS, short-period body wave magnitude, mb, the local magnitude, ML, also commonly known as the magnitude on the Richter scale [13,14,15,16]. Notably, ML requires a local calibration process that takes into account site and path effects that make it unique to a region [17]. Accordingly, using a variety of earthquake magnitude types in earthquake research or practical applications is cumbersome and computationally inconsistent as some agencies may use different standards for the same magnitude [18].
To overcome this issue, seismologists and earthquake engineers conduct magnitude homogenization. Magnitude homogenization entails developing relationships between the various magnitude types to a single magnitude type. These relationships typically relate Mw from Ms, mb, ML, or any other additional magnitude types relevant to the region of interest [19,20,21]. Magnitude homogenization is not a trivial matter as there are considerations with regression techniques and relationship priority, which might or might not influence calculations [20,22,23]. The reader is encouraged to refer to the work of Pujols [24] as it provides a good review on regression issues stemming from magnitude homogenization. The work essentially suggests Deming regression may not always be the best method in predicting earthquake magnitudes. Moreover, few low magnitude earthquake events list an MW, making it difficult for certain types of application.
Given this backdrop, this study proposes a variety of relationships to homogenize earthquake magnitudes estimated within the South Korean region to MW. This involves developing an earthquake catalog, which should include events within and immediately outside of South Korea, approximately 200 km away, to allow the results to be applicable and consistent with seismic hazard studies. Regression techniques, such as ordinary least squares and total squares regression, will be applied to this expanded catalog to help understand how these techniques influence ranking and priority amongst the various magnitude types.

2. Materials and Methods

Several earthquake catalogs will be required to develop appropriate magnitude homogenization relationships for the South Korean region. Specific catalogs used in this study include:
  • International Seismological Centre (ISC), Reviewed ISC Bulletin. This is a global catalog of seismic events recorded from all over the world starting from 1900. The ISC bulletin is updated periodically [25,26]. Many international seismological agencies submit data to the ISC. These agencies include the United States Geologic Survey National Earthquake Information Center (NEIC) as well as the Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization International Data Center (IDC). The NEIC was formerly known as the National Earthquake Information Service (NEIS), while the IDC was formerly known as the Experimental International Data Center (EIDC).
  • Global Centroid Moment Tensor catalog (GCMT). This is an earthquake moment tensor catalog for global earthquakes [27]. Data starts from 1976.
  • ISC-GEM Global Instrumental Earthquake Catalog. This catalog focuses primarily on large earthquakes in the ISC Bulletin, where the data is more reliable, to improve, extract, and constrain certain earthquake parameters [19,28,29,30]. When available, ISC-GEM uses MW stated by GCMT. Data starts from 1904.
  • Korea Meteorological Administration (KMA). This is a local catalog of seismic events local to the Korean peninsula [31]. Most of the data is recorded as ML due to historical reasons [21]. Data starts from 1978. This online database is in Korean.
A search is made within these catalogs to compile a set of earthquakes relevant to the South Korean region. Events from the beginning of 1900 until the end of 2020 were considered. The search region was restricted to within 200 km of the mainland border and the islands of South Korea within 31° to 41° N and 122° to 134° E. Depth was limited to 40 km as any earthquake deeper could be below the crust and from the mantle. Earthquakes originating in the mantle have different wave propagation behavior and mechanisms than those within the crust, concerns typically not accounted for in seismic hazard analyses. Additionally, when the option was available, a minimum magnitude of 2.5 was selected as it is assumed earthquakes with magnitudes at 2.5 or less would not influence magnitude homogenization model development. It is rare to see an earthquake catalog with listed events at MW below three. Moreover, there will be no distinction between a main shock and foreshocks or aftershocks.
Using the compiled earthquake catalog, earthquakes with a listed MW in addition to other magnitude types will be plotted. Data of the same magnitude type from related seismological agencies will be grouped into one representative agency. For example, MS from NEIC will include MS data from NEIC as well as NEIS, and mb data from IDC will include mb data from both IDC and EIDC.
