Reflectivity decomposition: Theory and application

Sparse reflectivity inversion of processed reflection seismic data is intended to produce reflection coefficients that represent boundaries between geological layers. However, the objective function for sparse inversion is usually dominated by large reflection coefficients which may result in unstable inversion for weak events, especially those interfering with strong reflections. We propose that any seismogram can be decomposed according to the characteristics of the inverted reflection coefficients which can be sorted and subset by magnitude, sign, and sequence, and new seismic traces can be created from only reflection coefficients that pass sorting criteria. We call this process reflectivity decomposition. For example, original inverted reflection coefficients can be decomposed by magnitude, large ones removed, the remaining reflection coefficients reconvolved with the wavelet, and this residual reinverted, thereby stabilizing inversions for the remaining weak events. As compared with inverting an original seismic trace, subtle impedance variations occurring in the vicinity of nearby strong reflections can be better revealed and characterized when only the events caused by small reflection coefficients are passed and reinverted. When we apply reflectivity decomposition to a 3D seismic dataset in the Midland Basin, seismic inversion for weak events is stabilized such that previously obscured porous intervals in the original inversion, can be detected and mapped, with good correlation to actual well logs.

Seismic reflectivity inversion using an L1-norm basis-pursuit method and GPU parallelisation

Seismic reflectivity inversion problem can be formulated using a basis-pursuit method, aiming to generate a sparse reflectivity series of the subsurface media. In the basis-pursuit method, the reflectivity series is composed by large amounts of even and odd dipoles, thus the size of the seismic response matrix is huge and the matrix operations involved in seismic inversion are very time-consuming. In order to accelerate the matrix computation, a basis-pursuit method-based seismic inversion algorithm is implemented on Graphics Processing Unit (GPU). In the basis-persuit inversion algorithm, the problem is imposed with a L1-norm model constraint for sparsity, and this L1-norm basis-pursuit inversion problem is reformulated using a linear programming method. The core problems in the inversion are large-scale linear systems, which are resolved by a parallelised conjugate gradient method. The performance of this fully parallelised implementation is evaluated and compared to the conventional serial coding. Specifically, the investigation using several field seismic data sets with different sizes indicates that GPU-based parallelisation can significantly reduce the computational time with an overall factor up to 145. This efficiency improvement demonstrates a great potential of the basis-pursuit inversion method in practical application to large-scale seismic reflectivity inversion problems.

Application of sparse-layer inversion and harmonic bandwidth extension for a channel system in Southern Alberta, Canada

Sparse-layer reflectivity inversion decomposes a seismic trace into a limited number of simple layer responses and their corresponding reflection coefficients for top and base reflections. In contrast to sparse-spike inversion, the applied sparsity constraint is less biased against layer thickness and can thus better resolve thin subtuning layers. Application to a 3D seismic data set in Southern Alberta produces inverted impedances that have better temporal resolution and lateral stability and a less blocky appearance than sparse-spike inversion. Bandwidth extension harmonically extrapolated the frequency spectra of the inverted layers and nearly doubled the usable bandwidth. Although the prospective glauconitic sand tunes at approximately 37 m, bandwidth extension reduced the tuning thickness to 22 m. Bandwidth-extended data indicate a higher correlation with synthetic traces than the original seismic data and reveal features below the original tuning thickness. After bandwidth extension, the channel top and base are more evident on inline and crossline profiles. Lateral facies changes interpreted from the inverted acoustic impedance of the bandwidth-extended data are consistent with observations in wells.