How to convolve a wavelet with a signal to make a wedge model?

Dear Afshin Aghayan

I asked my question in public but I have not got any help. I would appreciate if you can help me as I am new in MATLANB :(.

I have a signal and I want to convolve it with a wavelet and make a wedge model. It is a seismic wedge model and I want to make a single low impedance layer wedge model. I truly appreciated in advance!

My wavelet code is:

%.............................................

fr=30;% frequency

dt=.002;

T=0.1;

tt=-T:dt:T;

tsh=0.008;%time shifting

tr=round(length(tt)/2);

t=tt(tr:end);

zpr=(1-tt.^2*fr^2*pi^2).*exp(-tt.^2*pi^2*fr^2);%zero-phase ricker

figure(10)

plot(zpr)

%................................................

My signal is:

%...............................................

data=xlsread('1');

amp=data(:,2);%us/f

time=data(:,1);%ms

tim=time(1:1:end);

am=amp(1:1:end);

len=length(tim);

for i=1:len

if am(i)==-999.25

am(i)=am(i-1);

end

end

data1=zeros(len,2);

tti=round(tim);

for j=2:len

r(j)=(am(j)-am(j-1))/(am(j)+am(j-1));% reflection coefficients

end

plot(r)

%%%%%%%%%

I can convolve the wavelet and signal to make a simple synthetic trace but not a wedge.

%..............................................................

s=conv(r,zpr);

if mod(length(zpr),2)==0

s=s(length(zpr)/2:end-length(zpr)/2);

else

s=s((length(zpr)-1)/2:end-(length(zpr)-1)/2);

end

ls=length(s);

s(ls)=[];

[m1 n1]=size(s);

if m1==1

s=s';

end

n=10;

dx=2;

scal=5;

figure(1)

for i=1:n

b=(i-1)*dx;

a=scal*s+b;

c=a;

a(a<b)=b;

plot(c,tti,'black')

hold on

fill(a,tti,'k','linestyle','none');

end

hold off

set(gca,'YDir','reverse')

xlim([-dx (n+1)*dx])

ylim([700 2826])

ylabel('millisecent')

title('synthetic trace made of zero-phase ricker') ;

Answer 1

[Afshin Aghayan]

I wrote the following code a long time ago (2011) that can create seismic events based on their slope like wedge model. I hope it can be useful for you.

% This function diplays siemic events based on slope

clc
number=input('How maney events do you want to see? ');
x=input('Enter number of traces : ');
d=input('Enter trace interval in m : ');
t=input('Enter maximum recording time in ms : ');

f=input('Enter frequency of the Ricker wavelet (Hz) : ');

% Ricker wavelet equal ricker=(1-2(pi*f*t)^2)*exp(-(pi*f*t)^2))
n=(0:100);
wavelet=(1-2*(pi*f*(n-50)*0.001).^2).*exp(-(pi*f*(n-50)*0.001).^2);

% Creating the impedance matrix
ImpMatrix=zeros(t,x);
for num=1:number
    
    slope=input(['Enter slope of the event#' num2str(num) ' in degree (e.g. 0 means horizontal line) : ']);
    t0=input(['Enter start time of the event#' num2str(num) ' in ms : ']);
    if t0==0; t0=1; end % In the case t0=0, we assume that the event is recorded at the first sample
    
    for i=1:x
        k=d*i;
        t1=k*tand(slope)+t0;
        if ceil(t1)<=t && ceil(t1)>0
            ImpMatrix(ceil(t1),i)=1;
        end
     end
       
end
  
fieldCon=conv2(ImpMatrix,wavelet','same');
field=fieldCon(1:t,:);

%================================Display===================================
if exist('wigb') == 2 % check wigb function exists 
    figure, wigb(field);
    ylabel('Time (ms)'), xlabel('Trace no.')
    ylim([1 t])
end

figure,imagesc(field)
ylabel('Time (ms)'), xlabel('Trace no.')

% Afshin Aghayan
% 2011