How can I account for the magnitude of each event in this kernel density estimation?

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 latfull
% load longfull
% load longmatrix
% load latmatrix
% load coord
load long5
load lat5
% AA = importdata('completenondecl3.csv');
long = (long5);
lat = (lat5);
step = 0.009;
x = min(long):step:max(long);
y = min(lat):step:max(lat);
[X,Y]= ndgrid(x,y); % creates grid
R = 0.05; % circle radius
plot(long,lat,'.r') % plot data
P = X*0; % no. of points inside each circle 
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; % find smaller distances
        D(ix) = scale*D2(ix); % write smaller distances
        P(i,j) = sum(exp(-D(ix)/2/sig^2))/T; %write ID
        N(i,j) = sum(ix); % no. of points inside (i,j) circle
%         plot(long(ix),lat(ix),'ob') %plot data inside circle (if exists)
        if sum(ix) % if there are points inside
            viscircles([x(i),y(j)], R,'edgeColor','g'); % plot circle
        else
%           viscircles([x(i),y(j)], R,'edgecolor','r'); % plot circle
        end
    end
end
p = P/(pi*6.^2);
G = rot90(flip(p),3);
imagesc(x,y,G);
colorbar
hold off
axis equal 

Answer 1

[darova]

I think the question is too hard. Don't know if someone on this forum could handle it

But i'll take a shot: what about this smart step?

EDITED:

It happens because of different sizes of arrays you multiplies

Here are some steps to success

• step 1: transpose data

load Mo5
Mo5 = Mo5';         % sesmic moment is a column - make a row
                    % D(ix) is a row

• step 2: do calculations only if data exists

[Harith Kubaisy]

I appreciate your witty comment. Believe it or not, I have tried this before posting, and MATLAB gives the following error:

Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 1-by-2.

[darova]

I didn't belive it until check it by myself! Don't know why this happens

Here are some steps to success

• step 1: transpose data

load Mo5
Mo5 = Mo5';         % sesmic moment is a column - make a row
                    % D(ix) is a row

• step 2: do calculations only if data exists

[Harith Kubaisy]

Thank you darova. You're a star indeed. I will accept your answer, but please edit your original reply so that in case someone looks for a solution, they can find it without looking through the comments.

I have a question though: why do the calculations after the 'if' condition in this case, where as in my previous task, the earthquake kernel density, the calculations were made before that line?

[darova]

Because you didn't have Mo5 before? It never happens to me before. Learning something new all the time!

[Harith Kubaisy]

You and I both. Thank you a lot.

[darova]

my plesure

[karim]

Please can i ask your help, after you obtain results, how did you plot the data?

[karim]

Darova, please i dont have skills on coding, i need this code to calculate Kernel seismic moment density, can you please write me the full code, then i will copy it directly. Thank you so much