Continuing with the previous examples, this suggests a few agencies will have listed events with an MW, such as ISC-GEM and GCMT. Data from GCMT is used as the base reference [19,20] and therefore this study will treat MW,GCMT as the base MW. Additionally, although not an international seismological agency, NIED is considered to have accurate constraints of the moment tensors for earthquakes in Japan and the surrounding regions [19,20]. Therefore, earthquakes listed with a MW from NIED will be included in a base list. This base list will contain MW data as the dependent variable in regression, with MW,GCMT having first priority, MW,ISC-GEM having second priority, and MW,NIED having third priority. Earthquake data where there are five or fewer earthquakes from a single representative agency of one non-MW magnitude type will not be considered in the regression.
Two regression approaches are considered; ordinary least squares (OLS) and total least squares (TLS) regression. Whereas OLS regression minimizes the residuals of the dependent variable, TLS regression attempts to minimize a distance metric that is a function of residuals between the dependent and independent variables. When this function is the Euclidean distance, the method is called orthogonal regression. TLS herein refers to orthogonal regression. An effective TLS technique, Deming regression, is not considered here as the bivariate method requires errors with known variances. Although ISC provides a magnitude error estimate in their Bulletin, other seismological agencies do not. The reader should note that when the ratio of the known variances is one, Deming regression is the same as orthogonal regression. The resultant regressions for MW will be termed MW,proxy herein. Regressions will not be performed on agencies that list four or fewer earthquakes for a specific magnitude type.
To help prioritize magnitude relations, the standard deviation will be used as a metric. For OLS, σOLS is defined as the standard deviation of the residuals. For TLS, σTLS is defined as the standard deviation of the Euclidean distances between data points and the regressed model. These standard deviations will serve as a metric to help prioritize and rank the magnitude homogenization relationships.

3. Results

The resultant earthquake catalog has 1544 earthquakes with contributions from multiple agencies. Table 1 describes the seismological agencies and their country of operation. As previously shown, these agencies are typically described by a three or four letter code. Note that BJI and PEK are treated as the same agency, while NEIC, NEIS, and CGS are also treated as the same agency.
Table 2 describes the base list and shows the number of events with an assigned MW per seismological agency. There are 15 and 14 events in GCMT and ISC-GEM, respectively, with an overlap of five events. These five events shared the same magnitudes. NIED listed 135 events with a reported MW, however only nine events shared a MW,GCMT listing. As a result, there are 149 events with a listed MW by ISC-GEM, GCMT, or NIED. Surprisingly, there are only eight and seven events with a reported MW by NEIC and JMA, respectively. Table 2 also lists the number of earthquakes listed by ISC-GEM, GCMT, NIED, NEIC, and JMA that share an event listed in GCMT. These data suggest most of the ISC-GEM and NIED data are not listed within the GCMT database.
A plot of MW versus MW,NEIC and MW,JMA is presented in Figure 1 to help ascertain how correlated the MW data set are. Data compiled from a previous study in Africa is also shown in the background of Figure 1 to show that the dataset are within previous work [20]. Overall, MW,NEIC and MW,JMA show a general one-to-one relation, but there is some slight scatter. Performing linear and total squares regression on the data set results in:
Mw,proxy = 1.119 MW,NEIC − 0.636; σOLS = 0.166; 4.6 ≤ MW,NEIC ≤ 6.4
Mw,proxy = 1.158 MW,NEIC − 0.842; σTLS = 0.110; 4.6 ≤ MW,NEIC ≤ 6.4
Mw,proxy = 1.000 MW,JMA − 0.000; σOLS = 0.045; 4.1 ≤ MW,JMA ≤ 5.5
Mw,proxy = 1.007 MW,JMA − 0.036; σTLS = 0.045; 4.1 ≤ MW,JMA ≤ 5.5
With coefficients of determination R2 = 0.941 and 0.986 for Equations (1) and (2), respectively. The regression coefficients are similar with the σOLS being greater than σTLS for both relationships. These relationships also suggest MW,JMA is a better indicator of MW than MW,NEIC.
