In the past two decades, seismic ambient-noise cross correlation (CC) has been one of the most important technologies in seismology. Usually, only the fundamental-mode surface-wave dispersion was extracted from the ambient noise. Recently, with the frequency–Bessel transform (F-J) method, overtone dispersion can also be extracted from the ambient noise and it adds significant value in inversion. This method has also been verified to be effective for array seismic records of earthquake events. In this article, we describe our algorithm and a Python package called CC-FJpy. For the F-J method, we use the Nvidia’s graphics processing unit to accelerate the computation, which can achieve a 100-fold computational efficiency. We have encapsulated our experiences and technologies into CC-FJpy and tested the CC-FJpy by ambient-noise and earthquake data to ensure its speed and ease of use. Our open-source package CC-FJpy can benefit the development of surface-wave studies using ambient noise and make it easier to start with high-mode surface waves.
Frequency–Bessel (F-J) transform method can obtain higher-mode Rayleigh dispersion curves by multistation ambient noise data superposition (Wang et al., 2019). Because the dispersion curves of the overtones can provide more information compared with the single fundamental mode, the nonuniqueness of surface-wave inversion can be reduced. Because of the limited number of receivers, the integral in the process of transformation cannot be calculated precisely and there exists a kind of crossed artifacts which cuts off the real dispersion curves and contaminates the spectrum. Forbriger (2003) proposed to use the Hankel function instead of the Bessel function to conduct the transformation to remove the crossed artifacts. However, this method can reduce the resolution of the spectrum from ambient noise data. In this article, we give a complete workflow to deal with ambient noises which can eliminate the crossed artifacts without reducing the resolution. The Kramers–Kronig relations are used to obtain complete cross-correlation functions and a modified F-J transform is conducted to finally acquire the spectrum without crossed artifacts.
In this paper, we develop a series of exponential probability density functions for modeling different distributions of elevation angle (EA) of arrival signals in different tree-dimensional (3D) coverage area scattering environments, and implement the modeling of channel characteristics. First, by assuming that the distribution of azimuth angle is uniform, in this paper the closed-form expressions of power spectrum density (PSD) for both symmetric and asymmetric situations of EA are derived. It can be observed from the analysis results that the PSD is closely correlated to EA function and the boundary angles βmin and βmax of the arrival signals and also to the Doppler shift. Then the spatial fading correlation (SFC) of MIMO multi-antenna signals in 3D environment is derived and simulated. The results show that the SFC between MIMO multi-antenna elements is closely related to βmin and βmax, and the parameter of EA function has little effect on SFC. The exponential EA probability function which is introduced in this paper can be applied to channel parameter estimation of multiple wireless communication environments. Compared with traditional models, this model presents the parameter estimation that satisfies theoretical and empirical values, and this model also expands the modeling of statistical channel in 3D environment.
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