# Seismic Imaging of Receiver Ghosts of Primaries Instead of Primaries Themselves

## Abstract

The three key steps of modern seismic imaging are (1) multiple attenuation, (2) velocity estimation, and (3) migration. The multiple-attenuation step is essentially designed to remove the energy that has bounces at the free surface (also known as "multiples"), since velocity estimation and migration assume that data contain only primaries (i.e., seismic events that have reflected or diffracted only once in the subsurface and have no free-surface reflection). The second step consists of estimating the velocity model such that the migration step can be solved as a linear inverse problem. This thesis concerns the multiple attenuation of towed-streamer data. We have proposed a new method for attenuating multiples and discussed how this method affects velocity estimation and migration. The multiple-attenuation approach used today in the E&P industry is based on the scattering theory. It is carried out in two steps: (1) the prediction of multiples using data only, and (2) the subtraction of multiples contained in the data using predicted multiples. One of the interesting features of these multiple-attenuation methods is that they do not require any knowledge of the subsurface. However there are still two drawbacks that limit the usage of these methods. They are (1) the requirement of acquiring very large 3D datasets which are beyond the capability of current seismic acquisition technology, and (2) the requirement of acquiring near-offset (including zero-offset) data. The method developed in this thesis can potentially overcome these two problems. The novelty of our approach here is to image receiver ghosts of primaries--events which have one bounce in the subsurface and one bounce at the free-surface that is also the last bounce--instead of primaries themselves. We propose to predict two wavefields instead of a single wavefield, as is presently done. One wavefield contains all free-surface reflections, including receiver ghosts of primaries, ghosts of multiples, and multiples. The other wavefield does not contain receiver ghosts of primaries. We pose the problem of reconstructing receiver ghosts of primaries as solving a system of two equations with three unknowns. The two wavefields are used to construct the two equations. The three unknowns are (1) the receiver ghosts of primaries, (2) the multiples contained in the wavefield containing the receiver ghosts of primaries, and (3) the multiples contained in the other wavefield. We solve this underdetermined system by taking advantage of the fact that seismic data are sparse. We have validated our approach using data generated by finite-difference modeling (FDM), which is by far the most accurate modeling tool for seismic data. Starting with a simple 1D model, we verified the effectiveness of predicting data containing multiples and receiver ghosts of primaries. Then we used the sparsity of seismic data to turn the system of two equations with three unknowns into a system of two equations with two unknowns on a datapoint basis. We have also validated our method for complex geological models. The results show that this method is effective, irrespective of the geology. These examples also confirm that our method is not affected by missing near-offset data and does not require special seismic 3D acquisition.