Expanding Moment Magnitude Pools for Earthquake Magnitude Homogenization

Abstract

A comparison on the influence of different moment magnitude pools on magnitude homogenization regressions was presented. The control moment magnitude pool is composed of earthquake records from GCMT. One version of expanding this base is to add earthquakes with a moment magnitude recorded by seismological agencies related to GCMT. Another approach to expanding the base is to add earthquakes from seismological agencies and projects that show a significant statistical correlation to GCMT via hypothesis testing. These moment magnitude pools were developed for Indonesia and South Korea. Magnitude homogenization was conducted by performing linear least squares regressions between the three moment magnitude pools and commonly used magnitude types from international seismological agencies ISC and NEIC. Magnitude homogenization regressions were also conducted on local Indonesian and South Korean agencies, DJA and KMA, respectively, with their various magnitude types. Most of the moment magnitude pools involving DJA and virtually all South Korean-related agencies ended up being identical, primarily due to the local magnitude types available for DJA, and the low number of earthquakes recorded for South Korea. A majority of the regression parameters for Indonesia and South Korea were statistically similar for surface and body wave magnitude types.

1. Introduction

Studies on earthquake risk and recurrence generally derive components from an earthquake catalog. These catalogs are collections of earthquake events containing at a minimum information regarding earthquake occurrence, hypocenter, magnitude, and magnitude type. One of the drawbacks to such a catalog is the diversity of magnitude types recorded, making it very difficult to make comparisons and to derive consistent parameters from the catalog. Seismologists and earthquake engineers generally develop and apply magnitude homogenization relationships to the catalog so that the magnitude data is unified under one specific magnitude type [1,2,3,4].

A typical magnitude type that modern earthquake risk and recurrence studies utilize is the moment magnitude, M_W [5]. Generally, regressions are made between M_W from a reliable agency against the remaining magnitude types in the target earthquake catalog, usually surface wave magnitude, M_S, body wave magnitude, m_b, local magnitude M_L, and on occasion to M_W from other agencies. The representative M_W from these magnitude homogenization regressions are typically called proxy magnitude, M_W,proxy. However, most resultant earthquake catalogs do not explicitly indicate which magnitudes are M_W,proxy.

Catalogs containing many earthquakes with reliably recorded M_Ws make magnitude homogenization easier, as the pool of available events for homogenization is wider. However, many catalogs do not have many low M_W events as well as regional seismicity limitations. Additionally, a better understanding of M_W can help in the seismic risk assessment of regional infrastructure [6]. Some studies have tried to expand the pool of M_Ws for regression through the identification of similar or reliable sources [3,4,7] while others suggest the regression results from magnitude homogenization help indicate magnitude type similarity [2,3,4,8], although similarity and reliability were variably defined.

This study attempts to compare three approaches in extending the earthquake catalog M_W pool and its effects on magnitude homogenization. One of these three approaches can be considered the control, where the M_W pool is from a single reliable seismological agency. Another approach is to pool together M_W records from agencies associated with the control agency in addition to other relatively reliable sources. The third approach is to develop the M_W pool by utilizing statistical hypothesis testing to determine which agencies’ magnitudes are significantly similar to those from control agencies or other related agencies. These three approaches are to be applied to earthquake catalogs of a seismically active region, Indonesia, and a relatively less active region, South Korea. The scope is limited to earthquake records from major global seismological agencies and a local agency to each region. By comparing different regions and focusing on certain sources, the results can help reveal what additional impacts the three approaches have on magnitude homogenization.

2. Materials and Methods

2.1. Earthquake Catalog Construction

Several global sources will be used to construct Indonesian and South Korean earthquake catalogs for examination. The focal earthquake data source is the Global Centroid-Moment-Tensor (GCMT) Project [9]. This catalog contains events with M_W from centroid moment tensor solutions and as such is considered the most reliable source of M_W records [3,10,11,12]. Records start from 1976. Prior to 2006, GCMT was previously known as the Harvard CMT Project.

Another important seismological agency is the International Seismological Centre (ISC). The ISC houses a global earthquake catalog called the Reviewed ISC Bulletin, containing data from a variety of seismological agencies and projects since 1900 [13,14,15,16]. Each seismological agency or project that submits data to the ISC is identified by a code, for example, the Harvard CMT Project is identified as HRVD. Although several seismological agencies and projects submit M_W records to the ISC Bulletin, the ISC itself currently does not record or compute a M_W magnitude type in the ISC Bulletin. However, the ISC houses a M_W catalog called the ISC-GEM Global Instrumental Earthquake Catalogue (ISC-GEM). This catalog contains three kinds of earthquake events: (i) those published by GCMT, (ii) M_W,proxy estimates from re-computed M_S and m_b records, and (iii) events taken from literature [12,17,18,19].

Another global agency, the United States Geologic Survey National Earthquake Information Center, USGS NEIC, has submitted earthquake records to the ISC Bulletin since 1980 [20,21]. The ISC Bulletin also contains older NEIC data, when it was known as the National Earthquake Information Service, NEIS. The USGS also works with a variety of seismic networks such as the U.S. Geological Survey, GS, Coast and Geodetic Survey of the United States CGS, and the United States Coast and Geodetic Survey, USCGS that also contribute to the ISC Bulletin. For ease of use, recordings from USGS networks will be classified under the heading of NEIC. Unlike the ISC, the NEIC does publish CMT-based M_Ws in their bulletins [10,11,21,22].