To help increase the base list of MW, some statistical hypothesis testing is conducted to determine if Equations (1a) and (2a) are similar to a one-to-one line (slope = 1, intercept = 0) representing what MW estimates should be. Hypotheses testing performed on Equation (1a) found no significant difference against a slope of 1, tcrit(6,0.05) = 2.45, p = 0.34 and no significant difference against an intercept of 0, tcrit(6,0.05) = 2.45, p = 0.33. Hypotheses testing performed on Equation (2a) found no significant difference against a slope of 1, tcrit(4,0.05) = 2.78, p = 0.82 and no significant difference against an intercept of 1, tcrit(4,0.05) = 2.78, p = 0.82. This implies the relationships described by Equations (1a) and (2a) are not different from a one-to-one line. Hypotheses testing is not conducted on the TLS results as the residuals are not well-defined within the framework. As such, it is assumed the results from statistical hypothesis testing encompass the results from TLS. Due to this, the MW,NEIC and MW,JMA data are considered as MW and placed in the base list, with MW,JMA having priority over MW,NEIC. In actuality, only one additional event was added to the base list, for a total of 149 earthquakes with a listed MW. Given a baseline MW, Table 3 presents the number of events that contain MW and any magnitude (i.e., MS, mb, ML etc.) according to agency. The table shows most of the data for analyses are from IDC and JMA with very limited data sets from KEA, a North Korean agency.
A plot of Mw and MS pairs from multiple agencies is shown in Figure 2. MS data from ISC, NEIC, BJI, MOS, and IDC is shown in Figure 2a–e, respectively. The figures show relatively little scatter and the data appear linear with R2 = 0.935, 0.725, 0.940, 0.899, and 0.908 for ISC, NEIC, BJI, MOS, and IDC, respectively. Furthermore, the MS data does not show signs of saturation, a phenomenon where magnitude does not change as MW continues to increase. Mathematically, MS saturation tends to reveal itself with earthquakes approaching MS~8. On the lower end of the magnitude range, the figure shows NEIC, BJI, and MOS to have no data pairs MS < 4, while ISC and IDC have data pairs for MS < 4. For comparison, the ISC data generally plots closer to the right-side boundary of a global earthquake catalog data set [19].
OLS regressions on the MS data result in the following relationships:
Mw,proxy = 0.723 MS,ISC + 1.661; σOLS = 0.184; 3.0 ≤ MS,ISC ≤ 7.0
Mw,proxy = 0.550 MS,NEC + 2.772; σOLS = 0.237; 4.4 ≤ MS,NEIC ≤ 6.7
Mw,proxy = 0.815 MS,BJI + 0.859; σOLS = 0.158; 3.9 ≤ MS,BJI ≤ 6.5
Mw,proxy = 0.681 MS,MOS + 1.820; σOLS = 0.149; 4.0 ≤ MS,MOS ≤ 6.9
Mw,proxy = 0.777 MS,IDC − 1.565; σOLS = 0.198; 2.6 ≤ MS,IDC ≤ 6.5
Additionally, TLS regressions on the MS data result in the following relationships:
Mw,proxy = 0.741 MS,ISC + 1.579; σTLS = 0.149; 3.0 ≤ MS,ISC ≤ 7.0
Mw,proxy = 0.601 MS,NEIC + 2.513; σTLS = 0.206; 4.4 ≤ MS,NEIC ≤ 6.7
Mw,proxy = 0.836 MS,BJI + 0.756; σTLS = 0.122; 3.9 ≤ MS,BJI ≤ 6.5
Mw,proxy = 0.706 MS,MOS + 1.698; σTLS = 0.122; 4.0 ≤ MS,MOS ≤ 6.9
Mw,proxy = 0.807 MS,IDC − 1.453; σTLS = 0.155; 2.6 ≤ MS,IDC ≤ 6.5
Figure 2 shows that both OLS and TLS regressions produce similar relationships for the magnitude ranges presented.
