Deblending based on the frequency-structure weighted threshold: The case of the slope-constrained f-k transform

In the process of separating blended data, conventional methods based on sparse inversion assume that the primary source is coherent and the secondary source is randomized. The L1-norm, the commonly used regularization term, uses a global threshold to process the sparse spectrum in the transform domain; however, when the threshold is relatively high, more high-frequency information from the primary source will be lost. For this reason, we analyze the generation principle of blended data based on the convolution theory and then conclude that the blended data is only randomly distributed in the spatial domain. Taking the slope-constrained frequency-wavenumber ( f- k) transform as an example, we propose a frequency-dependent threshold, which reduces the high-frequency loss during the deblending process. Then we propose to use a structure weighted threshold in which the energy from the primary source is concentrated along the wavenumber direction. The combination of frequency and structure-weighted thresholds effectively improves the deblending performance. Model and field data show that the proposed frequency-structure weighted threshold has better frequency preservation than the global threshold. The weighted threshold can better retain the high-frequency information of the primary source, and the similarity between other frequency-band data and the unblended data has been improved.

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.

R-EPSI and Marchenko equation-based workflow for multiple suppression in the case of a shallow water layer and a complex overburden: a 2D case study in the Arabian Gulf

Suppression of surface-related and internal multiples is an outstanding challenge in seismic data processing. The former is particularly difficult in shallow water, whereas the latter is problematic for targets buried under complex, highly scattering overburdens. We propose a two-step, amplitude- and phase-preserving, inversion-based workflow, which addresses these problems. We apply Robust Estimation of Primaries by Sparse Inversion (R-EPSI) to suppress the surface-related multiples and solve for the source wavelet. A significant advantage of the inversion approach of the R-EPSI method is that it does not rely on an adaptive subtraction step that typically limits other de-multiple methods such as SRME. The resulting Green's function is used as input to a Marchenko equation-based approach to predict the complex interference pattern of all overburden-generated internal multiples at once, without a priori subsurface information. In theory, the interbed multiples can be predicted with correct amplitude and phase and, again, no adaptive filters are required. We illustrate this workflow by applying it on an Arabian Gulf field data example. It is crucial that all pre-processing steps are performed in an amplitude preserving way to restrict any impact on the accuracy of the multiple prediction. In practice, some minor inaccuracies in the processing flow may end up as prediction errors that need to be corrected for. Hence, we decided that the use of conservative adaptive filters is necessary to obtain the best results after interbed multiple removal. The obtained results show promising suppression of both surface-related and interbed multiples.