1 INTRODUCTION

Indonesia is an archipelago with more than 17 000 islands and lies longitudinally from 94° to 141° with a wide range of geomagnetic fields. Geomagnetic fields also change over time and this is called secular variation. This variation results from the activities in the earth’s internal structure (Alken et al., 2021). A secular variation always changes and is hard to predict in months to millions of years (Geese et al., 2011). Based on this environmental condition, the regional geomagnetic measurement and modeling in the repeat stations are conducted periodically.

Some government and private sectors urgently need an accurate regional geomagnetic model of Indonesia. The economy, research, and mining sectors need a geomagnetic map with a declination accuracy of 0.1° and total intensity accuracy of 50 nT (Macmillan and Rycroft, 2010). The geomagnetic field measurement in Indonesia has been conducted by Badan Meteorologi, Klimatologi dan Geofisika, or Meteorological, Climatological, and Geophysical Agency of Indonesia (BMKG) at the repeat stations every epoch (five years) since 1985.

The geomagnetic field chart in each epoch is produced based on its measurement. The previous epoch (i.e., 2015.0) used 68 repeat stations as the data source. However, due to the COVID-19 pandemic at epoch 2020.0, some repeat stations were not accessible. Hence, only 49 repeat stations were observed and involved in the survey. Those locations involved are evenly distributed across Indonesia, as can be seen in Fig. 1. This decision optimally leveraged the limited locations to produce a good regional geomagnetic model.

Fig. 1.
figure 1

Distribution of the 49 repeat stations and 21 observatories for epoch 2020.0.

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All the repeat stations are in airport areas. Airports are accessible and vast, so it is easy to find a location isolated from electromagnetic noise. They are also available for a long period (more than 100 years). They can also be used to calibrate the runway azimuth (Loubser and Newitt, 2009; Rasson and Delipetrov, 2006) to support airport operations. The geomagnetic survey locations in each listed airport were marked by the lightning rod tip at the air traffic control tower, located at a distance more than 200 meters from the station to diminish any electromagnetic noise. The fixed location of the measurement across epochs could support the measurement of the secular variation value.

Regional geomagnetic field modeling needs a different method than global geomagnetic field modeling because the harmonic spherical equation analysis used by global modeling is not suitable for a limited orthogonal area (Mandea and Purucker, 2005). Moreover, the modeling for regional geomagnetic fields for epoch 2020.0 used fewer data than the previous epoch. The collocated cokriging (CC) method is proven to have enhanced accuracy for Indonesia’s regional geomagnetic field modeling (Syirojudin et al., 2022). By using this method, this paper aims to model regional geomagnetic fields for epoch 2020.0 and the crustal geomagnetic field model in Indonesia.

2 DATA AND METHODS

We used the following tools that were already calibrated and used in the survey:

1) The GSM-19T, a proton precision magnetometer, operated on its base station mode with a resolution of 0.01 nT. The accuracy of 0.2 nT is used to measure the geomagnetic field’s total intensity component (F).

2) The Mag-01H, a declination inclination magnetometer (DIM) with a resolution of 0.1 nT and a directional accuracy of three seconds, is used to measure the declination (D) and inclination (I) components of the geomagnetic field.

3) The MinGeo 010, a DIM with a resolution of 0.1 nT and a directional accuracy of one second, is also used to measure the D and I components of the geomagnetic field.

4) A GPS Garmin-76 PCX is used to measure the location’s longitude, latitude, and elevation.

The theodolite of the DIM is also used to observe the sun and measure the true azimuth (concerning geographic north) to provide the direction reference. The measurement process is based on the international standard from the International Association of Geomagnetism and Aeronomy (Newitt et al., 1996). The measurement is carried out at two periods each day, i.e., the morning and afternoon sessions. Each session fills five data observation forms using the DIM tool and three such forms using the DIM theodolite. Because the range of the D value in Indonesia is quite small, the measurement of the true azimuth reference mark is performed until an accuracy of five seconds in deviation is reached.

Pre-processing is needed before the main analysis because the measurement in a different location is carried out at a different time. The geomagnetic data obtained from the 49 locations are deducted by the diurnal variation data from the 21 observatory stations in Indonesia, followed by a deduction from the secular variation data to produce the epoch 2020.0 figures. The deduction is varied depending on the measurement time and location.

