DETERMINATION OF THE LOCAL MAGNITUDE SCALE (ML) FOR MONGOLIA

1. INTRODUCTION

Mongolia is located in East Asia, bordered on the north by the Siberian craton, on the south – by the India-Eurasia collision zone, and on the east – by the Pacific Plate, a remote subduction zone. The collision between the Indian and Eurasian plates and the subduction of the Pacific and Philippine Sea plates have had a profound effect on tectonic deformation in Asia [Wei et al., 2012]. Since 55 million years ago, the Indian Plate has been moving northward, causing the uplift of the Himalayas, the Tibetan Plateau, the Tien Shan, the Altai, and the Sayan Mountains [Molnar, Tapponnier, 1975; Hao et al., 2019]. This movement of the Indian Plate also affects the tectonic evolution of western China and Mongolia. GNSS monitoring of geodynamic activity of Mongolia has revealed the compressional forces exerted by the Indian Plate on the Eurasian Plate, as well as the relative direction and velocity of crustal motion. In western Mongolia, the displacement ranges from 10 mm/year in the southern region to 4 mm/year in the northern region, while the central and eastern regions show an east/southeast displacement at a rate of 4 mm/year [Calais et al., 2003]. As a result, western and central Mongolia are highly seismically active, whereas the eastern and southeastern regions are relatively less active.

The local magnitude (M_L), originally introduced in [Richter, 1935], has become a globally recognized standard and remains one of the most widely used magnitude types in earthquake catalogs. Designed as an empirical method to qualitatively assess earthquake strength, the Richter scale [Richter, 1935] continues to serve as a critical metric in both scientific analyses and real-time public communications. Region-specific calibration of the local magnitude (M_L) scale is critical for improving the reliability of seismic hazard assessments and for enhancing the accuracy of earthquake magnitude estimations in tectonically heterogeneous regions.

In Mongolia, since the installation of seismological stations in 1957, different approaches have been employed to determine the local magnitudes of earthquakes. The energy class K method – an indicator of earthquake strength widely used in the former Soviet Union, Mongolia and Cuba – was applied from 1957 to 2002. Since 2003, local magnitudes have been calculated using the equation developed in [Ulziibat, 2001], which remains in use to the present day. [Ulziibat, 2001] introduced the initial M_L equation, aligning with the Richter scale for Mongolia and stemming from the analysis of earthquake records obtained at short-period stations operated from 1994 to 2000. However, this formula showed a notable dependence on the epicentral distance. A revision in [Mungunsuren, Tatsuhiko, 2013] incorporated data from 143 local and regional earthquakes with magnitudes between 3.5 and 6.7, documented at 23 short-period stations in Mongolia from 2005 to 2012. This update became necessary because of the lack of the data and data quality and due to station instrument response.

Subsequently, the seismic network was modernized, going digital with the inclusion of broadband stations, enhancing the station density in Mongolia, and enabling the use of digital recordings for calculations. These new stations offer increased gain resulting in broader frequency response and dynamic range. Nonetheless, Mongolia still lacks a robust method for developing M_L equation parameters using comprehensive seismic data over an extended duration.

This situation has driven efforts to recalibrate the M_L equation parameters with the utmost accuracy, focusing specifically on Mongolia.

2. DATA AND METHOD

The functioning of the Mongolian seismic network can be categorized into four distinct periods: from the mid-1957s to 1994, characterized by photographic recording; from 1995 to 2005, featuring primary stations with short-period digital instruments alongside photographic recording; from 2005 to 2012, including stations with both short-period and broadband digital instruments; from 2013 onward, marked by the use of short-period, broadband, or accelerometer digital instruments. Since the installation of the first digital seismic station in Mongolia in 1994, there has been a steady increase in the number of digital short-period stations.