Two local seismological agencies will be used, one for Indonesia and one for South Korea. The Indonesian agency, Badan Meteorologi, Klimatologi dan Geofisika, DJA, which previously went by the identifier of BMKG, offers a variety of magnitude types, in the ISC Bulletin. The South Korean agency, Korea Meteorological Administration, KMA, mostly offers M_L although the local magnitude scale calibration had some issues [4,23,24].

A search of the catalogs is limited to a zone that extends 200 km away from each country’s borders and 50 km deep. For Indonesia, this zone is approximated by coordinates 95° E to 141° E and 11° S to 6° N. For South Korea, this zone is approximated by 122° E to 134° E and 31° N to 41° N. Data up to 2020 will be considered. There will be no distinction between main shocks, foreshocks, and aftershocks. With no distinction between dependent events and a compilation from multiple catalogs, there is a potential for duplicates in the resultant catalogs. For this study, two events are classified as duplicates if the time of occurrence is within 30 s of each other and within an epicentral distance of 0.1°. In case of duplicates, data from global catalogs take precedent over local regional catalogs in the order of GCMT, ISC-GEM, ISC, and NEIC [3,11,12], with all magnitude types assigned to the final entry.

2.2. Magnitude Homogenization

The general procedure for magnitude homogenization is to estimate a relationship between a target magnitude type from a pool of other magnitude types. To do so, regressions are made from the compiled earthquake catalogs for M_W against other magnitude types. For this study, ordinary least squares regression will be applied, with a parametric form of:

M_W,proxy = β₁ × M + β₀

(1)

where β₀ is the intercept, β₁ is the slope, and M is the magnitude type from an agency of interest.

Although much of the literature purports the advantages of orthogonal type regressions [1,3,25], many of these presentations assume equal measurement variance to perform their regressions as such uncertainty parameters are typically not available in the input magnitudes. Several studies suggest the a priori assumption of equal uncertainties is not true [7,11,26,27]. Moreover, the resultant regressions would suggest the input also be a random variable, which makes use of such regressions impractical. This is not to say that ordinary least squares regression is better, but that the impact of varying M_W pools should not be significantly affected by regression type. Interestingly, at least one study on magnitude homogenization comparing linear and orthogonal regressions showed similar results when there were few outliers [4].

2.3. Magnitude Pool Expansion

The target scale for homogenization herein is M_W from GCMT, (M_W,GCMT) due to reasons stated previously. The magnitude homogenization regressions using the pool of M_W,GCMT records from the compiled catalogs are considered the controls in this study. From this, two approaches are used to expand the M_W,GCMT pool for magnitude homogenization.

One is to include all relevant sources related to GCMT. These include HRVD and ISC-GEM. However, only ISC-GEM records with a listed M_W,GCMT or a M_W from a bibliographic source are included. This excludes records where ISC homogenization was applied. Moreover, since bibliographic sources are included, earthquakes from the ISC Event Bibliography (EVBIB) with a recorded M_W are also included. Most of the records in EVBIB are in ISC-GEM. This extended M_W pool is called M_{W,GCMT-related}.

Another approach is to use statistical hypothesis testing [4,8]. The assumption is if one moment magnitude type from any source is significantly similar enough to the control pool M_W,GCMT, then the remaining magnitudes of the same magnitude type from the same source would also be similar to M_W,GCMT. Hypothesis testing herein involves applying t-tests to regression parameters β₁ and β₀ derived from magnitude homogenization with other M_W formats. For this study, t-tests are conducted when a magnitude type from a specific agency or project has at least 5 data pairs due to regression calculation issues. For each comparison, a calculated t-statistic, t, is used to estimate a p-value from Student’s t-distribution. This p-value represents the probability that, given a model, results as extreme as the observed results could occur. p-values are compared to a pre-determined threshold, α, where p-values less than or equal to α suggest a rejection of the null hypothesis, H₀, and that the differences are statistically significant. Using an α = 0.05, the null hypotheses are H₀:β₁ = 1 and H₀:β₀ = 0, which is a one-to-one line in magnitude homogenization space. The t-statistic for H₀:β₁ = 1 is:

$$\mathrm{t}=\frac{{\mathsf{\beta }}_1-1}{\mathit{SE}\left({\mathsf{\beta }}_1\right)}$$

(2)

where SE(β₁) is the standard error of the estimate of β₁ and is taken as:

$$\mathit{SE}\left({\mathsf{\beta }}_1\right)=\sqrt{\frac{\mathrm{MSE}}{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\overline{x}\right)}^2}}$$

(3)

where i is the index, n is the number of data points, x_i are the dependent variable, x¯ is the mean of the dependent variable, and MSE is the mean squared error taken as:

$$\mathrm{MSE}=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{n-2}$$

(4)

where y_i is the dependent variable and ŷ_i is the appropriate regression model. However, when applying hypothesis testing for the equivalence of two regressed slopes, that is H₀:β₁ = β_a, the t-statistic becomes:

$$\mathrm{t}=\frac{{\mathsf{\beta }}_1-{\mathsf{\beta }}_{\mathrm{a}}}{\sqrt{\mathit{SE}{\left({\mathsf{\beta }}_1\right)}^2+\mathit{SE}{\left({\mathsf{\beta }}_{\mathrm{a}}\right)}^2}}$$

(5)

where β_a is the target regressed slope for comparison.

