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Least-squares migration (LSM) can produce high quality migration images from seismic data, but with high computational cost. To reduce this cost, phase-encoding techniques have been introduced, but at the expense of crosstalk noise in the image. In this dissertation, a multisource least-squares algorithm (MLSM) is proposed to eliminate the crosstalk noise and also significantly increase computational efficiency by applying plane-wave encoding to the data. I denote variations of this method as plane-wave least-squares migration (PWLSM) and regularized plane-wave least-squares migration (RPWLSM).

There are four main chapters in this dissertation.

In Chapter 2, the theory of multisource crosstalk reduction is presented and numerically validated, which provides the basis for Kirchhoff MLSM and PWLSM. Numerical results suggest that: (1) combining polarity and time statics produces a better migration image than computed with either polarity or time statics alone; (2) MLSM achieves the best crosstalk reduction when the encoding function varies at each iteration.

In Chapter 3, MLSM is used with Kirchhoff migration for a marine acquisition geometry. Application of wave-equation MLSM to marine streamer data is typically hampered by the variable location of receivers for any shot. However, this problem does not exist for Kirchhoff MLSM, which can be applied to marine streamer data without any restrictions on the acquisition geometry. Kirchhoff MLSM achieves the best performance by changing the encoding function at each iteration. MLSM achieves a significant savings in IO and memory costs, but does not reduce the CPU cost, which suggests a better phase-encoding technique is needed.

In Chapter 4, a 2D plane-wave encoding technique is developed for Kirchhoff LSM to produce high quality images (compared to standard Kirchhoff migration) with a significant gain in computational efficiency (compared to Kirchhoff LSM). A finite-difference solver for the eikonal equation is developed for calculation of plane-wave travel times. To remedy the high sensitivity of PWLSM to the migration velocity accuracy, RPWLSM is developed where each plane-wave is migrated to give its own migration image, hence it increases the robustness of this algorithm when the migration velocity model contains bulk errors. By noting that images from different plane-wave gathers with slightly different encoding param- eters are similar, a regularization term is adopted to encourage this similarity. Numerical tests on synthetic and field data are performed to illustrate the benefits and limitations of PWLSM and RPWLSM.

In Chapter 5, the proposed algorithms of PWLSM and RPWLSM are extended from 2D to 3D. For 3D narrow azimuth streamer geometries an inline only plane-wave encod- ing strategy (also known as the cylindrical-wave encoding) is adopted. Cylindrical-wave least-squares migration (CWLSM) and regularized cylindrical-wave least-squares migration (RCWLSM) methods are tested on synthetic and field data. Results show the improved quality of 3D PWLSM and CWLSM images compared to standard Kirchhoff migration with an acceptable computational cost.