To increase seismic activity monitoring and expand seismological studies in Mongolia, numerous short-period seismometers were upgraded to high-sensitivity broadband seismometers between 2013 and 2015. The number of seismic stations in Mongolia has increased annually, with the current infrastructure comprising 35 permanent broadband stations (depicted as yellow triangles in Fig. 1), along with numerous mini-arrays and five regional digital three-component short-period seismometers. In the Ulaanbaatar area, sixteen of these broadband stations are equipped with CMG-3ESPC (60 and 120 s) broadband seismometers by Güralp Inc., featuring a sensitivity of 2000 V/m/s. A CMG-DM24S3EAM data logger (Güralp Inc.) is linked to each sensor. All stations consistently capture seismic data at a sampling rate of 50 Hz. The Mongolian seismic network consists of stations distributed throughout the country, transmitting real-time data to the Mongolian National Data Center at the Institute of Astronomy and Geophysics in Ulaanbaatar, Mongolia. Additionally, as part of the Central Mongolian Seismic Experiments [Meltzer et al., 2019], temporary broadband seismic arrays utilizing IRIS-PASSCAL instruments were set up in western Mongolia, such as the Govi-Altay region (14 stations) and the Khovsgol region (26 stations) between August 2014 and March 2016, and in the Hangay Dome area (72 stations) from June 2012 to July 2014 (depicted as blue triangles in Fig. 2). These temporary broadband seismic stations used the STS-2 seismometers and Quanterra Q330 digitizers with a sampling frequency of 100 Hz. By incorporating local data from both temporary and permanent broadband seismic stations, totaling 144 stations, installed and operated throughout Mongolia, we have developed a local magnitude formula.

2.1. Data selection

We analyzed around 20000 amplitude data from the Mongolia seismic catalog for the period 2012–2019, using recordings from 144 broadband stations. The selection criteria included local magnitudes (M_L) between 3.5 and 5.6, a signal-to-noise ratio greater than 1.5, epicentral distances less than 1,000 km, and recordings from at least five stations per event. Based on these criteria, 261 seismic events were selected, resulting in a final dataset comprising 8616 amplitude records. Fig. 2, a illustrates the sample distribution relative to epicentral distance, Fig. 2, b illustrates the magnitude (M_L) relative to epicentral distance, and Fig. 2, c presents the distribution of the event samples as a function of M_L.

Initially, all original waveforms were deconvolved with their respective instrument responses. Subsequently, the frequency response of the Wood – Anderson torsion seismograph for displacement was convolved, following the procedure described in [Uhrhammer, Collins, 1990], as this response has been adopted in the IASPEI standard procedures [IASPEI, 2005, 2013].

2.2. Method

The M_L scale, tailored for southern California’s shallow quakes, incorporated an epicentral distance correction as outlined in [Richter, 1935] and revised in [Richter, 1958]. [Richter, 1935] introduced a local magnitude calculated using the logarithm (logA) of the maximum trace amplitude (A) in millimeters. This measurement was taken using the horizontal components of a standard Wood – Anderson seismometer with specified parameters: a free period T=0.8 s, magnification 2800, and a damping factor 0.8 [Anderson, Wood, 1925]. According to [Richter, 1935] scale, an event with M_L=0 at 100 km epicentral distance produces a peak amplitude of 0.001 mm on a standard Wood – Anderson seismograph when S=0 and, similarly, an M_L=3 event yields a peak amplitude of 1 mm at 100 km. Using the original Richter relation (Equation 1) as a foundation, we employed the method introduced in [Hutton, Boore, 1987] to define the empirical distance correction function for calculating M_L,

M_L=log10A(R)−log10A₀(R)+S, (1)

−log10A₀=alog10A(R/100)−b(R−100)+3 (2)

where log10A(R) represents the observed zero-to-peak amplitude in millimeters in a WA seismogram, –logA₀ is the empirical distance correction, S is the empirically derived station correction, R is the epicentral distance in kilometers, and a and b are the respective empirical coefficients for geometric spreading and anelastic attenuation specific to the region. A constant 3 is added to adhere to the initial Richter M_L definition. To develop the new magnitude scale, we blend equations (1) and (2) to yield a precise distance-correction function as

M_Li−S_j−a·log10(R_ij/100)−b(R_ij−100)=log10A_ij+3;

i=1,2,...m; j=1,2,...n (3)

where A_ij is the maximum horizontal zero-to-peak amplitude of the i th event at the j th station, M_Li is the magnitude of the ith event, S_j is the station correction of the j th station, R_ij is the hypocentral distance from the ith event to the jth station, m is number of events, and n is number of stations. Equation (3) can be written in a standard matrix form as Gm=d, which represents a typical linear inversion prolem in geophysics that can be soved using the least squares method from [Alsaker et al., 1991; Miao, Langston, 2007; Nguyen et al., 2011].