If the null hypothesis for the slope is not rejected, then another t-test is applied to the regressed intercept. The t-statistic for H₀:β₀ = 0 is:

$$\mathrm{t}=\frac{{\mathsf{\beta }}_0-0}{\mathit{SE}\left({\mathsf{\beta }}_0\right)}$$

(6)

where SE(β₀) is the standard error of the estimate of β₀ and is taken as:

$$\mathit{SE}\left({\mathsf{\beta }}_0\right)=\sqrt{\mathrm{MSE}}\sqrt{\frac{1}{n}+\frac{{\overline{x}}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\overline{x}\right)}^2}}$$

(7)

Similar to the t-test for two regressed slopes, hypothesis testing between two regressed intercepts has a similar t-statistic as calculated in Equation (5) with the substitution of Equation (7) into Equation (5) for the standard error of the estimate of β₀. If both null hypotheses for regressed slope and intercept are not rejected, then there is no significant difference between the relationships or regressions.

However, the ISC-GEM and EVBIB catalogs present special cases to the M_W,GCMT pool for hypothesis testing. Data from ISC-GEM could not undergo hypothesis testing as it would be comparing a subset of ISC-GEM data from GCMT sources against the same subset of GCMT data, resulting in β₁ = 1, β₀ = 0, and SE(β₁) = 0. Therefore, ISC-GEM data is included in the M_W pool. Conversely, EVBIB has similar issues with ISC-GEM, but the data in EVBIB is not found in GCMT. This would result in no β₁ or β₀ from magnitude homogenization. The inclusion of EVBIB is under the assumption that if unedited data from ISC-GEM is reliable and included, then the data from EVBIB, i.e., similar bibliographic sources in ISC-GEM, should also be reliable and thus included in the M_W pool for homogenization.

The M_W pool from GCMT, ISC-GEM, and EVBIB is used to derive magnitude homogenization regressions with other M_W types from other agencies. Those moment magnitude types and sources that do not reject the null hypotheses are added to an extended M_W pool called M_{W,GCMT-hypothesis} for magnitude homogenization with other non-moment magnitude types.

The control and expanded catalogs, i.e., M_W, M_W-related, and M_W-hypothesis, are used for estimating regressions involving global agencies ISC and NEIC, as well as local regional agencies DJA and KMA. Although other agencies and projects may be considered in the magnitude expansion approach, they are not explicitly considered for magnitude homogenization herein.

3. Results

Compiled catalogs for both Indonesia and South Korea resulted in magnitude types M_W, M_WW, M_WC, M_WB, M_WR, M_WP, M_Wppsm, M_S, M_SZ, M_S20, m_b, M_L, M_Lv, M_D, and M. Note that M is an unknown magnitude type and can be treated as a M_L type as noted by ISC [28]. The seismological agencies and projects that supplied these magnitude types are listed in

Table 1. Seismological agencies and projects that provided relevant earthquake data for this study.

Code	Agency	Country	Status
CGS	Coast and Geodetic Survey of the United States	U.S.A.	Inactive
DJA	Badan Meteorologi, Klimatologi dan Geofisika	Indonesia	Active
EVBIB	Data from publications listed in the ISC Event Bibliography	Unknown	Inactive
GCMT	The Global CMT Project	U.S.A.	Active
GS	U.S. Geological Survey	U.S.A.	Active
HRVD	Harvard University	U.S.A.	Inactive
IPGP	Institut de Physique du Globe de Paris	France	Active
ISC	International Seismological Centre	U.K.	Active
ISC-GEM	Global Instrumental Earthquake Catalogue	U.K.	Active
ISC-PPSM	International Seismological Centre Probabilistic Point Source Model	U.K.	Active
ISS	International Seismological Summary	U.K.	Inactive
JMA	Japan Meteorological Agency	Japan	Active
KMA	Korea Meteorological Administration	South Korea	Active
MOS	Geophysical Survey of Russian Academy of Sciences	Russia	Active
NEIC	National Earthquake Information Center	U.S.A.	Active
NEIS	National Earthquake Information Service	U.S.A.	Active
NIED	National Research Institute for Earth Science and Disaster Resilience	Japan	Active
P&S	Pacheco and Sykes catalog [29]	Unknown	Inactive
USCGS	United States Coast and Geodetic Survey	U.S.A.	Active

. Although the search of the global and local catalogs returned several more seismological agencies and magnitude types not mentioned, they were not considered to remain in the scope of this study.

