According to the national standard “Regulations for Earthquake Magnitude” （GB 17740−2017）, the calibration function used by China’s seismic network to determine the short-period body-wave magnitude （m_b） is primarily applicable for the epicentral distance （Δ） range of 5°＜Δ＜100°. While this standard meets the monitoring requirements for teleseismic events, it poses severe technical challenges for the Northeast China deep seismic zone. Located in the deep zone of the subduction of the Pacific Plate beneath the Eurasian Plate, this area experiences frequent deep-focus earthquakes. For small-to-medium deep-focus earthquakes, due to their great focal depth, severe energy attenuation during propagation, and generally small magnitudes, effective signals are often clearly recorded only by near-field stations within an epicentral distance of 5°. Since the existing national magnitude standards lack calibration functions for the Δ＜5° region, the records from these near-field stations in Northeast China cannot be used to accurately determine magnitude m_b. This has led to under-recording of such events in China’s earthquake catalogs, severely constraining the in-depth scientific understanding of regional deep tectonic activities and seismic risks.

Based on the earthquake catalog from the International Seismological Centre （ISC）, this study selects deep-focus earthquake events in the Northeast China deep seismic zone since 2010. Fully utilizing waveform data recorded by 14 seismic stations from the regional networks in Heilongjiang and Jilin provinces, we conducted systematic research focusing on the attenuation characteristics of body-wave amplitudes within the 5° epicentral distance range. In the data processing stage, the original vertical component waveforms of 125 earthquake events recorded by these 14 stations were simulated into DD-1 short-period displacement records. By precisely measuring the maximum amplitude A （unit: μm） and the corresponding period T （unit: s） within the P-wave train, we identified a total of 740 PMZ phases available for magnitude calculation. Following the principles of body-wave magnitude determination, we performed inversion calculations for all valid earthquake-station pairs, ultimately obtaining 740 discrete Q （Δ, h） data points. In-depth analysis of these data reveals that Q （Δ, h） exhibits significant non-linear characteristics with variations in epicentral distance, focal depth, and hypocentral distance. Traditional calibration functions typically use exponential or logarithmic functions for fitting; however, the data in this study show a strong dispersion due to the complexity of deep seismic wave propagation paths in heterogeneous media and the multiplicity of energy attenuation mechanisms. Consequently, a single parametric model cannot accurately characterize the complex variations in the near-field region. To address this, we introduced the Kriging interpolation method from geostatistics to perform spatial interpolation on the calculated discrete Q （Δ, h） values, successfully constructing a continuous m_b magnitude calibration function model covering the entire study area （0°−5°）.

The results show that the newly constructed calibration function Q （Δ, h） values range between 4.45 and 4.86. Overall, Q （Δ, h） decreases non-linearly with decreasing epicentral distance and increasing focal depth. Notably, in the interval of Δ＝200−420 km and h＝400−550 km, the variation of Q （Δ, h） is most intense, exhibiting extremely high sensitivity to spatial location. This zone of intense variation may essentially reflect the combined effects of mineral phase transitions in the mantle transition zone and the subducting slab remnants, providing valuable seismological evidence for the study of the mantle structure in the Northeast China deep seismic zone. Interpolation variance and residual analysis verified the reliability of the Kriging interpolation results. The overall Kriging variance is less than 0.23, and 97.43% of the residuals fall within −1.0, 1.0 and follow a normal distribution, indicating the high precision of the interpolation model. Further magnitude verification shows that the standard deviation of the deviation between single-station magnitudes calculated using the new calibration function and the network average magnitude is 0.308, while the standard deviation of the deviation between network average magnitudes and ISC magnitudes is only 0.319. These results strongly demonstrate that this near-field calibration function not only eliminates local deviations in singlestation measurements, ensuring unbiased and consistent magnitude determination within the network, but also yields results highly consistent with international authoritative agencies, possessing high internal stability and external conformity. The practical application of this calibration function is significant, effectively lowering the minimum magnitude of completeness （M_c） of the region from the original 4.4 to 3.5 and establishing a more complete deep-focus earthquake catalog. Furthermore, key seismicity parameters calculated based on the new catalog （such as the b-value） are highly consistent with regional physical models, aligning with the intrinsic physical mechanisms of deep-focus earthquakes. This achievement not only enriches the catalog of small-to-medium deep-focus earthquakes in the Northeast China deep seismic zone, but also lays a solid data foundation for scientifically assessing seismic risks in the region.

In summary, this study successfully constructed a body-wave magnitude （m_b） calibration function Q （Δ, h） applicable to the near-field （0°−5°） of the Northeast China deep seismic zone. These findings compensate for the inability to use regional seismic stations in Northeast China to determine magnitude m_b for small-to-medium deep-focus earthquakes, filling a critical gap in China’s near-field deep-focus m_b determination. It provides key support for deepening the scientific understanding of deep tectonic activities and seismic hazards in the region, as well as offering important theoretical basis and technical reference for earthquake monitoring research under similar geological conditions.