Depth of Moho beneath the Tanghai-Shangdu seismic array profile from ambient noise autocorrelation

Ambient noise encompasses both surface and body waves. Although surface-wave extraction is more common, the extraction of body waves is not as widespread, with its application in the Earth’s deep subsurface exploration typically confined to regions with simpler geological structures. A linear broadband seismic array, deployed in the North China Craton, spans from the southeast （Tanghai） to the northwest （Shangdu） and traverses plain, mountainous, and plateau regions. This study endeavors to extract Moho-reflected P-waves （PmP） from three years of array recordings （2006–2009）, with the extracted body waves utilized to determine the depth of the Moho interface beneath the array.　　The process of extracting PmP from ambient noise involves six steps. In the first step, continuous recordings of the vertical component of the PmP are divided into segments of 1 h durations. In the second step, the recorded segments undergo bandpass filtering in a frequency range of 2−4 Hz for most stations and 1−2 Hz for a select few. The third step involves phase autocorrelation of the filtered segments. In the fourth step, a two-step stacking process is applied to the phase autocorrelation functions from multiple time intervals at the same seismic station. A linear stacking is initially performed within the group of autocorrelation functions, followed by a phase-weighted stacking of the group results to generate a seismic trace. In the fifth step, the second-order derivative of the envelope of the stacked traces is computed. Finally, in the sixth step, within a time window containing vertically reflected P-waves from the Moho interface which is determined based on prior information （i.e., Moho depth and assumed error of 5% in average crustal P-wave velocity）, the time corresponding to the maximum value of the second-order derivative is selected. This time is converted to the Moho depth using the average crustal velocity.　　Following the six steps, the data from the Tanghai–Shangdu array are processed. In terms of the time window for P-wave selection, the prior Moho depth was obtained from the results of receiver function inversion. The assumed average crustal P-wave velocity was 6.3 km/s in the northwest section （Inner Mongolia Plateau and Yanshan Orogenic Belt） and 5.7 km/s in the southeast section （Bohai Bay） of the seismic array. Data were unavailable for two of the 51 seismic stations within the array, while the autocorrelation functions of three stations displayed periodic oscillations, thus posing challenges in identifying the PmP signals. Ultimately, data for Moho depths were obtained for 46 stations. Along the Tanghai–Shangdu array, the Moho depth demonstrated a general trend of deepening from southeast to northwest, ranging from approximately 33 to 42 km. Minor fluctuations of a few kilometers were observed on the array profile. Compared to the receiver function results used as prior information, the Moho depths determined utilizing noise autocorrelation functions exhibited an average deviation of 0.8 km, with a corresponding two-way travel time deviation of approximately 0.3 s.　　The PmP in the ambient noise cross-correlation functions of three groups of station pairs were investigated to validate the extracted P-waves and determined Moho depths. These station- pair groups had three common midpoint stations respectively located in two end sections and in the middle section of the seismic array. The optimal crustal average velocity （v^*） and PmP arrival time with zero offset （$t_{0}^{*}$） were chosen within a considerably wide velocity range and time window. This selection aimed to maximize the energy of the stacked PmP waves for the common midpoint. The Moho depths determined from v^* and $t_{0}^{*}$ were highly consistent with the results obtained from autocorrelation functions. The discrepancies in Moho depths at the three common midpoint stations, progressing from northwest to southeast, were 0.5 km, 0.68 km, and 2.02 km, respectively.　　The PmP obtained through monthly stacking of autocorrelation functions showed distinct seasonal variations. By contrast, the results from annual stacking remained relatively stable over the entire three-year observation period. This indicated that the noise sources that contributed to the PmP in North China showed substantial variations at the seasonal scale but exhibited great stability on an annual scale.　　For various stations, the resulting stacked traces of autocorrelation functions exhibited notable variations in the shape, amplitude, and duration of the PmP. To elucidate the features of the reflected waves, we conducted simulations using two representative velocity models, each characterized by distinct crust-mantle transition zones. The results indicated that PmP waves from the thin crust-mantle transition zone with a large velocity gradient exhibited shorter durations and stronger amplitudes, resembling the reflection waves observed at station K005. By contrast, reflection waves from the thick crust-mantle transition zone with a small velocity gradient showed longer durations and weaker amplitudes, similar to those observed at station K040. Based on these findings, we concluded that the crust-mantle transition zones beneath the Tanghai–Shangdu array feature distinct velocity gradient patterns.　　The prevalence of seismic ambient noise facilitates the acquisition of valuable body wave data, particularly in regions that experience fewer seismic events. Body waves extracted from ambient noise carry rich information about the Earth’s interior, akin to seismic waves generated by active or passive sources. Thus, extracting reflected P-waves from autocorrelation functions of ambient noise and using them to delineate internal Earth interfaces such as the Moho holds significant promise.