3.1. Indonesia

A map showing the epicenters of the search results is shown in Figure 1, demonstrating high seismicity in the region. A total of 105,327 events are in the Indonesian catalog with major contributions from ISC, NEIC, and DJA. Although moment magnitudes from NEIC include M_W, M_WW, M_WC, M_WB, M_WR, there is an issue of timing. NEIC published M_W from 1980 to 2013 and then changed to a combination of M_WW, M_WC, M_WB, and M_WR thereafter [22,30]. Indonesian earthquakes with NEIC moment magnitudes are plotted in Figure 2, demonstrating the timeframes when each type is valid. On the other side, Figure 3 shows DJA has an approximate 4-year gap for earthquakes with a recorded M_W, from 2007 to 2009 and then from 2013 to 2019, however for M_WP, DJA seems to show continuous record-keeping from 2007 to 2019. Additionally plotted in Figure 3 are some of the earthquakes from bibliographic-based sources, namely EVBIB and P&S. EVBIB only goes from 1964 to 1976, while the catalog from P&S spans 1907 to 1987. Note that both EVBIB and P&S are no longer operational, as shown in Table 1.

A tally of the different magnitude types is shown in

Table 2. Number of earthquakes by seismological agency and magnitude type for Indonesia.

	Number of Events per Magnitude Type
Agency	MW 1	MS	mb	ML	MD	M
DJA	1239	27	11,486	30,980 3	3531	249
EVBIB	42	0	0	0	0	0
GCMT	3915	0	0	0	0	0
HRVD	944	0	0	0	0	0
IPGP	95	0	0	0	0	0
ISC	0	12,498	45,569	0	0	1
ISC-GEM	2779	0	0	0	0	0
ISC-PPSM	31	0	0	0	0	0
NEIC	1341	3538 2	35,740	12	0	0
MOS	16	3127	8677	0	0	167
P&S	48	33	0	0	0	0

¹ Includes all recorded moment magnitude types. ² Includes M_SZ and M_S20 magnitude types. ³ Includes M_Lv magnitude type.

. To present a more concise tally, all types of moment magnitude are listed under M_W, all surface wave type magnitudes for NEIC are listed under M_S, and all local magnitude types for DJA are listed under M_L.

The table shows that the initial number of earthquakes recorded under M_W,GCMT is 3915. The number of earthquakes in the M_{W,GCMT-related} pool is 3977, with additions of 53, 3, and 6 events from ISC-GEM, EVBIB, and HRVD, respectively. The initial base of the M_{W,GCMT-hypothesis} pool contained 3971 earthquakes from GCMT, ISC-GEM (GCMT and bibliographic sources), and EVBIB as stated previously. After hypothesis testing, the number increased to 4014, with contributions from NEIC, P&S, and MOS, the only sources that did not reject the null hypotheses for both regression slopes and intercepts, with more details shown in

Table 3. Hypothesis testing results against a M_W pool from GCMT, ISC-GEM, and EVBIB for the Indonesian catalog. Significance level α = 0.05.

Agency	Number of Data Pairs	Slope, β1	Intercept, β0	Standard Deviation, σ	t-Statistic β1/β0	p-Value β1/β0	Significantly Different?
DJA MW	326	0.955	0.232	0.187	2.54/2.31	0.00/0.02	Yes
DJA MWP	693	1.031	−0.189	0.191	1.84/2.06	0.07/0.04	Yes
HRVD	938	0.990	0.041	0.032	4.84/3.75	0.00/0.00	Yes
IPGP	95	0.943	0.312	0.089	3.03/2.71	0.00/0.01	Yes
ISC-PPSM	30	1.235	−1.760	0.146	2.83/3.35	0.01/0.00	Yes
NEIC MW	811	0.991	0.071	0.123	1.07/1.42	0.29/0.16	No
NEIC MWW	329	0.961	0.256	0.089	3.97/4.71	0.00/0.00	Yes
NEIC MWC	19	0.914	0.547	0.041	3.38/3.35	0.00/0.00	Yes
NEIC MWB	160	0.992	0.138	0.099	0.48/1.40	0.63/0.16	No
NEIC MWR	5	0.865	0.771	0.044	2.15/2.46	0.12/0.09	No
NEIC MW,all	1171	0.976	0.165	0.114	3.99/4.70	0.00/0.00	Yes
MOS	16	0.929	0.763	0.266	0.71/1.06	0.05/0.31	No
P&S	14	0.799	1.576	0.262	1.16/1.21	0.27/0.25	No

. The table shows that only the M_W, M_WB, and M_WR magnitude types from NEIC had significantly similar slopes and intercepts to a one-to-one line. Test results resulted in 6, 0, 3, 34, and 0 events being added from NEIC M_WR, NEIC M_WB, NEIC M_W, Pacheco and Sykes [29], and MOS, respectively. Note that hypothesis testing suggested HRVD recorded moment magnitude events were significantly different from a one-to-one line.

The resultant magnitude homogenization regressions for all surface wave magnitude types considered herein, i.e., M_S,ISC, M_S,NEIC, M_S20,NEIC, M_SZ,NEIC, are shown in

Table 4. Magnitude homogenization regression results from all moment magnitude pools for surface wave magnitude types.

