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 $\omega$.
1. Basic descriptions Matched filed processing (MFP) is a location algorithm that was first applied in ocean acoustics (Baggeroer and Kuperman, 1988). It has been widely used to locate quakes or microseisms in seismology (e.g., Cros et al., 2011; Gal et al., 2018). We here give a short and simple derivation of MFP as follows. 1.1 MFP power Computing the Fourier spectrum vector, $$\boldsymbol{u}(\omega) = [u_1(\omega), u_2(\omega), \cdots, u_N(\omega)]^T, \tag{1}$$ where, $N$ is the total number of receivers, $T$ means transpose operator, $u_i(\omega)$ is the Fourier spectrum of recordings by receiver $i$, and $\omega$ is angular frequency.