A multi-frequency receiver function inversion approach for crustal velocity structure

Highlights

• Multi-frequency receiver functions are used in waveform inversion.

• Reliable crustal velocity model can be obtained.

• The code is suitable for both radial and transverse receiver functions.

• Good constraints can accelerate the convergence in the inversion.

Abstract

In order to constrain the crustal velocity structures better, we developed a new nonlinear inversion approach based on multi-frequency receiver function waveforms. With the global optimizing algorithm of Differential Evolution (DE), low-frequency receiver function waveforms can primarily constrain large-scale velocity structures, while high-frequency receiver function waveforms show the advantages in recovering small-scale velocity structures. Based on the synthetic tests with multi-frequency receiver function waveforms, the proposed approach can constrain both long- and short-wavelength characteristics of the crustal velocity structures simultaneously. Inversions with real data are also conducted for the seismic stations of KMNB in southeast China and HYB in Indian continent, where crustal structures have been well studied by former researchers. Comparisons of inverted velocity models from previous and our studies suggest good consistency, but better waveform fitness with fewer model parameters are achieved by our proposed approach. Comprehensive tests with synthetic and real data suggest that the proposed inversion approach with multi-frequency receiver function is effective and robust in inverting the crustal velocity structures.

Introduction

Teleseismic receiver function waveform contains the P-to-S converted phases generated at subsurface velocity discontinuities and can be derived from teleseismic waveforms by the deconvolution of the vertical component from the horizontal components (Langston, 1979, Owens et al., 1984). The receiver functions have been widely used to estimate the shear velocity structures of the shallow and deep crust, the undulation of the Moho, 410 and 660 km discontinuities (Andrews and Deuss, 2008, Huang et al., 2015, Kosarev et al., 1999, Li et al., 2014, Li et al., 2016, Vinnik et al., 1983, Zheng et al., 2005, Zhu and Kanamori, 2000). The receiver function waveform inversion has been proven to be effective and reliable to determine the shear wave velocity, Vp/Vs ratio, and crustal thickness as well as the undulation of lithosphere-asthenosphere boundary (LAB) (Borah et al., 2014, Graw et al., 2015, Janiszewski et al., 2013, Julia et al., 2000, Kurose and Yamanaka, 2006, Lawrence et al., 2006, Li et al., 2012, Li et al., 2013, Mangino et al., 1993, Midzi and Ottemoller, 2001, Yuan et al., 1997). In crustal shear velocity structure studies, most previous inversion algorithms utilized single receiver function waveform with a fixed low-pass frequency. Since receiver function waveforms with different frequencies could include both long- and short-wavelength structures at the same time, it would be a better idea to estimate the crustal velocity structures based on multi-frequency receiver function waveforms. As shown in Fig. 1, the nature of the crust-mantle boundary as a gradational change dominates the large-scale receiver function waveforms at low frequency (e.g. frequency is 0.48 Hz), while a low-velocity zone located in 15–20 km in Fig. 1b results in the small-scale receiver function waveforms at high frequency (e.g. frequency is 1.93 Hz).

Levin et al. (2016) estimated the vertical extent, or sharpness, of the Moho transition based multi-frequency receiver functions, in which the maximum vertical extent was calculated by the highest frequency where the Ps pulse does not lessen. However, the receiver function waveform inversion was not carried out in the study of Levin et al. (2016). Tomfohrde and Nowack (2000) developed a frequency-band inversion method, in which receiver function waveforms with different frequency bands are used to investigate the crustal structure beneath the Taiwan orogen. The method greatly stabilizes the iterative waveform inversion in which the longer wavelength structure can be recovered at lower frequency and then with the upper cutoff frequency increasing, more details would appear (Tomfohrde and Nowack, 2000). Similarly, in order to acquire the trustworthy velocity model, Wu et al. (2007) decomposed the receiver function waveforms into five resolution scales via Mallat's pyramid algorithm, and then invert the S-wave velocity from the coarsest-scale to finer-scale receiver functions iteratively. The coarsest-scale receiver functions can recover the large-scale velocity model, which is taken as the initial model in the further inversion for finer structures. Receiver functions with finer scale can be used in the inversion to enhance the detailed structure, and the final velocity structure would be obtained after several iterations (Wu et al., 2007).

Although the frequency-band inversions conducted by Tomfohrde and Nowack (2000), as well as the wavelet modeling approach of Wu et al. (2007) can constrain the velocity with different scales, they are conducted by linear inversion. Since the receiver function inversion is known to be highly non-linear and non-uniqueness of its solutions (Ammon et al., 1990), global optimizing techniques such as the DE algorithm, Genetic Algorithms (GA) and Simulated Annealing (SA) have been implemented successfully for receiver function waveform inversion (Li et al., 2010, Shibutani et al., 1996, Vinnik et al., 2004). Differential Evolution (DE) algorithm shows better performance in resolving nonlinear problems (Storn and Price, 1997), and we will apply it to the multi-frequency receiver function inversion to improve computer efficiency.

In this study, our goal is to propose a new tool suitable for receiver function inversions. In the following, we begin with a brief review of receiver function inversion approach. The approach can provide a constraint on the large- and small-scale velocity structures at the same time and achieve the global optimal solution with fewer model parameters (e.g., a small number of layers). Next, synthetic receiver functions are constructed to test the validity of our method. Real receiver functions from the KMNB station in the southeast China and the HYB station in India are also used to corroborate the proposed approach.