I need to answer this question by using (Matlab program) please .. Applications:

Question

I need to answer this question by using (Matlab program) please ..
Applications: .The direct ray travels along a straight line through the top layer from source to detector at velocity v. top layer to the detector, travelling along its entire path at the top layer velocity vl of the interface at the higher The reflected ray is obliquely incident on the interface and is reflected back through the .The refracted ray travels obliquely down to the interface at velocity v1, along a segment velocity v2, and back up through the upper layer at Receiver (R Source DERECT WAVE REFLECTED WAVE Velocary c# Velocity MEAD WAVE B Ray paths for a layer over a halfspace. Fig. 3 Seismic rays travel time. . Express the traveltime that each ray (direct, reflected, refracted) takes to travel from source to receiver in function of source-receiver distance x (offset), depth h and the velocities of the layers (vl and v2). Plot the different functions in one single plan (t-x). Use the following: 2, .V-[800, 2500], 20m, geophone spacing: 05:100 3. 0 10 20 30 4050 60 70 80 0 100 Direct 0.02 0.04 0.06 0.08 Refracted Refected Mutiple 0.12 0.14 0.16 0.18 Fig. 4 Curves obtained using mfile

Explanation / Answer

Answer i.)

function [reflected_ray,redirected_ray,direct_ray,multiple_ray]=compute_acoustic_ray_path(z,b,reflected_ray,redirected_ray,direct_ray,multiple_ray,T)

[z,ia,ib] = unique(z);

if size(z,1)==1
b=b(ia);
else
b=b(ib);
end

[z,idx_sort]=sort(z);
b=b(idx_sort);

g_down=(b(2:end)-b(1:end-1))./(z(2:end)-z(1:end-1));
g_down=[g_down g_down(end)];

g_up=-(b(1:end-1)-b(2:end))./(z(1:end-1)-z(2:end));
g_up=[g_up(1) g_up];

if direct_ray>0
g=g_down;
else
g=g_up;
end

xi=(cos(direct_ray(1))/b(1));

while t_ray(end)<=T
%t_ray(end)
[~,idx]=nanmin(abs(z_ray(end)-z));

i=length(reflected_ray);

if direct_ray(i)<0
idx_plus=nanmax(idx-1,1);
elseif direct_ray(i)>0
idx_plus=nanmin(idx+1,length(z));
else
idx_plus=idx;
end


if idx==idx_plus&&idx~=1
return;
end

if xi==0
direct_ray(i+1)=direct_ray(i);
reflected_ray(i+1)=reflected_ray(idx);
redirected_ray(i+1)=redirected_ray(i)+1/(g(idx))*log(b(idx_plus)/b(idx)*(1+sqrt(1-xi^2*b(idx)^2))/(1+sqrt(1-xi^2*b(idx_plus)^2)));
z_ray(i+1)=z(idx_plus);
else

if idx_plus==1&&idx==1 %case where it hits the surface
if g(idx)==0%case where velocity stays the same
beta_ray(i+1)=-beta_ray(i);
r_ray(i+1)=r_ray(i)+(z(2)-z(1)/tan(beta_ray(i+1)));
t_ray(i+1)=t_ray(i)+((z(2)-z(1))/c(1));
z_ray(i+1)=z(1);
if beta_ray(i+1)>0
g=g_down;
else
g=g_up;
end
else
multiple_ray(i+1)=pi/2-(multiple_ray(i)-pi/2);
reflected_ray(i+1)=reflected_ray(i)+(reflected_ray(i)-reflected_ray(i-1));
redirected_ray(i+1)=redirected_ray(i)+(redirected_ray(i)-redirected_ray(i-1));
b_ray(i+1)=b(1);
if multiple_ray(i+1)>0
g=g_down;
else
g=g_up;
end
end

else
if g(idx)==0
multiple_ray(i+1)=multiple_ray(i);
reflected_ray(i+1)=reflected_ray(i)+((b(idx_plus)-b(idx))/tan(multiple_ray(i+1)));
redirected_ray(i+1)=reflected_ray(i)+((b(idx_plus)-b(idx))/c(idx));
direct_ray(i+1)=direct(idx_plus);
else
if (xi*b(idx_plus))^2<1
multiple_ray(i+1)=sign(multiple_ray(i))*acos(b(idx_plus)*xi);
reflected_ray(i+1)=reflected_ray(i)+(1/(xi*g(idx))*(sqrt(1-xi^2*b(idx)^2)-sqrt(1-xi^2*b(idx_plus)^2)));
redirected_ray(i+1)=redirected_ray(i)+1/(g(idx))*log(b(idx_plus)/b(idx)*(1+sqrt(1-xi^2*b(idx)^2))/(1+sqrt(1-xi^2*b(idx_plus)^2)));
direct_ray(i+1)=z(idx_plus);

else
multiple_ray(i+1)=-multiple_ray(i);
xi=(cos(mltiple_ray(i+1))/b(idx));
reflected_ray(i+1)=reflected_ray(i)+2/(xi*g(idx))*(sqrt(1-xi^2*b(idx)^2));
redirected_ray(i+1)=redirected_ray(i)+2/(g(idx))*log(1/(b(idx)*abs(xi))*(1+sqrt(1-xi^2*b(idx)^2)));
multiple_ray(i+1)=z(nanmax(idx-1,1));

if direct_ray(i+1)>0
g=g_down;
else
g=g_up;
end
end
end
end
end
end

end

%Above code will help you to find the velocity of Reflected, Redirected, Direct, Multiple rays.

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