Similar to Figure 2, a plot of Mw and mb pairs from multiple agencies is shown in Figure 3. mb data from ISC, NEIC, BJI, MOS, and IDC is shown in Figure 3a–e, respectively. The data show some scatter but appear linear with R2 = 0.891, 0.806, 0.814, 0.821, and 0.804 for ISC, NEIC, BJI, MOS, and IDC, respectively. The data also hint at potential magnitude saturation at mb ~ 6, which is what is expected. Similar to the MS data, the figure shows NEIC, BJI, and MOS to have no data pairs mb < 4, while ISC and IDC have data pairs for mb < 4. Additionally, the ISC data generally plot closer to the right-side boundary of a global earthquake catalog data set [19], similar to that shown in Figure 2.
OLS regressions on the mb data result in the following relationships:
Mw,proxy = 0.898 mb,ISC + 0.649; σOLS = 0.198; 3.3 ≤ mb,ISC ≤ 5.9
Mw,proxy = 1.064 mb,NEIC − 0.233; σOLS = 0.263; 3.7 ≤ mb,ISC ≤ 5.9
Mw,proxy = 1.360 mb,BJI − 1.555; σOLS = 0.260; 4.0 ≤ mb,BJI ≤ 5.8
Mw,proxy = 1.057 mb,MOS − 0.312; σOLS = 0.224; 4.1 ≤ mb,MOS ≤ 6.2
Mw,proxy = 1.090 mb,IDC + 0.113; σOLS = 0.281; 3.1 ≤ mb,IDC ≤ 5.1
Additionally, TLS regressions on the mb data result in the following relationships:
Mw,proxy = 0.948 mb,ISC + 0.430; σTLS = 0.157; 3.3 ≤ mb,ISC ≤ 5.9
Mw,proxy = 1.201 mb,NEIC − 0.874; σTLS = 0.174; 3.7 ≤ mb,ISC ≤ 5.9
Mw,proxy = 1.572 mb,BJI − 2.532; σTLS = 0.147; 4.0 ≤ mb,BJI ≤ 5.8
Mw,proxy = 1.185 mb,MOS − 0.946; σTLS = 0.150; 4.1 ≤ mb,MOS ≤ 6.2
Mw,proxy = 1.242 mb,IDC − 0.470; σTLS = 0.183; 3.1 ≤ mb,IDC ≤ 5.1
Figure 3 shows TLS regressions on NEIC, BJI, MOS, and IDC data to be steeper relative to OLS regressions most likely due to the 2005 March 20 MW 6.6 Fukuoka earthquake.
Figure 4 plots MW and ML pairs from multiple agencies. Data from KMA, JMA, BJI, KEA, and IDC are shown in Figure 4a–e, respectively. In the ISC Bulletin, magnitudes listed as M should be treated equivalent to ML [16]. Since the local magnitude in the JMA seismological bulletin is listed as MJMA, the local magnitude used by JMA will be termed MJMA herein for consistency. Data from JMA, BJI, and KEA appear linear with decent scatter having R2 = 0.895, 0.838, and 0.930 for JMA, BJI, and KEA, respectively. The KMA data appear relatively scattered with R2 = 0.780 while the IDC data appear the most scattered with R2 = 0.408.
The figures show there is a lack of ML data pairs for BJI and KEA at ML < 4, while KMA, JMA, and IDC are showing a good amount of data for ML < 4. Interestingly, Figure 4a appears to show a type of magnitude saturation where, as ML decreases, MW stays within a small range. Considering this, a bilinear relationship is proposed where an OLS and TLS regression is applied on magnitude pair data above ML = 3.6, but kept constant for ML < 3.6. In this approach, R2 for data where ML < 3.6 is 0.810, a moderate increase from 0.780, but still suggesting a linear relationship.
