  Tracer tests in natural porous media sometimes show abnormalities that
suggest considering a fractional variant of the Advection Diffusion Equation
supplemented by a time derivative of non-integer order. We are describing an
inverse method for this equation: it finds the order of the fractional
derivative and the coefficients that achieve minimum discrepancy between
solution and tracer data. Using an adjoint equation divides the computational
effort by an amount proportional to the number of freedom degrees, which
becomes large when some coefficients depend on space. Method accuracy is
checked on synthetical data, and applicability to actual tracer test is
demonstrated.
