Correct interpretation of results becomes an important issue when dealing with nonlinear phenomena of Solid Earth geophysics. Direct linearization of nonlinear processes can cause sufficient mistakes and even cardinally change the interpretation. In this paper a simple and effective procedure for structural recognition and visualization of nonlinear potential sources is presented. This procedure is based on parametric analysis of corresponding transients: switch and localized waves. Conditions for the formation of transitional waves and properties of these waves have been studied. The proposed approach is illustrated on a simple example of potential linear thermal source with nonlinear cubic disturbance. The procedure presented in this paper can be applied for detection of viscous heating and nonlinear heat diffusion in complicated media.