OLS regressions on the ML data result in the following relationships:
Mw,proxy = 0.968 ML,KMA + 0.199; σOLS = 0.257; 2.5 ≤ ML,KMA ≤ 3.6
Mw,proxy = 3.6; 3.6 < ML,KMA < 5.8
Mw,proxy = 0.866 MJMA + 0.339; σOLS = 0.185; 3.3 ≤ MJMA ≤ 7.0
Mw,proxy = 1.026 ML,BJI − 0.584; σOLS = 0.210; 4.4 ≤ ML,BJI ≤ 6.0
Mw,proxy = 0.888 ML,KEA + 0.184; σOLS = 0.188; 3.8 ≤ ML,KEA ≤ 6.0
Mw,proxy = 0.806 ML,IDC + 1.514; σOLS = 0.501; 2.5 ≤ ML,IDC ≤ 4.6
Additionally, TLS regressions on the ML data result in the following relationships:
Mw,proxy = 1.085 ML,KMA − 0.314; σTLS = 0.190; 2.5 ≤ ML,KMA ≤ 3.6
Mw,proxy = 3.6; 3.6 < ML,KMA < 5.8
Mw,proxy = 0.911 MJMA + 0.159; σTLS = 0.138; 3.3 ≤ MJMA ≤ 7.0
Mw,proxy = 1.133 ML,BJI − 1.139; σTLS = 0.143; 4.4 ≤ ML,BJI ≤ 6.0
Mw,proxy = 0.919 ML,KEA + 0.041; σTLS = 0.139; 3.8 ≤ ML,KEA ≤ 6.0
Mw,proxy = 1.434 ML,IDC − 0.662; σTLS = 0.341; 2.5 ≤ ML,IDC ≤ 4.6
In addition to MW and MJMA, JMA also uses a displacement magnitude, MD,JMA, and a velocity magnitude, MV,JMA [32,33,34]. Earthquakes with these JMA displacement and velocity-based magnitudes and a corresponding MW are plotted in Figure 5. The data for MD,JMA is not as plentiful, ranging from MD,JMA~4.0 to 6.0. On the other end, MV,JMA appears to be associated with events at the lower magnitude range, with MV,JMA~3.5 to 5.0. Both magnitudes show linear behavior and little scatter.
OLS regressions on these magnitude types result in the following relationships:
Mw,proxy = 0.684 MV,JMA + 0.916; σOLS = 0.075; 3.5 ≤ MV,JMA ≤ 5.0
Mw,proxy = 0.916 MD,JMA + 0.312; σOLS = 0.109; 4.2 ≤ MD,JMA ≤ 5.8
Additionally, TLS regressions on these magnitude types result in the following relationships:
Mw,proxy = 0.934 MD,JMA + 0.226; σTLS = 0.080; 3.5 ≤ MV,JMA ≤ 5.0
Mw,proxy = 0.694 MV,JMA + 0.879; σTLS = 0.062; 4.2 ≤ MD,JMA ≤ 5.8
As stated previously, the σ’s will be used to prioritize magnitude relations. Note that σTLS treats the residual as the shortest distance from data points to the regressed line. Table 4 compares the ranking of each relationship in ascending order for OLS and TLS. The table shows that based on σ, MV,JMA, MD,JMA, MS,MOS, and MS,BJI have the highest, second, third, and fourth highest priorities, respectively. However, after these first four magnitude types, there appears to be a difference in rankings depending on the type of regression used. For example, the MS,ISC to MW relationship has the fifth lowest σOLS, but is ranked ninth when considering σTLS. The largest discrepancy appears to be with mb,BJI, where it is ranked fourteenth under OLS regression but ranked eighth under TLS regression. Interestingly, the magnitude type by the most local agency, ML,KMA, ranked thirteenth under OLS and fifteenth under TLS conditions. The table also suggests mb data are more scattered relative to MS data as both OLS and TLS regressions show higher σ’s.

4. Discussion

In terms of performance, residuals from MS regressions are plotted in Figure 6. These plots show the OLS and TLS residual biases for each regression are essentially zero. Additionally, TLS residuals also show less variability relative to OLS residuals. The regression residuals for MS,IDC appear more scattered especially at MS,IDC < 4, with three events beyond 2σ for both OLS and TLS regressions. Even so, these plots suggest a linear model can be appropriate for MS regressions.
Residuals from mb regressions are plotted in Figure 7. These plots show the OLS and TLS residual biases for each regression are close to zero, however there appears to be considerable scatter within the residuals for each regression, with each regression having about three events beyond 2σ for OLS regressions. Interestingly, the TLS regression for mb,NEIC in Figure 7b had no events outside of 2σ. Although the figure shows decent scatter across magnitudes, there does not appear to be any trend, suggesting a linear model can be appropriate for mb regression.
