I am trying to execute a two-part analysis on Earthquake distribution. The first is the Earthquake Kernel Density Estiamtion (Eqn.1) which is done already by the script beneath. The second part I'm struggling with is the Seismic Moment Kernel Density Estimation. In theory, the equations for both is almost identical, with only the seismic moment being added to the numerator (Eqn.3)
Principle (After Sharon et al., 2020):
A regional scan is carried out in a 1 km (0.009 decimal degrees) interval 2-D grid, in the horizontal coordinates. For each grid point, both parameters are calculated utilising all recorded events within a 6 km (0.05 decimal degrees) radius. The parameters are calculated based on the kernel density estimation as an approach to obtain the spatial distribution through a probability density function, using the distance to weight each event from a reference point (each grid point, the common centre of its adjacent events).
where N is the total number of events within the radius r, M0(n) is the seismic moment released from an event n ac- cording to Eq. (2), d(n) is the distance between an event n and the circle centre, σ is the standard deviation of the Gaussian function and T is the duration of the earthquake catalogue; units are joules per squared kilometre per year (J km−2 yr−1).
For simplicity, I have reduced my dataset to 10 events (attached in this post), which are long5 and lat5. These are coordinates of the earthquake events in decimal degrees (North and East). I have also attached a file that contains the seismic moment released by each of these events.
My question is: How to account for the seismic moment of each earthquake inside the script, to make it calculate the new density automatically while accounting for seismic moment?
clc,clear
load long5
load lat5
long = (long5);
lat = (lat5);
step = 0.009;
x = min(long):step:max(long);
y = min(lat):step:max(lat);
[X,Y]= ndgrid(x,y);
R = 0.05;
plot(long,lat,'.r')
P = X*0;
T = 2019-1916+1;
sig = 2;
scale = (pi/180*earthRadius/1000)^2;
hold on
for i= 1:length(x)
for j=1:length(y)
D2 = (long-x(i)).^2 + (lat-y(j)).^2;
ix = D2 < R^2;
D(ix) = scale*D2(ix);
P(i,j) = sum(exp(-D(ix)/2/sig^2))/T;
N(i,j) = sum(ix);
if sum(ix)
viscircles([x(i),y(j)], R,'edgeColor','g');
else
end
end
end
p = P/(pi*6.^2);
G = rot90(flip(p),3);
imagesc(x,y,G);
colorbar
hold off
axis equal
