Due to the low observation cost and high signal-to-noise ratio of deep signals, the reception function is currently the most commonly used method for detecting crust-mantle structures. However, its resolution is much lower than that of deep reflection, and it can usually only provide the basic characteristics of crustal deformation, and cannot play a key role in the investigation and research of intracrustal deformation, seismic structure, and ore-controlling structure. Although in recent years, the resolution of receiving function imaging has been improved by encrypted observation of short-period dense arrays, but this improvement is limited due to the limitation of seismic wave frequency. Resolution is not only related to the spacing between the stations, but also to the frequency or wavelength of the seismic wave. Since the teleseismic body wave signal used by the reception function travels 3,000 to 10,000 kilometers, its high-frequency components are attenuated, and the low frequency limits the improvement of the spatial resolution of the reception function.
In order to improve the resolution of the natural seismic method to detect the velocity structure of the earth's crust, Zhang Liangyu, a master's student of the State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, and Tian Xiaobo, a supervisor, proposed a Pn wave reception function method. The refracted wave commonly used in seismology is the P wave generated by the earthquake in the crust from the crust down to the top of the mantle at a critical angle and glides along the top of the mantle. Pn mainly appears in the range of 2°-15° epicenter, the propagation distance is far small, and the attenuation is reduced, as shown in Figure 2, compared with the teleseismic body wave (less than 3 Hz), the Pn wave is rich in high-frequency components (20-30 Hz).
Fig.1 Schematic diagram of PN wave propagation path. The dotted lines of different colors indicate the propagation paths of Pn waves at different epicenter distances
Fig.2. Comparison of waveform frequency ranges of teleseismic P waves and Pn waves. The blue and red vertical dotted lines are 15 and 20 seconds in length for the waveform signal capture time window, respectively. The P-wave of a wideband station teleseismic is a P-wave record of a magnitude 5.6 earthquake with an epicenter of Xi'an Station at a distance of 41.6° (about 4500 km). The Pn wave at the broadband station is the Pn wave record of a magnitude 5.6 earthquake with an epicenter of 6.2° (about 700 km) from the station. Due to the limitation of the sampling rate of broadband array data, the frequency that can be analyzed is up to 10 Hz. The short-period station Pn wave is a Pn wave record for a magnitude 4.8 earthquake with an epicenter at a distance of 11.1° (about 1200 km).
The traditional reception function is obtained by deconvolution of the teleseismic waveform, which needs to meet the three assumptions of plane wave, no other seismic phase interference and near-perpendicular incidence. In this study, it was noted that the Pn wave has the following characteristics: (1) the Pn refracted wave enters the crust at a critical angle when it returns to the crust, and the propagation angle of the refracted wave returning to the crust remains unchanged in a long gliding propagation distance, that is, the refracted wave meets the plane wave requirement when it returns from the upper mantle to the crust, and (2) the Pn waveform is 5°-15° away from the epicenter(3) The Pn wave and its converted S wave can be separated by the particle motion polarization analysis recorded by the waveform, and the near-perpendicular incidence requirement is not required. Therefore, the Pn wave waveform can be recorded in the range of 5°-15° from the epicenter, the waveform can be intercepted by the appropriate time window length, the Pn wave component and the S wave component can be separated by polarization analysis and coordinate rotation, and then the Pn wave reception function can be obtained by using the deconvolution of these two components. As shown in Fig. 3, the Pn wave record is synthesized by the numerical simulation of the wave field of the double-layer crustal model, and the Pn wave reception function obtained by the deconvolution operation includes the conversion waves of the Moho surface and the Conrad interface.
Through the theoretical synthesis model analysis (Fig. 3) and the comparison of the Pn wave reception function with the teleseismic reception function of the actual broadband station (Fig. 4), it is shown that the Pn wave reception function can reliably reflect the crustal velocity structure. At the same time, it can be seen that the amplitude of the conversion wave in the receiving function of the Pn wave is significantly greater than that in the teleseismic reception function because the upward propagation angle of the Pn wave is much larger than that of the Pn wave in the teleseismic reception function. This feature is helpful for imaging or velocity inversion of interfaces with small velocity differences in the shell through the Pn wave reception function. The new method is applied to the north-south short-period dense array across the Yinshan Mountains to obtain the time profile of the Pn wave reception function (as shown in Fig. 5). Through the comparison of different frequency ranges, it can be seen that the waveform frequency of the reception function can be greatly increased due to the high frequency component of the Pn wave.
Fig.3 Theoretical model synthesis of Pn wave and its Pn wave reception function. (a) is a simple double-layer crustal model, including the Moho interface and the Conrad interface; (b) the 3-component waveform of the Pn wave with an epicenter distance of 12° synthesized by numerical simulation of the wave field, in which the amplitude is reduced by 20 times after 300 seconds, (c) the Pn wave component and the converted S-wave component of the coordinate system rotation projection according to the polarization direction, the Pn wave reception function is obtained by deconvolution of these two components, and (d) the Pcs and Pms are the transformed waves from the Conrad interface and the Moho interface, respectively
Fig.4 Comparison between PN wave reception function and teleseismic reception function. (a) and (b) are Xi'an and Kunming respectively. The timelines of the Pn wave reception function (PnRF) and the teleseismic reception function (tel-RF) have been dynamically corrected with unified ray parameters. The vertical red dotted and blue dashed lines in the figure are based on the prediction of the arrival of the Moho surface transition wave based on the previous crustal velocity model
Fig.5. Time profile of Pn wave reception function of short-period dense array. (a), (b), and (c) use low-pass filtering with Gaussian coefficients of 5.0, 10.0, and 15.0, respectively. The red dotted line indicates the transition wave phase that can be tracked continuously, with about 6 seconds being the transition wave phase of the Moho surface
Due to the high frequency, this method can improve the resolution of natural seismic crustal structure detection to a level close to that of deep seismic reflection from artificial sources (as shown in Figure 6). The current natural seismic conversion wave method (remote seismic reception function) has a low frequency (< 3.0 Hz), while the Pn wave frequency with an epicenter distance of 5°-15° can be as high as more than 20 Hz, and the Pn wave reception function of this frequency has a shallow lateral and vertical resolution of 1-3 km and 0.2 km respectively at 40 km, which is very close to the detection level of deep seismic reflection. Therefore, this method is expected to be a "powerful tool" for the detection of fine structure of orogenic belts, large metallogenic belts and large seismic belts.
Fig.6. Resolution of different detection methods. The black solid, dashed and dotted lines are the variation of the resolution of different frequency waveforms of tele-RF with depth, the red solid, dashed and dotted lines are the resolution of Pn wave reception function (PnRF) with depth, and the blue solid line is the resolution of deep reflection (DSR) with depth
研究成果发表在国际地学权威学术期刊JGR-Solid Earth（张良雨，田小波*. Pn-wave receiver function [J]. Journal of Geophysical Research: Solid Earth, 2024, 129: e2023JB028318. DOI: 10.1029/2023JB028318.）。 研究受到国家自然科学基金（42030308,41974053）的资助。
Editor: Fu Shixu (East China Normal University)
Proofreading: Wan Peng