Waveform Inversion of 4D Seismic Data Using the Ray-born Approximation in the Frequency Domain

We present a method for inverting 4D seismic data with respect to perturbations in the seismic velocities caused by fluid movements in a reservoir. The method applies to changes in the seismic waveform data before and after production and is based on the ray-Born approximation for the scalar wave equation. The inversion is performed in the frequency domain, and we make use of all (discrete) frequencies involved in the spectra of used signals. We used a numerical reservoir simulator to simulate water injection in an initially oil-filled reservoir. The numerical reservoir model involved one injector and four producers. One baseline and two monitor 3D seismic surveys performed 2 and 4 years after production were translated into perturbations in the squared slowness using a petro-elastic model. Our model allows for arbitrary systems of multiple sources and receives, but a seabed acquisition system consisting of one source and four cables with 64 receivers was used in the numerical experiment reported in the abstract. Random (white) noise was added to the data. The waveform inversion, based on a regularized(damped) least squares method, was capable of mapping the movement of the oil/water interface in the reservoir.