Conclusions

Chapter 2 presents the novel technique of multisource least-squares reverse time migration to improve the quality of RTM images and increase the computational efficiency For the 2D examples, the quality of the LSRTM images depends on the accuracy of the migration velocity model and the number of sub-supergathers in the input file. The best image for the 2D HESS VTI model is obtained by migrating eight supergathers with 30 iterations, which shows balanced amplitudes, is almost free of migration artifacts and crosstalk noise, and demonstrates a speedup of 3.75 compared to conventional RTM. The 3D examples illustrate the advantages of least-squares migration: balancing the reflector amplitudes, improving the spatial resolution, and reducing migration artifacts. The empirical examples show that the multisource LSRTM can produce images of better quality with similar computation cost. In the future, the multisource LSRTM algorithm can be tested with more complex physical models such as elastic medium, TTI medium, or viscoelastic medium, than the acoustic medium, and 3D field data tests will further validate the proposed new method.

In Chapter 3, I implemented a frequency-selection encoding strategy to speed up the least-squares reverse time migration of marine data. Traditional random phase encoding method is not applicable to marine data due to the mismatch in acquisition geometry between the observed data and the calculated synthetic data. With frequency-selection encoding, all the shots are encoded with encoding functions that are orthogonal to each other in the frequency domain, so the calculated synthetic data can be effectively decoded at the receiver locations for comparison with the observed data. Because of the data redundancy in the frequency domain, the frequency sampling rate can be large, which leads to significant computational savings. Numerical tests on part of the Marmousi2 model and a field dataset from Gulf of Mexico show that the frequency-selection encoding can significantly improve the efficiency of the LSRTM and reduce its cost to the level of conventional shot domain RTM. Empirical results suggest that the LSRTM with frequency-selection encoding is an efficient method to produce better images than conventional RTM. 3D application of this method is very significant with an additional degree of freedom. How to optimally choose a subset of shots from thousands of shots is an interesting topic for future research.

In Chapter 4, I presented the general theory of super-virtual diffraction interferometry where the signal-to-noise ratio (SNR) of diffraction arrivals can be theoretically increased by the factor $\sqrt {N}$ , where $N$ is the number of receiver and source positions associated with the recording of the diffractions. There are two steps to this methodology: correlation and summation of the data to generate traces with virtual diffraction arrivals, followed by the convolution and stacking of the data with the virtual traces to create super-virtual diffractions. This method is valid for any medium that generates diffraction arrivals due to isolated subwavelength scatterers. There are at least three benefits with this methodology: 1). the diffraction arrivals can be used as migration operators (Schuster, 2002; Brandsberg-Dahl et al., 2007; Sinha et al., 2009); 2). the diffraction arrivals can be used for estimating source and receiver statics; 3). estimation of velocities by traveltime tomography or MVA

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