Question
What are the theories behind MALT?

To describe briefly the theory of MALT, you could follow the description in Section 2 (Brief description of the analytical approach) of [1]. You can refer to [2] for the part of image theory. Basically, all the grounding analysis theory have a similar procedure no matter what kind of soil is involved.

1. Green's function problem, namely, point source solution. If the soil model is of a multilayer type, you solve a Poisson equation with the boundary conditions at the soil interfaces. You will obtain expression of the point source solution in a form of an integral. This integral can be transformed into a series if all the layer thicknesses are a multiple of a base layer thickness (note that such a base layer thickness always exists, e.g., h1=2.4, h2=9, h3=15, base layer thickness = 0.6). In fact, this series solution can be directly obtained by the image method. Each series term corresponds an image.
2. After obtaining the point source solution, you can obtain the solution for a conductor segment by a simple integration.
3. A grounding network can always be subdivided into a set of smaller conductor segments. Based on the Moment Method, you can set up the equation with the current from the segments as unknown and then solve the current distribution.
4. Now you can compute the potential anywhere and also other electrical quantities such as step and touch voltages.
   

The references are in the following. Reference [3] has a good description of the general grounding analysis procedure which maybe useful to you.

[1] F.P. Dawalibi, J. Ma, and R.D. Southey, "Behavior of grounding
systems in multilayer soils: a parametric analysis", IEEE
Transactions on PWRD, Vol. 9, No. 1, pp. 334-342, Jan. 1994.

[2] A.B. Oslon and I.N. Stankeeva, "Application of Optical Analogy
to Calculation of Electric Fields in Multilayer Media", Electric
Technology, U.S.S.R., 1979, No. 4, pp. 68-75.

[3] J. Ma, F.P. Dawalibi, and W.K. Daily, "Analysis of grounding
systems in soils with hemispherical layering", IEEE Transactions
on PWRD, Vol. 8, No. 4, pp. 1773-1781, Oct. 1993.