The next step is to process the data using the CC method to produce the geomagnetic figures for epoch 2020.0. CC is a geostatistical method with the best linear unbiased estimator (Webster and Oliver, 2008). It uses two or more variables to estimate the produced data model. In this paper, the geomagnetic data obtained from the survey are used as the primary data, and the main and crustal geomagnetic figures from the enhanced magnetic model (EMM 2017) are used as the secondary data. The following CC equation is used to compute the resulting value (Rivoirard, 2001) as shown in Equation (1).

$${{Z}_{{{\text{CC}}}}}\left( {{{x}_{0}}} \right) = \mathop \sum \limits_i {{\lambda }_{i}}{{Z}_{1}}\left( {{{x}_{i}}} \right) + \mu {{Z}_{2}}\left( {{{x}_{0}}} \right).$$
(1)

ZCC is the data estimation result of the CC method, λ is the weight of each location in the primary data (repeat station data), Z1 is the primary data, μ is the weight of each set of secondary data (EMM 2017), and Z2 is the secondary data.

The variogram model of both the primary and secondary data is computed to produce their parameter values (the range, sill, and nugget). Three types of variograms (i.e., primary data, secondary data, and cross or primary to secondary) are used for each geomagnetic component. The cross variogram (primary to secondary parameters) used in the CC model is in the range of 3.41, the sill 0.0023, and the nugget 0.0001 for the D component; the range of 27.8, the sill 228.1, and the nugget 10.2 for the I component; and the range of 24.12, the sill 6.3e + 6, and the nugget 6.3e + 5 for the F component as shown in Fig. 2.

Fig. 2.
figure 2

Semi-variogram of geomagnetic data from epoch 2020.0 for the CC method. Spherical variogram of D component consists of (a) repeat stations as primary data, (b) EMM as secondary data, and (c) primary to secondary data. I component for spherical variogram consists of (d) repeat stations as primary data, (e) EMM as secondary data, and (f) primary to secondary data. F component spherical variogram consists of (g) repeat stations as primary data, (h) EMM as secondary data, and (i) primary to secondary data.

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The secular variation is computed by subtracting the geomagnetic data of epoch 2020.0 from that of epoch 2015.0, then dividing them by five to get the annual change value. The annual change factor is used to compute and predict each year’s geomagnetic values from 2020.0 until 2025.0. However, the geomagnetic values of the six observatories were obtained empirically because they obtained daily measurements throughout the year.

3 RESULTS AND ANALYSIS

3.1 The Effect of Reducing the Number of Repeat Stations

We compared the analysis of reducing the number of repeat stations of the 2020.0 epoch with regional geomagnetic data for computing modeling from the previous epoch (i.e., epoch 2015.0) using the same method. The regional geomagnetic modeling of the 2020.0 epoch using the CC method results in a small root mean square error (RMSE) or σ for each component, i.e., σd = 1.18 minutes for D, σi = 11.1 minutes for I, and σf = 36.6 nT for F. The regional geomagnetic model for epoch 2015.0 resulted in a similar RMSE of 1.05 minutes for D, 10.98 minutes for I, and 35.4 nT for F.

The results show that a decrease in the number of repeat stations involved in the survey at epoch 2020.0 is not significantly different, even though fewer repeat stations were used in 2020.0 (28% fewer stations than the previous epoch). Fewer data in the CC method are compensated by semi-variogram secondary data generated from International Geomagnetic Reference Field (IGRF). Using variograms from secondary data is the advantage of the CC method (Abedi et al., 2015; Rivoirard, 2001). For the D component, the regional geomagnetic model for epoch 2020.0 indicates a RMSE of 0.13 minutes higher than epoch 2015.0. The I component’s RMSE is 0.12 minutes higher, and the F component’s RMSE is 1.2 nT higher than that of the previous epoch. This statement has been proven in our previous research, where the 28% data difference did not significantly affect this method (Syirojudin et al., 2022). The RMSE also still fulfills the required accuracy value in the mining sector, which is 0.1° for the D component and 50 nT for the F component (Macmillan and Rycroft, 2010).

3.2 Regional Geomagnetic and Secular Variation Charts of the 2020.0 Epoch

The regional geomagnetic model of Indonesia varies spatially in latitude and longitude. Indonesia lies from –12° to 8° and 94° to 141°, so it is impossible to have regular or linear variation caused by the dynamic structure under wide regional areas (Heirtzler and Nazarova, 2003; Korte and Lesur, 2012). The resulting regional geomagnetic chart of epoch 2020.0 has more detail than the global model provided in Fig. 3. It is caused by the global model typically limited by the accuracy and the resolution (Maus et al., 2005). Moreover, the global model uses only a small number of observatory stations in Indonesia, i.e., KPG, PLR, TND, and TUN (Alken et al., 2021). The D component in Indonesia is distributed along the longitude and has zero value. It divides into two regions, positive values eastward (from the middle to eastern Indonesia) and negative values westward (in western Indonesia). The I component in the whole of Indonesia provides the negative values with a straight-line contour. The F component of the geomagnetic measurement has distribution along latitude with positive values from 39 000 to 46 000 nT.

Fig. 3.
figure 3

Geomagnetic chart for epoch 2020.0 using the CC method in Indonesia; (a) D component with Δ = 0.5°, (b) I component with Δ = 5°, and (c) F component with Δ = 1000 nT.