Magnitude Type	Pool	Slope, β1	Intercept, β0	Correlation, R2	Standard Deviation, σ	Number of Data Pairs
MS,ISC	MW,GCMT	0.644	2.282	0.873	0.181	3820
	MW,GCMT-related	0.651	2.249	0.878	0.184	3873
	MW,GCMT-hypothesis	0.661	2.202	0.887	0.185	3904
MS,NEIC	MW,GCMT	0.737	1.753	0.886	0.190	1268
	MW,GCMT-related	0.735	1.763	0.887	0.190	1291
	MW,GCMT-hypothesis	0.736	1.758	0.889	0.190	1295
MS20,NEIC	MW,GCMT 1	0.737	1.737	0.877	0.163	200
	MW,GCMT-related 1	0.737	1.737	0.877	0.163	200
	MW,GCMT-hypothesis 1	0.737	1.737	0.877	0.163	200
MSZ,NEIC	MW,GCMT	0.695	2.019	0.896	0.166	707
	MW,GCMT-related	0.694	2.023	0.895	0.166	714
	MW,GCMT-hypothesis	0.694	2.024	0.895	0.166	714

¹ Pool of M_W data did not change for the corresponding magnitude type.

. The results show little variation when considering different moment magnitude pools. Moreover, the M_W,GCMT, M_{W,GCMT-related}, and M_{W,GCMT-hypothesis} pools ended up being comprised of the same events when paired with M_S20,NEIC earthquakes. Although regressions with M_S20,NEIC and M_SZ,NEIC resulted in the lowest σ, they also used the fewest number of data points in their regressions. Interestingly, the regression results using M_S,NEIC and M_S20,NEIC were not significantly different, t(1461,0.05) = 1.962, p = 0.956 for the slope and p = 0.477 for the intercept, but were significantly different between M_S,NEIC and M_SZ,NEIC, t(2005,0.05) = 1.962, p = 0.000 for the slope and p = 0.000 for the intercept. Similar t-test results when either M_{W,GCMT-related} or M_{W,GCMT-hypothesis} are used. This implies that M_S,NEIC and M_S20,NEIC datasets can be combined to perform magnitude homogenization, a related topic mentioned in a previous study [3].

Hypothesis testing was also conducted on regression parameters across moment magnitude pools. For M_S,ISC regression parameters, only results from M_W,GCMT and M_{W,GCMT-hypothesis} showed a significant difference with t(7720,0.05) = 1.960, p = 0.002 for the slope and p = 0.003 for the intercept. For M_S,NEIC and M_SZ,NEIC regression parameters, hypothesis testing found no significant differences across moment magnitude pools. Hypothesis testing was not conducted on regression parameters from M_S20,NEIC.

Figure 4a–d show M_{W,GCMT-related} against M_S,ISC, M_S,NEIC, M_S20,NEIC, and M_SZ,NEIC, respectively. Additionally shown in the figures are the data from M_W,GCMT for comparison. As suggested from the aforementioned regressions results, there are very few differences between the datasets. Figure 5 also shows similar results for M_{W,GCMT-hypothesis} against M_S,ISC, M_S,NEIC, and M_SZ,NEIC. Note that all resultant regressions appear similar to each other.

The resultant magnitude homogenization regressions for all body wave magnitude types considered herein, i.e., m_b,ISC, m_b,NEIC, m_b,DJA, are shown in

Table 5. Magnitude homogenization regression results from all moment magnitude pools for body wave magnitude types.

Magnitude Type	Pool	Slope, β1	Intercept, β0	Correlation, R2	Standard Deviation, σ	Number of Data Pairs
mb,ISC	MW,GCMT	1.066	−0.203	0.735	0.259	3915
	MW,GCMT-related	1.072	−0.231	0.736	0.262	3963
	MW,GCMT-hypothesis	1.078	−0.263	0.738	0.263	3970
mb,NEIC	MW,GCMT	1.127	−0.589	0.753	0.251	3909
	MW,GCMT-related	1.132	−0.610	0.754	0.253	3954
	MW,GCMT-hypothesis	1.141	−0.657	0.746	0.254	3963
mb,DJA	MW,GCMT	0.968	0.036	0.682	0.268	1711
	MW,GCMT-related	0.968	0.035	0.681	0.268	1712
	MW,GCMT-hypothesis	0.970	0.024	0.683	0.268	1717

Pool of M_W data did not change for the corresponding magnitude type.

. There were significantly more data points for regression across the board and increasing σ as the moment magnitude pool went from M_W,GCMT to M_{W,GCMT-hypothesis}.

Hypothesis testing was also conducted on regression parameters across moment magnitude pools. For m_b,ISC and m_b,DJA regression parameters, hypothesis testing found no significant differences across moment magnitude pools. However, for m_b,NEIC regression parameters, all three moment magnitude pools resulted in significantly different parameters. Results from M_W,GCMT differed from M_{W,GCMT-related} and M_{W,GCMT-hypothesis} in the intercept with t(7859,0.05) = 1.960, p = 0.02 and t(7868,0.05) = 1.960, p = 0.00, respectively. Results from M_{W,GCMT-related} significantly differed from M_{W,GCMT-hypothesis} with t(7913,0.05) = 1.960, p = 0.00.

The resultant magnitude homogenization regressions for M_{W,GCMT-related} against m_b,ISC, m_b,NEIC, and m_b,DJA are shown in Figure 6a–c, respectively. Additionally shown in the figures are the data from M_W,GCMT for comparison. There is considerable scatter, as evident with the relatively high σs. Even though there appear to be differences in regression results for each magnitude type, the differences appear negligible when plotted.

