Background Passive dense array surface wave tomography plays a significant role in probing the earth’s interior with the development of a large number of dense seismic arrays, attracting researchers’ growing interest in imaging applications in various scales. These array methods, like beamforming and MASW (multichannel analysis of surface wave) have been widely used to estimate dispersion curves in past several decades. A new array stacking technique, the frequency-Bessel (F-J) transform, was proposed about five years ago with some main advantages of extracting dispersion curves of high-resolution and broad frequency band (Wang et al.
1. Background Ambient noise tomography has been a very popular imaging strategy of investigating the earth’s interior in past over two decades. The basic principle of this method is that stacked cross-correlations from noise recordings made by two receivers can be approximately the Green’s function from one receiver to another. We have the need of synthesizing ambient noise for validating this important idea, or exploring characteristics of ambient noise. Here we introduce a simple way of computing synthetic ambient noise.
Background Ambient noise tomography is widely used to image th earth’s interior in past over two decades for various scales. Stacked cross-correlations from seismic ambient noise can be approxmately the Green’s functions between receivers. Surface waves extracted from ambient noise cross-correlations are frequently utilized to estimate multi-layered shear wave velocity structure. The key to surface wave imageing is reliable dispersion curves. Two-staion techniques, like frequency-time analysis (Levshin et al., 1989), image transform (Yao et al.
Visualization is frequenctly used to show scientific ideas or experimental results, but it is difficult for us to master. There are many styles for different individuals for they favor different colors, markers, and line styles. Color choice is very important to visualize data among above terms. Here we give some colors for making clear our ideas. 1. Empirical probability image We usually use hit counts to compute empirical probability from large datasets, for example, the power spectral density curve of ambient seismic noise.
1. MUSIC algorithm The naive beamforming technique, Bartlett beamformer, has a poor resolution although its stability and robustness are good. Schmidt proposed a new beamformer algorithm call multiple signal classification (MUSIC) for addressing the resolution while keeping the stability of beamformer (1986). Here we briefly introduce the MUSIC algorithm and also give some Python codes to show how this technique works. Assuming a signal $u(t)$ and its Fourier spectrum $U(\omega)$ of a receiver, we have a signal vector of an array composed of $N$ receivers at frequency $\omega$.