Professor Mueller's research is primarily focused on the study and analysis of actively deforming structures and earthquakes. He uses a variety of techniques that blend field geology with analysis of young sedimentary deposits, geomorphology and geophysics. Aimed at understanding how earthquakes act to build geologic structures and the boundary conditions that control coupled deformation and erosion, projects have taken him to Taiwan, Japan, Baja California, Italy the American Midcontinent and the Southwest USA. His work also seeks to understand how erosion drives stresses in the upper crust and how this affects active flow of ultraweak rock salt in the Paradox Basin of Utah. Professor Mueller has also worked to define how blind thrust faults grow early in the history of Mars and Mercury in response to secular cooling and how they might inform the evolution of the brittle to ductile transition and heat flow on these planets.
Erosional forcing of upper crustal strain, Seismotectonics of fold and thrust belts and transtentional fault systems, Origins of coastal uplift in Southern CA and Baja, Earthquake hazards, Ancient compressive structures and crustal rheology on Mars and Mercury