How to create a vertical interpolated surface?

[DylanCunningham]

I'm not sure if I am just using the available tools incorrectly or there currently is no tool available that can solve my problem, but I will try to explain my problem the best I can;

So I have performed an ERT servery to acquire various resistivity values at depth along a straight survey line. I have a point file along the line where the electrodes were located with measured values directly below these points, giving me a vertically oriented 2D array of points. What I am trying to do is interpolate a raster surface between these points to essentially create a cross-section raster that displays the variation in resistivity with respect to depth.

If the explanation of what I am trying to do does not make any sense, the output I am trying to achieve looks like the inversion image on the ERT Wikipedia page (Electrical resistivity tomography - Wikipedia ). 

I have tried the various interpolation tools available in ArcScene, but they can't return a vertically oriented raster.

I have included one of the data sets i'm trying to interpolate if you want to try something out.

If anyone has a suggestion on what to try or where I might be going wrong I would be very appreciative!

[DanPatterson_Retired]

3D interpolation is on the roadmap for ArcGIS Pro

https://community.esri.com/docs/DOC-12346-arcgis-pro-roadmap-september-2018 

Have you looked at slices?  Is this a profile along a line? or samples over an area?

If it were a profile along a line you could map distance versus depth and interpolate that

[DylanCunningham]

I have attempted to use the various 3D interpolation functions and the slice.

However, they only return a horizontal raster surface that does not show how resistivity changes with depth. 

I am trying to get a vertical profile along a line.

The point distribution is shown the first images below, and I am trying to get something similar to the third.

[DanPatterson_Retired]

Dylan, that is why I asked if your data were along a profile line.

If they are, you need to calculate the distance between the X, Y locations, that becomes your horizontal axis (X.

Depth is your Y axis.

Resistivity is now your value at location (distance, depth) not at (X, Y).

So it is a 'map', just turned on an axis.  Currently Arc* is not the platform to do that.  There are many graphing packages (including some supplied with ArcGIS PRO) that handle this type of data.

For 3d plots where x and y have spacing

Sample plots in Matplotlib — Matplotlib 2.2.3 documentation 

2D interpolation regardless what the 2 axes are

Contour plot of irregularly spaced data — Matplotlib 2.2.3 documentation