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I need to model a fault plane below the earth's surface and find distances from different points on the surface of the earth.
I know the dimensions of the plane and its orientation but I can do that on a paper.
How to set this up in ArcGIS and find the distances I need?
The short answer for a "vertical fault" (meaning perfectly vertical) is no. But yes if it has a dip.
Surface continuity (2.5D vs. 3D)
Functional surfaces are considered continuous. That is, if you approach a given x,y location on a functional surface from any direction, you will discover the same z-value at the location. This can be contrasted with a discontinuous surface, where different z-values could be obtained depending on the approach direction. An example of a discontinuous surface is a vertical fault displacing the surface of the earth. http://webhelp.esri.com/ArcGISdesktop/9.3/index.cfm?TopicName=What_is_a_functional_surface?
If your plane is vertical, you will have to use a 3D application other that ArcGIS. ArcGIS is a 2.5 D environment, unlike a exploration/geological software which is 3D (Geosoft Target standalone, Leapfrog Mining, GEMS, etc.)
So, in terms of "planes" you can only create planes that are NOT perfectly vertical HOWVER you can visualize a perfectly vertical planes created in external applications such as a 3D DXF in ArcScene.
To create a fault you will need at minimum 3 x,y,z coordinates ideally 4 coordinates for your fault has a rectangular shape. You can, of course, have a highly complex fault created from many XYZ points but remember that if any triangle in the resulting TIN ends up having a vertical face, it will either not display at all in ArcScene or there will be an artifact.
The approach to create a plane is to create a TIN (Triangulated Irregular Network) surface from XYZ points:
Step 1: Import points into a point feature class
Step 2: Create a TIN
That's it. You can now visualize the TIN in ArcScene in 3D.
ArcGIS does provide a true 3D data (multipatch feature class) but it is not fully fleshed out data type and cannot be simply created by drawing in 3D space. Multipatch should flly enclose a volume. You can convert TIN to multipatch but without a "volume" it can't be used as input into geoprocessing tools.
Here http://www.geol-gis.ch/en/dt-dipping-plane you will find information about a tool that creates a 3D square plane of determined orientation, dip and width, at determined coordinates. The output is a 3D polygon.
