Scale properties of the seismic wavefield – perspectives for full waveform matching

Starting from the nondimensionalization of equations of motion we partition the set of the velocity models in equivalence classes, such that the full waveform of an element in a given class can be calculated from the full waveform of any other element in the same class by scaling model parameters. We give a formal derivation of the seismic wavefield scale properties and we prove their capability through the use of numerical examples. Besides this, we introduce how the scale properties can be used to save computational time in full waveform modeling and inversion. In forward modeling we can use them for the calculation of the full waveform of any model in the same equivalence class of a model whose full waveform has been previously calculated. In full waveform inversion, scale properties can be used for full waveform matching: Given an experimental seismogram and a synthetic one, we can choose, in the same class of the synthetic model, another element whose waveform is closer to the experimental one.