Interpolation of layers to obtain a layer in the orthogonal plan

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Dear all,
I have three variables S1, S2 and S3 with the size (1000x1000) all that represent the sound levels in three different layers at three different depths. Now, I want to use those layers to calculate the sound levels in an orthogonal plan (kind of perpendicular cut of those layers), by using the interpolation of those three layers (see the figure below).
What and how can I do that?
Thank you all in advance.
Ricardo Duarte
Ricardo Duarte on 22 Sep 2021
Yes, I have three slices (see the file attached).
What I want is to do a cut in the perpendicular axes (cutting plan) and extract the resulting new layer.
Thank you for your help.

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Accepted Answer

Adam Danz
Adam Danz on 22 Sep 2021
Edited: Adam Danz on 22 Sep 2021
Load data
data1 = load('S1.mat');
data2 = load('S2.mat');
data3 = load('S3.mat');
depths = [1 5 10];
Concatenate layers to 3D array
layers = cat(3, data1.Layer1_1m_, data2.Layer2_5m_, data3.Layer3_10m_);
Select a slice along the x axis. The select the a YZ plane at x=5
xIdx = 5; % x-slice
yzSlice = squeeze(layers(xIdx, :, :)); % yz plane at x=xIdx
newZ = min(depths) : max(depths); % interpolated z values
sliceInterp = interp1(depths, yzSlice', newZ)'; % interplated plane
Plot results. Circles and lines (-o) are the raw data. Dots are the interpolation.
plot(depths, yzSlice', 's-')
hold on
set(gca, 'ColorOrderIndex', 1) % reset color order to match
plot(newZ, sliceInterp', '.')

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