Conversely, regressions against M_{W,GCMT-hypothesis} for against m_b,ISC, m_b,NEIC, and m_b,DJA are shown in Figure 7a–c, respectively, as well as the data from M_W,GCMT for comparison. Again, similar to the results from M_{W,GCMT-related}, the regression models appear virtually identical with considerable scatter in the data across magnitudes. Given these results, it appears that surface wave magnitudes would be better for magnitude homogenization purposes due to the relatively lower σs.

The resultant magnitude homogenization regressions for local magnitude types are shown in

Table 6. Magnitude homogenization regression results from all moment magnitude pools for local magnitude types from DJA.

Magnitude Type	Pool	Slope, β1	Intercept, β0	Correlation, R2	Standard Deviation, σ	Number of Data Pairs
ML,DJA	MW,GCMT 1	0.515	2.578	0.313	0.389	102
	MW,GCMT-related 1	0.515	2.578	0.313	0.389	102
	MW,GCMT-hypothesis 1	0.515	2.578	0.313	0.389	102
MD,DJA	MW,GCMT 1	1.140	−0.435	0.498	0.335	125
	MW,GCMT-related 1	1.140	−0.435	0.495	0.335	125
	MW,GCMT-hypothesis 1	1.140	−0.435	0.498	0.335	125
MLv,DJA	MW,GCMT 1	0.768	1.076	0.744	0.222	1287
	MW,GCMT-related 1	0.768	1.076	0.744	0.222	1287
	MW,GCMT-hypothesis	0.771	1.062	0.746	0.222	1293

¹ Pool of M_W data did not change for the corresponding magnitude type.

. The results show little variation across the moment magnitude pools. For M_L,DJA and M_D,DJA, the addition of related and significantly similar catalogs and bibliographic sources did not expand the expand the M_W,GCMT pool, essentially saying that DJA did not have additional moment magnitude records outside of GCMT. Although M_Lv,DJA presented the same moment magnitude events with M_W,GCMT and M_{W,GCMT-related}, the pool from M_{W,GCMT-hypothesis} contained an additional 6 events, all low magnitudes from M_WR,NEIC. Even so, the regression results do not differ by much.

Since all three moment magnitude pools for M_L,DJA and M_D,DJA are identical, no hypothesis testing was needed. Still, hypothesis testing conducted on regression parameters from M_W,GCMT and M_{W,GCMT-hypothesis} did not reveal any significant differences. This suggests that all three moment magnitude pools resulted in similar magnitude homogenization regression parameters.

The resultant magnitude homogenization regressions for M_{W,GCMT-related} against M_L,DJA, M_D,DJA, and M_Lv,DJA are shown in Figure 8a–c, respectively. Since the moment magnitude pools for M_{W,GCMT-related} and M_{W,GCMT-hypothesis} did not differ for M_L,DJA and M_D,DJA only the results from M_{W,GCMT-related} are plotted for brevity. Additionally, since the moment magnitude pools for M_W,GCMT and M_{W,GCMT-hypothesis} are different for M_Lv,DJA, only the results for M_{W,GCMT-hypothesis} are presented. Data from M_W,GCMT are presented in all plots for comparison. As suggested previously, the regressions do not make much of a difference when plotted.

3.2. South Korea

A map showing the epicenters of the search results is shown in Figure 9, suggesting low seismicity in the region. There are a total of 1544 events in the South Korean catalog with major contributions from ISC, KMA, JMA, and NIED. South Korean-related earthquakes with NEIC moment magnitudes are plotted in Figure 10, demonstrating the general sparsity of events available to compile a catalog, especially in comparison to the Indonesian catalog compiled herein. On the other side, Figure 11 shows KMA recorded many low magnitude events in the Korean peninsula since its inception in 1978.

A tally of the different magnitude types is shown in

Table 7. Number of earthquakes by seismological agency and magnitude type for South Korea.

	Number of Events per Magnitude Type
Agency	MW 1	MS	mb	ML	MD	M
GCMT	15	0	0	0	0	0
HRVD	3	0	0	0	0	0
ISC	0	46	100	0	0	0
ISC-GEM	17	0	0	0	0	0
JMA	7	0	0	0	0	479
KMA	0	0	0	1053	0	0
NEIC	8	12 2	71	1	0	1
NIED	135	0	0	0	0	0

¹ Includes all recorded moment magnitude types. ² Includes M_SZ and M_S20 magnitude types.

. To present a more concise tally, all types of moment magnitude are listed under M_W and all surface wave type magnitudes for NEIC are listed under M_S. Relative to Indonesia, there are significantly fewer earthquakes to consider for catalog development. Understandably, there are no EVBIB events recorded for South Korea. Moreover, relative to international agencies, there are notable record contributions from local and regional Japanese agencies, JMA and NIED.

