Full Waveform Inversion Using Wave Equation Reflectivity Modeling

Summary Full Waveform Inversion (FWI) is routinely used to improve the accuracy and resolution of velocity models. However, utilizing reflections to produce low-wavenumber updates creates more operational challenges than using transmitted events. In order to simulate backscattered sensitivity kernels, FWI needs hard boundaries in the velocity/density models. Alternatively, one can apply the wave equation and first-order Born approximation to decompose the seismic wavefields into background and perturbation. Here, we derive an acoustic wave equation in terms of vector reflectivity to be used as the wave’s propagation engine of FWI. The new derivation results from the change of variables from impedance to reflectivity in the variable density wave equation. The main advantages of its insertion in our FWI algorithm are the following: it does not require the construction of density/hard boundaries in the velocity model to generate reflections; it allows the use of reflected events without the need of solving two different wave equations in the forward and backward propagation; it is more accurate than the method based on the first-order Born approximation to perturbation theory. We show synthetic and field data examples illustrating the advantages of the new algorithm.