Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions

In a very general setting, we discuss possibilities of applying $p$-adics to geophysics using a $p$-adic diffusion representation of the master equations for the dynamics of a fluid in capillaries in porous media and formulate several mathematical problems motivated by such applications. We stress that $p$-adic wavelets are a powerful tool for obtaining analytic solutions of diffusion equations. Because $p$-adic diffusion is a special case of fractional diffusion, which is closely related to the fractal structure of the configuration space, $p$-adic geophysics can be regarded as a new approach to fractal modeling of geophysical processes.