The table shows the initial number of earthquakes recorded under M_W,GCMT is 15. The number of earthquakes in the M_{W,GCMT-related} pool is 17, with additions of 2 and 0 events from ISC-GEM and HRVD, respectively. Although HRVD should not be considered in this study due to the low number of events, it is shown here only for completeness as it is relevant to GCMT-related studies. Note EVBIB did not appear in search results. The initial base of the M_{W,GCMT-hypothesis} pool contained 17 earthquakes from GCMT and ISC-GEM (GCMT and bibliographic sources). After hypothesis testing, the number increased to 20, with contributions from NEIC and JMA, the only sources that did not reject the null hypotheses with more details shown in

Table 8. Hypothesis testing results against a M_W pool from GCMT and ISC-GEM for the South Korean catalog. Significance level α = 0.05.

Agency	Number of Data Pairs	Slope, β1	Intercept, β0	Standard Deviation, σ	t-Statistic β1/β0	p-Value β1/β0	Significantly Different?
HRVD	3	1.019	−0.144	0.056	0.27/0.35	0.83/0.79	No
JMA	5	1.000	0.000	0.071	0.00/0.00	1.00/1.00	No
NEIC MW	3	1.354	−2.065	0.015	14.05/14.23	0.05/0.04	Yes
NEIC MWW	3	1.053	−0.240	0.053	0.43/0.38	0.74/0.77	No
NEIC MWB	1	N/A	N/A	N/A	N/A/N/A	N/A/N/A	N/A
NEIC MWR	4	0.846	0.792	0.122	0.83/0.74	0.49/0.54	No
NEIC MW,all	7	1.039	−0.182	0.148	0.34/0.30	0.75/0.78	No
NIED	5	0.938	0.371	0.036	2.88/3.25	0.02/0.01	Yes

N/A = not applicable.

. The contributions from HRVD are superseded by records in GCMT. In terms of NEIC moment magnitudes, the table shows that only the M_WW and M_WR magnitude types had significantly similar slopes and intercepts to a one-to-one line. Note that there are no M_WC records in the search results. The test results show two and one events being added from JMA M_W and NEIC M_WR, respectively.

The resultant magnitude homogenization regressions for all surface wave magnitude types considered herein, i.e., M_S,ISC, M_S,NEIC, M_S20,NEIC, M_SZ,NEIC, are shown in

Table 9. Magnitude homogenization regression results from all moment magnitude pools for surface wave magnitude types.

Magnitude Type	Pool	Slope, β1	Intercept, β0	Correlation, R2	Standard Deviation, σ	Number of Data Pairs
MS,ISC	MW,GCMT	0.663	1.988	0.885	0.169	14
	MW,GCMT-related	0.624	2.161	0.919	0.164	16
	MW,GCMT-hypothesis	0.613	2.221	0.923	0.157	18
MS,NEIC	MW,GCMT 1	0.635	2.321	0.941	0.076	4
	MW,GCMT-related 1	0.635	2.321	0.941	0.076	4
	MW,GCMT-hypothesis 1	0.635	2.321	0.941	0.076	4
MS20,NEIC	MW,GCMT 1	N/A	N/A	N/A	N/A	2
	MW,GCMT-related 1	N/A	N/A	N/A	N/A	2
	MW,GCMT-hypothesis 1	N/A	N/A	N/A	N/A	2
MSZ,NEIC	MW,GCMT 1	N/A	N/A	N/A	N/A	1
	MW,GCMT-related 1	N/A	N/A	N/A	N/A	1
	MW,GCMT-hypothesis 1	N/A	N/A	N/A	N/A	1

¹ Pool of M_W data did not change for the corresponding magnitude type. N/A = not applicable.

. The results show little variation when considering different moment magnitude pools for M_S,ISC and M_S,NEIC, where the moment magnitude pools for M_S,NEIC did not differ from a GCMT base. Although regressions with M_S,NEIC resulted in very low σ, they also used very little data for regression. Unfortunately, there are not enough data pairs for M_S20,NEIC and M_SZ,NEIC to perform meaningful magnitude homogenization regression.

Hypothesis testing on the regression parameters from each moment magnitude pool using M_S,ISC data resulted in no significant differences, suggesting the resultant regression parameters are similar. Hypothesis testing was not conducted on regression parameters for M_S,NEIC, M_S20,NEIC, and M_SZ,NEIC as their moment magnitude pools were identical.

Figure 12a,b show M_{W,GCMT-related} against M_S,ISC and M_S,NEIC, respectively, while Figure 12c shows M_{W,GCMT-hypothesis} against M_S,ISC. Additionally shown in the figures are the data from M_W,GCMT for comparison. Regressions for M_S20,NEIC and M_SZ,NEIC are not shown as there is not enough data to conduct regressions. As suggested from the aforementioned regressions results, there are very few differences between the datasets.

The resultant magnitude homogenization regressions for all body wave magnitude types considered herein, i.e., m_b,ISC, m_b,NEIC are shown in

Table 10. Magnitude homogenization regression results from all moment magnitude pools for body wave magnitude types.

Magnitude Type	Pool	Slope, β1	Intercept, β0	Correlation, R2	Standard Deviation, σ	Number of Data Pairs
mb,ISC	MW,GCMT 1	1.056	−0.139	0.876	0.246	15
	MW,GCMT-related 1	1.056	−0.139	0.876	0.246	15
	MW,GCMT-hypothesis	0.951	0.399	0.762	0.259	17
mb,NEIC	MW,GCMT 1	1.163	−0.748	0.802	0.235	15
	MW,GCMT-related 1	1.163	−0.748	0.802	0.235	15
	MW,GCMT-hypothesis	1.000	0.100	0.778	0.250	17

¹ Pool of M_W data did not change for the corresponding magnitude type.