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The secular variation modeling using the CC method specifies a RMSE of 0.03 minutes at the D component, 0.06 minutes at I, and 0.1 nT at F. The secular variation isolines are depicted in Fig. 4. The resulting secular variation data show that Indonesia has a small value change. Any considerable weakening of the geomagnetic values was not observed as the same result in the Pacific region (Yukutake and Shimizu, 2018). An example of a significantly weakened geomagnetic value was observed in the south Atlantic and southern African regions (Finlay et al., 2016). The secular variation model confirms the global model of the IGRF-12. Most of the area in the resulting regional model expresses a negative secular variation value of the D component. However, the western region indicates positive secular variation values, while the eastern region specifies negative secular variation values of the I component. All regions provide positive values for the F component, with the northwest as its greatest value.

Fig. 4.
figure 4

Secular variation chart for epoch 2020.0 in Indonesia; (a) D component with Δ = 1 minute; (b) I component with Δ = 1 minute; and (c) F component with Δ = 10 nT.

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3.3 Crustal Geomagnetic Field of Indonesia

We also computed the resulting regional geomagnetic model’s discrepancy with the global geomagnetic model (i.e., the IGRF-12) to model the crustal field bias by calculating mean data values from the three latest epochs (2010.0, 2015.0, and 2020.0). The crustal field model resulting from the CC method shows favorable accuracy with a RMSE value of 1.74 nT and high correlation with EMM (R2 values 0.8895) as given in Fig. 5b.

Fig. 5.
figure 5

Crustal field of the geomagnetic F component in Indonesia resulted from the mean of epochs 2010.0, 2015.0, and 2020.0 and correlation with earthquakes; (a) comparing crustal field at repeat station from the CC model, EMM, and earth magnetic anomaly grid 2-arc minutes resolution version-3 (EMAG2_V3) generated from https://www.ncei.noaa.gov/access/metadata/ landing-page/bin/iso?id=gov.noaa.ngdc.mgg.geophysical_models:EMAG2_V3, (b) correlation crustal field between CC model and EMM, (c) boxplot of earthquake data from 2010 to 2020 with magnitude (M) ≥ 6 and crustal field, and (d) crustal of the geomagnetic field and earthquake epicenter in Indonesia.

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The crustal field indicated that 94% of the repeat stations exist in low crustal field values, and only three repeat stations (i.e., Naha, Ternate, and Ambon) have crustal field values above 150 nT for the F component as shown in Fig. 5a. This information has contributed considerably to the global model (i.e., IGRF), which models the main field only (Finlay et al., 2010; Maus et al., 2005; Thébault et al., 2015) and needs to remove the crustal geomagnetic field (Korte and Lesur, 2012; Maus, 2008). The three repeat stations with high crustal fields exist in the triple junction of the tectonic and small islands with active volcanoes (i.e., Naha and Ternate) and Paleozoic formations, i.e., Ambon (Darman, 2000; Katili, 1975; Verstappen, 2014).

The spatial distribution of the crustal field is caused by the properties of magnetized rocks below the Curie temperature (Thébault et al., 2010). The crustal field of the F component varies spatially from –280 to 320 nT as shown in Fig. 5d. The low value distribution of the crustal field correlates with the earthquakes that occurred in this region. As shown in Figs. 5c, 5d, the great earthquakes took place from 2010 to 2020 in the crustal field value under 120 nT. The subduction zone and fault line have a low crustal field caused by frictional heating (Mishima et al., 2009) and partial melting (Krien and Fleitout, 2008; Garnero et al., 2016) in this area. During the earthquake cycle, the collision of two layers of rock in the seismogenic zone raise the Curie temperature (Chester, 1994; Scholz, 1998) and decrease crustal magnetization (Gao et al., 2015). When rock reaches a threshold temperature, it melts, encouraging more movement and friction to produce a wider melting area (Behr and Platt, 2014). This process continues until the rock elasticity limit is reached in the seismogenic zone and an earthquake occurs (Wang and Barbot, 2020).

4 CONCLUSIONS

This study analyzes the repeat station measurements for the 2020.0 epoch and data from the three latest epochs to explore the accuracy of the regional geomagnetic field for the 2020.0 epoch and the crustal geomagnetic field in Indonesia. The following conclusions were reached.

(1) The fewer repeat station data for the 2020.0 epoch still resulted in high accuracy with a small RMSE in each component and did not significantly differ from the previous epoch. <…>

(2) The regional geomagnetic and secular variation charts for the 2020.0 epoch are more detailed than the global model and vary spatially in latitude and longitude. <…>

(3) 94% of the repeat stations exist in low crustal field values. <…>

(4) The low crustal field correlates with the great earthquake epicenter that occurred in Indonesia. <…>