# Multi-channel analysis of Surface waves (MASW)

# Vectors in GMT

Arrow styles in Cartesian coordinate system 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 PS=plot.ps PDF=plot.pdf R=0/10/0/10 J=X10i/7i gmt psbasemap -R$R -J$J -K -Bx1f0.1 -By1f0.1 -BWSen > $PS echo "1 1 0 2i" | gmt psxy -R -J -K -O -Sv1c+b >> $PS echo "1 2 0 2i" | gmt psxy -R -J -K -O -Sv1c+e >> $PS echo "1 3 0 2i" | gmt psxy -R -J -K -O -Sv1c+b+e >> $PS echo "1 4 0 2i" | gmt psxy -R -J -K -O -Sv1c+b+h1 >> $PS echo "1 5 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+h1 >> $PS echo "1 5 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+h1 -Gred >> $PS echo "1 6 0 2i" | gmt psxy -R -J -K -O -Sv1c+m -Gred >> $PS echo "1 7 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+l -Gred >> $PS echo "1 8 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+r -Gred >> $PS echo "1 9 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+a90 -Gred >> $PS echo "5 1 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+h-2 -Gred >> $PS echo "5 2 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+h-1 -Gred >> $PS echo "5 3 0 2i" | gmt psxy -R -J -K -O -Sv1c+e+h2 -Gred >> $PS echo "5 4 0 2i" | gmt psxy -R -J -K -O -Sv1c+b+e+h0 >> $PS echo "8 1 0 1i" | gmt psxy -R -J -K -O -Sv1c+bt >> $PS echo "8 2 0 1i" | gmt psxy -R -J -K -O -Sv1c+bc >> $PS echo "8 3 0 1i" | gmt psxy -R -J -K -O -Sv1c+ba >> $PS echo "8 4 0 1i" | gmt psxy -R -J -K -O -Sv1c+bA >> $PS echo "8 5 0 1i" | gmt psxy -R -J -K -O -Sv1c+bi >> $PS echo "8 6 0 1i" | gmt psxy -R -J -K -O -Sv1c+bI >> $PS echo "5 5 2i 0 45" | gmt psxy -R -J -K -O -Sm1c+b+e+h1 -Gred>> $PS echo "5 7 2i 0 90" | gmt psxy -R -J -O -Sm1c+b+e+h1 -Gred >> $PS gmt psconvert -E150 -Tg -A -P $PS ps2pdf $PS $PDF evince $PDF rm $PS Vectors in geographic coordinate system 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 R=-100/100/-70/70 J=M7i PS=geo_arrow.

# Boundary Conditions in PDE

Boundary condition is necessary when we find the numerial solutions to some equations. Here, we show you some kinds of boundary contions in solving partial difference equation.
1 Dirichlet (fixed) $$ \left \{ \begin{aligned} p(t, x_{min}) &= 0\\
p(t, x_{max}) &= 0 \end{aligned} \right. \tag{1}, $$ where, $p(t, x)$ is what we want to find, let’s say, pressure in acoustic wave equation.
2 Neumann $$ \left \{ \begin{aligned} p(t, x_{min}) &= p(t, x_{min}+\Delta x)\\

# EGFs from Cross-correlations of Noise Excited by a Circle-Shaped Configuration of Sources

New responses, if the wave field is diffuse, can be retrieved from interstaion cross-correlation of ambient noise. However, the cross-correlation time functions are asymmetric if the noise sources distribute unevenly. Here, we give you an example to show that how the cross-correlation functions vary with the angles of noise sources (red dots). We computed synthetic seismograms of earthquakes with angles from 1 to 360 degrees with an interval of 1 degree and data are recorded by two receivers (blue triangles); then we compute the cross-correlation time functions and align them with the angles; lastly, we stack all the cross-correlations to show you it’s symmetric under the condition that the noise sources distribute evenly.