How Can I Show the Velocity Profile Gradient in a 2-D Plot Using GNUplot?

[bert2002]

Homework Statement

I have written a program that desribes seismic wave propagation in a medium that has been given a specific velocity profile equation. The velocity at a specific x and z co-ordinate of the ray path is defined by this particular equation, and of course the velocity will vary depending on the position of the ray path .

I am trying to create a 2-D plot of the ray paths of x (horizontal) and z (vertical) position which i can do fine BUT i am having trouble in trying to show the velocity profile gradient as part of the background of the plot. I would like to be able to see exactly how the velocity profile changes with position and how this has affected the ray path.

Homework Equations

Here is an example of an arbitrary velocity profile equation that i have been using

$$v=a+bsin(cx)+dcos(ez)$$

Thanks

 

[gsal]

So, what exactly is the question?
are you looking for ideas on how to present the information?
what's the information?

if you have a scalar quantity, you can use color to represent the magnitude in the 2D x-z plane

if you have a vector, well, you use a vector field.

I think of velocity as a vector and speed as a scalar, so, I am not sure what you got as you call it velocity but seems to be a scalar.

 

[bert2002]

So, what exactly is the question?
are you looking for ideas on how to present the information?
what's the information?

if you have a scalar quantity, you can use color to represent the magnitude in the 2D x-z plane

if you have a vector, well, you use a vector field.

I think of velocity as a vector and speed as a scalar, so, I am not sure what you got as you call it velocity but seems to be a scalar.

Well the ray path is a vector quantity but the velocity profile equation will produce a scalar field for each point on the x/z plane.

as you say, i am looking to use colour to represent the magnitude of the scalar field in a 2-D plane, how can i do this ?

Thanks

 

[gsal]

I wouldn't know how to do that in GNUplot, I use matplotlib.

You need to read the docs, look for something along the lines of contour, colormap, cmap, image-showing commands, etc.

 

[LudusRex]

for seeking the input of GNUplot experts! As a scientist, it is important to accurately visualize and understand the data we are working with. In order to show the velocity profile gradient as part of the background of your plot, you can use the "splot" command in GNUplot. This will allow you to plot a 3-D surface, with the x and z coordinates representing the position and the y coordinate representing the velocity. You can use your velocity profile equation as the function for the surface, and then overlay your ray paths on top of it using the "plot" command. This will give you a visual representation of how the velocity changes with position and how it affects the ray paths. Additionally, you can adjust the viewing angle and color scale to better visualize the gradient. I hope this helps and good luck with your project!