# Matched Field Processing: a generalized beamforming

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.