Residuals from ML regressions are plotted in Figure 8. Residual bias from OLS and TLS regressions are zero with TLS residuals showing less variability relative to OLS residuals. The proposed regression for ML,KMA was bilinear to account for the stagnation at lower magnitudes and the residuals appear to agree in Figure 8a. It is not known if this saturation effect is a characteristic of lower magnitudes or an artifact of ML calibrated for Japan [21,35]. Interestingly, there are several events between 4.5 < ML,KMA < 5 where the bilinear model appears to underestimate magnitudes. Residuals for MJMA also appear to show events at MJMA~3.7 and 5.2 to be underestimated as shown in Figure 8b, with five events beyond 2σ for both OLS and TLS regressions, the highest amongst all models. However, this may be due in part to the relatively higher number of earthquakes assigned this magnitude type. Figure 8e shows the ML,IDC residuals that appear the most scattered across the magnitude range, resulting in relatively large σ. Even with a large σ, there are four and three events beyond 2σ for OLS and TLS regressions, respectively. Moreover, the decreasing behavior with ML,IDC suggest a linear model for regression may not have been appropriate. As such, the proposed regression relationship herein is not recommended for homogenization purposes but is presented for completeness.
Interestingly, the residuals for MV,JMA and MD,JMA appear the most linear of all the regressions presented herein as shown in Figure 9. This may be perhaps due to the limited number of earthquake events. However, the reason why there are so few events is that JMA started using MD,JMA and MV,JMA after discontinuing the use of MJMA in 2016. Nonetheless, all the data points fall within 2σ and suggest a linear model to be appropriate to the data.
Overall, these findings reinforce the notion that MW estimates from magnitude type regressions are dependent on regression type. A linear trend model appears to serve the data well with perhaps the exceptions of ML,KMA and ML,IDC. For magnitude types that exhibited more linear behavior, either OLS or TLS regression would yield similar results. Differences between OLS and TLS relationships appear when the data show events that seem to be significant outliers, relative to a linear trend.
An additional comparison is made between the proposed homogenization regressions herein against regressions from previous studies in Figure 10. As previously mentioned, a study based on global ISC data provided regressions for MS,ISC and mb,ISC [19]. Another study focused on the continent of Africa also offered homogenization relationships MS,ISC, mb,ISC, MS,NEIC, and mb,NEIC [20]. Both studies derived their relationships using orthogonal regression, which is comparable to the TLS approach used here. Figure 10a,b show the residuals to both global and African relationships for MS,ISC and mb,ISC, respectively. The global relationship appears to overestimate MS,ISC for the compiled data and shows a linearly increasing trend for the mb,ISC residuals, suggesting an inappropriate model. Figure 10c,d show the residuals from the African relationships for MS,NEIC and mb,NEIC, respectively. The residuals from the African model plot slightly above and away from the TLS MS,NEIC residuals, while the residuals from the African model plot mostly lower and away from the TLS mb,NEIC residuals.
A South Korean study presenting a local magnitude calibration also showed magnitude type relationships between MW, ML, and ML,KMA [21]. They separated between horizontal and vertical ML derivations, but each one showed similar results. The residuals from the horizontal model are presented in Figure 10e. These residuals show significantly more scatter relative to the TLS residuals shown herein and seem to suggest bias, especially at ML < 3.6. As mentioned previously, KMA used an ML scale calibrated for Japan, which may be a source for much of observed scatter. Additionally, the MW relationships provided in the South Korean study were compared against their proposed ML scale.

5. Conclusions

Several relationships estimating MW from various magnitude types typically encountered in the South Korean region were presented. These relationships are based on ordinary and total least square regression techniques. Of the relationships, the ones utilizing MV,JMA, MD,JMA, MS,MOS, and MS,BJI performed the best in terms of a standard deviation metric, while the relationship utilizing ML,IDC had the highest standard deviation. An inspection of the data showed most of the regressions with higher standard deviations tended to be of the mb type. The ML,KMA regression dataset showed little change with MW as ML,KMA decreased, which led to a bilinear regression model. Still, the resultant standard deviation was relatively high.
