The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions.

One-way wave equation migration is a powerful imaging tool for locating accurately reflectors in complex geologic structures; however, the classical formulation of one-way wave equations does not provide accurate amplitudes for the reflectors. When dynamic information is required after migration, such as studies for amplitude variation with angle or when the correct amplitudes of the reflectors in the zero-offset images are needed, some modifications to the one-way wave equations are required. The new equations, which are called “true-amplitude one-way wave equations,” provide amplitudes that are equivalent to those provided by the leading order of the ray-theoretical approximation through the modification of the transverse Laplacian operator with dependence of lateral velocity variations, the introduction of a new term associated with the amplitudes, and the modification of the source representation. In a smoothly varying vertical medium,the extrapolation of the wavefields with the true-amplitude one-way wave equations simplifies to the product of two separable and commutative factors: one associated with the phase and equal to the phase-shift migration conventional and the other associated with the amplitude. To take advantage of this true-amplitude phase-shift migration, we developed the extension of conventional migration algorithms in a mixed domain, such as phase shift plus interpolation, split step, and Fourier finite difference. Two-dimensional numerical experiments that used a single-shot data set showed that the proposed mixed-domain true-amplitude algorithms combined with a deconvolution-type imaging condition recover the amplitudes of the reflectors better than conventional mixed-domain algorithms. Numerical experiments with multiple-shot Marmousi data showed improvement in the amplitudes of the deepest structures and preservation of higher frequency content in the migrated images.

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Building accurate velocity models is of major interest for oil and gas companies because it improves the prospect evaluation and reduces the risk of geohazards. Full-waveform inversion (FWI) has become a popular method for finding high-resolution and accurate velocity and has been successfully applied to several offshore case studies. We develop a methodology that allows us to apply diving-wave FWI to a case study from the Colombian Caribbean area. The proposed diving-wave FWI methodology includes the wavelet estimation, velocity updates, and quality control (QC) processes. The QC is performed using the cost function, the crosscorrelation of the observed and synthetic gathers, and the analytical trace information. The first QC tool indicates the difference between observed and synthetic gathers; the other two verify that the observed and synthetic data are not cycle skipped. The velocity model obtained with the proposed methodology is the first successful case study performed in the Colombian Caribbean region. From the obtained model, we conclude that FWI is able to build a velocity model with better-resolved shallow depth areas that assist the subsequent pore pressure prediction and imaging processes.