The method for 4-D inversion of geophysical data for calculating distribution of subsurface material properties from geophysical data includes (a) defining measured data into space-time coordinates, and defining a reference space-time model vector (U) composed of many reference space model vectors (U) for a plurality of pre-selected reference times to simulate a space-time model vector (P) that is a geologic structure continuously changing in time; (b) approximating a numerical modeling for a geologic structure space model at an arbitrary time using Taylor series of numerical modeling for the reference space models, defining an objective inversion function to constrain each inversion in space and time domains, and obtaining a reference space-time model vector (U) from the measured data defined in space-time coordinates using the objective inversion function; and (c) obtaining a space-time model vector (P) from the reference space-time model vector (U) to calculate distribution of subsurface material properties changing in time.