An examination of the residuals showed the linear regression model, whether ordinary or total least squares, was appropriate for many magnitude types. For ML,KMA, a bilinear model constrained the residuals, while the decreasing pattern of the residuals for ML,IDC suggested a linear model was perhaps not a good fit to the regression dataset. As a result, it was not recommended for use in homogenization activities. Moreover, a comparison of the residuals were made against homogenization relationships derived from global, African, and South Korean data. Residuals from these models showed more scatter, bias, as well as obvious trends, suggesting the proposed homogenization relationships herein are more appropriate for the South Korean region.

Author Contributions

Conceptualization, E.Y.; methodology, E.Y.; software, E.Y.; validation, E.Y.; formal analysis, E.Y.; investigation, E.Y. and W.P.; resources, E.Y. and W.P.; data curation, W.P.; writing—original draft preparation, E.Y.; writing—review and editing, E.Y.; visualization, E.Y.; supervision, E.Y.; project administration, E.Y.; funding acquisition, E.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the 2022 Research Fund of the KEPCO International Nuclear Graduate School (KINGS), Republic of Korea.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Publicly available datasets were analyzed in this study. Any generated data can be found within this article.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Relationships between Mw,GCMT and Mw from ISC-GEM, NIED, NEIC, and JMA. Data by Weatherill et al. (2016) from a larger earthquake compilation related to Mw,GCMT versus Mw.NIED is shown in gray symbols in the background for comparison [20].
Figure 1. Relationships between Mw,GCMT and Mw from ISC-GEM, NIED, NEIC, and JMA. Data by Weatherill et al. (2016) from a larger earthquake compilation related to Mw,GCMT versus Mw.NIED is shown in gray symbols in the background for comparison [20].
Applsci 12 07215 g001
Figure 2. Relationships between Mw against MS from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression. Data by Di Giacomo et al. (2015) from a larger earthquake compilation related to Mw versus MS.ISC is shown in gray symbols in the background for comparison [19].
Figure 2. Relationships between Mw against MS from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression. Data by Di Giacomo et al. (2015) from a larger earthquake compilation related to Mw versus MS.ISC is shown in gray symbols in the background for comparison [19].
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Figure 3. Relationships between Mw against mb from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression. Data by Di Giacomo et al. (2015) from a larger earthquake compilation related to Mw versus mb is shown in gray symbols in the background for comparison [19].
Figure 3. Relationships between Mw against mb from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression. Data by Di Giacomo et al. (2015) from a larger earthquake compilation related to Mw versus mb is shown in gray symbols in the background for comparison [19].
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Figure 4. Relationships between Mw against ML from (a) KMA, (b) JMA, (c) BJI, (d) KEA, and (e) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression.
Figure 4. Relationships between Mw against ML from (a) KMA, (b) JMA, (c) BJI, (d) KEA, and (e) IDC. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression.
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Figure 5. Relationships between Mw and (a) MV and (b) MD by JMA. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression.
Figure 5. Relationships between Mw and (a) MV and (b) MD by JMA. The solid and dashed lines represent the regression type as indicated in the graph. N is the number of data points used for regression.
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Figure 6. Regression residuals for MS from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The shaded regions represent ±1σ from OLS regression.
Figure 6. Regression residuals for MS from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The shaded regions represent ±1σ from OLS regression.
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Figure 7. Regression residuals for mb from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The shaded regions represent ±1σ from OLS regression.
Figure 7. Regression residuals for mb from (a) ISC, (b) NEIC, (c) BJI, (d) MOS, and (e) IDC. The shaded regions represent ±1σ from OLS regression.
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Figure 8. Regression residuals for ML from (a) KMA, (b) JMA, (c) BJI, (d) KEA, and (e) IDC. The shaded regions represent ±1σ from OLS regression.
Figure 8. Regression residuals for ML from (a) KMA, (b) JMA, (c) BJI, (d) KEA, and (e) IDC. The shaded regions represent ±1σ from OLS regression.