. Both m_b,ISC and m_b,NEIC had identical moment magnitude pools between M_W,GCMT and M_{W,GCMT-related}. Regression σs are noticeably high for each regression given the number of data points available. Since M_W,GCMT and M_{W,GCMT-related} contained identical records against m_b,ISC and m_b,NEIC, there was no need to conduct hypothesis testing on their regression parameters. Hypothesis testing conducted on regression parameters derived from M_{W,GCMT-hypothesis} found no significant differences for m_b,ISC and m_b,NEIC results.

The resultant magnitude homogenization regressions for M_{W,GCMT-hypothesis} against m_b,ISC and m_b,NEIC are shown in Figure 13a,b, respectively. Additionally shown in the figures are the data from M_W,GCMT for comparison. Since regression results using M_W,GCMT and M_{W,GCMT-hypothesis} pools are identical, they are not plotted in the figure. Even though there appear to be some differences in regression results for each magnitude type, the differences appear negligible when plotted.

The resultant magnitude homogenization regressions for M_L,KMA are shown in

Table 11. Magnitude homogenization regression results from all moment magnitude pools for local magnitude types from DJA.

Magnitude Type	Pool	Slope, β1	Intercept, β0	Correlation, R2	Standard Deviation, σ	Number of Data Pairs
ML,KMA	MW,GCMT 1	0.596	2.027	0.814	0.181	12
	MW,GCMT-related 1	0.596	2.027	0.814	0.181	12
	MW,GCMT-hypothesis	0.725	1.371	0.882	0.174	14

¹ Pool of M_W data did not change for the corresponding magnitude type.

. Moment magnitude pools M_W,GCMT and M_{W,GCMT-related} are identical and therefore produced the same regression results. Although, the M_{W,GCMT-hypothesis} pool contains an additional two events, the regression results appear quite different even at a similar σ. Similar to the body wave results, hypothesis testing found no significant differences in regression parameters for M_L,KMA.

The resultant magnitude homogenization regressions for M_{W,GCMT-hypothesis} against M_L,KMA is shown in Figure 14. Since the moment magnitude pools for M_W,GCMT and M_{W,GCMT-related} did not differ, only the results from M_W,GCMT are included for brevity. The figure shows the regressions do seem to have a difference, however, the amount of data is limited.

4. Discussion

It is interesting to see that the techniques presented in expanding the pool of available moment magnitudes for magnitude homogenization only increased the pool size by at most 2% for the body and surface wave-related magnitude types and almost no increase for local magnitude types. These increases were primarily seen in the high seismicity study region. For a region of low seismicity such as South Korea, these techniques did not significantly influence regressed parameters.

It should be noted that in a previous study on magnitude homogenization in South Korea [4], the moment magnitude pool expansion technique was slightly biased in that it included data from NIED, which in this study was not directly related to the base M_W,GCMT and did not pass hypothesis testing for inclusion. However, other studies suggest that M_W from NIED is similar to M_W from HRVD and GCMT [3,30,31]. Although the use of literature was accepted in estimating seismic moments and thus moment magnitudes for M_{W,GCMT-related} herein, it is not sure if the use of literature in verifying consistency in agency magnitude types is warranted. For example, M_W,HRVD should be similar to M_W,GCMT, but hypothesis testing conducted previously demonstrates the linear regression parameters were significantly different.

It is noted that some works use bilinear regressions for their magnitude homogenization, such as the work by Scordilis [2]. Their work applied bilinear regression for MS data. However, their regression combined ISC and NEIC data and the inflection point where the regression is separated into two sections was subjectively chosen. The issue with the bilinear approach is that the standard deviations for each portion are different. Another team also implied this concern in their work [3]. Moreover, accounting for these differences ventures into the realm of nonlinear, or semi-nonlinear regression, which might violate some of the assumptions in hypothesis testing. This is a problem depending on how the resultant earthquake catalog is used and, to our knowledge, no one has provided a robust treatment of bilinear regressions for magnitude homogenization yet. We do not doubt there are better models out there, but these appear out of our scope.

In addition to limitations on linear regression models, there may be limitations due to ergodicity. Indonesia and South Korea do not represent all regions of varying seismicity. Even though the results suggest independence from seismicity, it may not ring true for other regions, especially those that have lower seismicity than South Korea. Moreover, the data for this study was taken from ISC, which did not record many low magnitude events. The verification of low magnitude events could significantly change the results.

5. Conclusions

Both approaches to expand moment magnitude pools for magnitude homogenization only increased the count by 1% with the most at 2%, with several of the expanded pools being identical to the base GCMT catalog. Magnitude homogenization regressions derived from these moment magnitude pools resulted in similar regression parameters. Additional statistical hypothesis testing concluded that for many magnitude types, the regression parameters were essentially the same across the different moment magnitude pools. Since these techniques were applied to both regions of high and low seismicity, it brings into question the effectiveness of the moment magnitude pool expansion techniques described herein.