The G-matrix, which consists of real values and is nonsingular, has dimensions (m×n+1)×(m+n+2), where m×n corresponds to the total number of amplitude measurements in the dataset. The linear system can be solved using the inverse of G. To ensure solution uniqueness, we apply a constraint that the sum of station corrections for a given event must be zero , as these corrections are only defined relative to each other [Menke, 2018].

The inverse matrix is computed using singular value decomposition [Press et al., 2007; Menke, 2018].

3. RESULTS AND DISCUSSION

For a total of 8616 amplitude data, converted to Wood – Anderson seismograms, 144 stations throughout Mongolia recorded 261 earthquakes with magnitudes greater than M_L 3.5 and epicentral distances ranging from 3 to 1000 km. To reduce the influence of outlying measurements defined by large residuals relative to the initial distance corrections derived from preliminary linear inversions, we applied an iterative outlier rejection procedure. Specifically, measurements with absolute residuals greater than 0.6 were considered outliers, corresponding to approximately two standard deviations (2σ) from the mean residual. Equation (2) was then solved repeatedly, starting with the full dataset of 8,616 measurements. After three iterations, a total of 170 measurements were identified as outliers and excluded from the final solution. Fig. 3, a presents the values of as a function of distance following the initial outlier removal step. Data points that fall outside of the specified bounds are marked with a blue line. Fig. 3, b shows the corresponding residual distribution at this stage. Fig. 3, c, d display the same types of plots: residuals versus distance and residual distribution, respectively, but for the final iteration, after all outliers had been identified and removed. The final distance correction functions were calculated in Equation (4) using these data and the methodology provided:

log10(A₀)=0.9287log10(R/100)+0.0012(R−100)+3. (4)

Based on defined distance correction functions, the magnitude formulas were converted to use amplitude measurements in nanometers and are expressed by Equation (5) as follows:

M_L=log10(A)+0.9287log10(R)+0.0012R−1.66 (5)

where A is the peak amplitude in nanometers as per a Wood – Anderson sensor simulation, and R is the hypocentral distance in kilometers.

Additionally, the regression analysis identified the station corrections, which are shown in App. 1, Table 1.1. Station correction factors were calculated to account for the local geological conditions at each station, with values ranging from –0.68 to +0.28. Fig. 4 illustrates distance correction functions derived from several regions: Southern California [Hutton, Boore, 1987], Northern Vietnam [Nguyen et al., 2011], Mongolia [Ulziibat, 2001; Mungunsuren, Tatsuhiko, 2013], Eastern Cuba [Diez Zaldivar et al., 2024], the central United States [Miao, Langston, 2007], and Mongolia (this study). Comparison of these functions indicates that the attenuation parameter b obtained in this study is higher than that reported for the central United States and the two previous magnitude scales for Mongolia. This increased value likely reflects greater seismic wave energy dissipation in the study area. Besides, as shown in Fig. 4, the distance correction curve derived in this study falls within two curves proposed for Northern Vietnam and Mongolia in [Mungunsuren, Tatsuhiko, 2013].

4. CONCLUSIONS

In this research, we derived new M_L scales for the horizontal component, using a dataset of 8446 amplitude readings from 261 earthquakes recorded between 2012 and 2019 at 144 broadband stations. These data enabled us to derive empirical coefficients for geometrical spreading and anelastic attenuation, which are essential for correcting the amplitude as a function of distance.

Station correction factors were also determined, reflecting local geological conditions beneath each station. The station corrections ranged from –0.68 to +0.28.

The new M_L scales offer more consistent magnitude estimations than the scale currently used in IAG’s routine seismic analysis. Based on these improvements, we recommend adopting the proposed M_L scales to replace the existing local magnitude scale used by the IAG.

5. ACKNOWLEDGEMENTS

The authors are grateful to everyone involved in the collection of seismic data for this research. We also thank the Institute of Astronomy and Geophysics of the Mongolian Academy of Sciences and the IRIS Data Management Center for their provision of seismic waveform data.

6. CONTRIBUTION OF THE AUTHORS

Baigalimaa Ganbat plays a key role in data curation, formal analysis, inquiry, software use, scripting, visualization, and primary paper drafting. The data resource was revised and edited by Ulziibat Munkhuu.

7. DISCLOSURE

The authors declare that they have no conflicts of interest relevant to this manuscript.

APPENDIX 1