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Figure 9. Regression residuals for (a) MV,JMA and (b) MD,JMA. The shaded regions represent ±1σ from OLS regression.
Figure 9. Regression residuals for (a) MV,JMA and (b) MD,JMA. The shaded regions represent ±1σ from OLS regression.
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Figure 10. Comparing residuals between proposed regressions and those from previous studies for (a) MS,ISC, (b) mb,ISC, (c) MS,NEIC, (d) mb,NEIC, and (e) ML,KMA.
Figure 10. Comparing residuals between proposed regressions and those from previous studies for (a) MS,ISC, (b) mb,ISC, (c) MS,NEIC, (d) mb,NEIC, and (e) ML,KMA.
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Table 1. Seismological agencies that supplied relevant earthquake event data for this study.
Table 1. Seismological agencies that supplied relevant earthquake event data for this study.
CodeAgencyCountry
BJIChina Earthquake Networks CenterChina
CGSCoast and Geodetic Survey of the United StatesU.S.A.
EIDCExperimental International Data CenterU.S.A.
GCMTThe Global Centroid Moment Tensor ProjectU.S.A.
IDCInternational Data CentreAustria
ISCInternational Seismological CentreU.K.
JMAJapan Meteorological AgencyJapan
KEAKorea Earthquake AdministrationNorth Korea
KMAKorea Meteorological AgencySouth Korea
MOSGeophysical Survey of Russian Academy of SciencesRussia
NIEDNational Research Institute for Earth Science and Disaster PreventionJapan
NEICNational Earthquake Information CenterU.S.A.
NEISNational Earthquake Information ServiceU.S.A.
PEKPekingChina
Table 2. Number of events with a listed Mw categorized by agency.
Table 2. Number of events with a listed Mw categorized by agency.
AgenciesNumber of Events with a MwNumber of Events with a Mw,GCMT
GCMT1515
ISC-GEM145
NIED1359
NEIC87
JMA75
Table 3. Number of earthquakes with a listed Mw as well as another magnitude type categorized by agency.
Table 3. Number of earthquakes with a listed Mw as well as another magnitude type categorized by agency.
AgenciesNumber of Equivalent Mw–M Pairs Used in Regression
ISC79
NEIC45
IDC139
JMA132
BJI80
MOS43
KEA14
KMA46
Table 4. Comparison of the different rankings of magnitude type regressions based on σOLS and σTLS.
Table 4. Comparison of the different rankings of magnitude type regressions based on σOLS and σTLS.
PriorityMagnitude TypeσOLSMagnitude TypeσTLS
1MV,JMA0.075MV,JMA0.062
2MD,JMA0.109MD,JMA0.080
3MS,MOS0.149MS,MOS0.122
4MS,BJI0.158MS,BJI0.122
5MS,ISC0.184MJMA0.138
6MJMA0.185ML,KEA0.139
7ML,KEA0.188ML,BJI0.143
8MS,IDC0.198mb,BJI0.147
9mb,ISC0.198MS,ISC0.149
10ML,BJI0.210mb,MOS0.150
11mb,MOS0.224MS,IDC0.155
12MS,NEIC0.237mb,ISC0.157
13ML,KMA 10.257mb,NEIC0.174
14mb,BJI0.260mb,IDC0.183
15mb,NEIC0.263ML,KMA10.190
16mb,IDC0.281MS,NEIC0.206
17ML,IDC0.501ML,IDC0.341
1 Regression is bilinear.
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Yee, E.; Park, W. Moment Magnitude Homogenization Relations in the South Korean Region from 1900 to 2020. Appl. Sci. 2022, 12, 7215. https://doi.org/10.3390/app12147215

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Yee E, Park W. Moment Magnitude Homogenization Relations in the South Korean Region from 1900 to 2020. Applied Sciences. 2022; 12(14):7215. https://doi.org/10.3390/app12147215

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Yee, Eric, and Wonsick Park. 2022. "Moment Magnitude Homogenization Relations in the South Korean Region from 1900 to 2020" Applied Sciences 12, no. 14: 7215. https://doi.org/10.3390/app12147215

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