1 Basic principles Detection of coherent seismic signals is an interesting topic in seismology. However, it’s difficult to identify these coherent signals with single station because of the low signal to noise ratios (SNRs). Based on the array processing techniques in radial astronomy, radar and acoustics, the seismic array methods have been developed well in the past several decades. Here, we just follow the articles contributed by (Capon, 1970; Euler et al.

1 Matrix <-> C/C++ array 1.1 Matrix -> C/C++ array .data() stores the address, so we can give the address to a pointer. 1.2. C/C++ array -> Matrix Using Map to convert a C/C++ array to a Matrix. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 #include <iostream>#include <Eigen/Dense> using namespace Eigen; using namespace std; int main(int argc, char *argv[]){ int n; n = atoi(argv[1]); MatrixXf b(n, 1); b = MatrixXf::Random(n, 1); cout << "b:\n" << b << endl; // convert Matrix b to C/C++ array c.

1. Settings of Eigen 1.1 Here Eigen3 Type sudo apt-get install libeigen3-dev to install Eigen3. It will be installed in the default directory /usr/include/eigen3. Just copy Eigen under /usr/include/eigen3 to the directory /usr/include. 1.2 Header files 1 2 #include <Eigen/Dense>using namespace Eigen; 1.3 Tips MatrixXd m(r, c); “X” means “dynamic”, “d” means basic data type “double”， “r” and “c” indicate no. of rows an columns.

Firstly, compute the FFT of real signal $x(n)$ $$ X(k) = \mathscr{F}[x(n)]=\sum_{n=0}^{N-1}x(n)e^{-\frac{i2\pi kn}{N}} \tag{1}. $$ Let the FFT of $h(n)$ be $H(k)$ to yield $$ H(k)= \begin{cases} &X(k), &\text{ for } k=0 \\ &2X(k), &\text{ for } k=1, 2, \cdots, \frac{N}{2}-1 \\ &0, &\text{ for } k=\frac{N}{2}, \frac{N}{2}+1,\cdots, N-1 \end{cases} \tag{2}. $$ The hilbert transform $h(n)$ of the real signal $x(n)$ is given by $$ h(n) = \mathscr{I} \{ \mathscr{F}^{-1}[H(k)] \} \tag{3}.

Geophydog’s research interests focus on multimodal surface waves, seismic tomography for resource exploration, seismic interferometry, array seismology, seismic ambient noise source, softwares for civil engineering purposes. These blog webpages are used to take academic notes for his researches, which comes with no any WARRANTY!!! Education 2019 – 2023, PhD of Mechanics, Department of Earth and Space Sciences, Southern University of Science and Technology (SUSTech) 2016 – 2019, Master of seismology, School of Earth Sciences and Eingineering, Nanjing University (NJU)