Seismic reflection inversion by basis pursuit

In this dissertation we develop a seismic reflection inversion procedure using a basis pursuit technique that reconstructs the subsurface microstructure from post-stack seismic data. We first explain the formula underlying basis pursuit inversion (BPI) for seismic reflection, before investigating the formula through the incorporation of a priori information.;Specifically, our BPI incorporates wedge models as the basis instead of any impedance starting models. The incorporation is achieved by dipole decomposition, which can decompose any reflector pair into an odd and even pair. By using the formulism, BPI recovers the subsurface structure in the form of reflection coefficients. Synthetic tests show the sensitivity of BPI, even given the inaccuracy of wavelets and the presence of noise contamination. Sparse-spike inversion (SSI) is another minimal L1 norm constraint least square methods which has been used in industry for decades. A comparison between BPI and SSI suggests the improvement of BPI.;We test BPI with several field data sets: an improved tie between well-log data with the inverted data illustrating the superior vertical resolution from BPI; improved imaging of subtle stratigraphic features with removing the wavelet effect; impact on the 3-D data set interpretation; and improved velocity structure. Various data applications show the industrial potential of BPI to be incorporated.;BPI is a type of L1 norm-constrained least square solution for inverse problem. Compared with the other two kinds of constraints (Lp, (p=0, 2) norm minimization), minimal L1 norm constraint is the best at recovering an accurate reflectivity series. A minimal L0 norm constraint can be obtained by use of a matching pursuit (MP) method that produces sparse solutions. A minimal L2 constraint can be obtained by use of general inversion method that produces smooth solutions. The BPI technique balances the sparseness and smoothness to achieve a dense spiky solution.