# Bandwidth Extension of Seismic Data, Impact on Seismic Attribute Computation

Bandwidth extension of seismic data is a desirable goal when the available data has inadequate frequency content. Though significant efforts are expended during processing of seismic data to preserve the frequency content, they may not be effective enough to resolve reservoir intervals below tuning. We describe the performance of the sparse-layer seismic reflectivity inversion to extend the seismic bandwidth. This method yields a reflectivity series, which can be subsequently filtered to a desirable bandwidth that provides optimum resolution. These broader band results give reasonably accurate synthetic ties to wells and can also be used to derive relative acoustic impedance. By tightening the seismic wavelet and enhancing lateral changes in phase, bandwidth extension also improves lateral resolution as measured by volumetric dip, coherence, and curvature attributes.

Given these improvements, we apply two different unsupervised machine learning methods to attributes computed from the bandwidth extended data and compare them to the results computed from the original data. We find bandwidth extension provides a higher level of detail, whether it is the lineaments corresponding to faults or the thin-layered lithointervals than classification of the original data.

## Sparse-Layer Seismic Reflectivity Inversion

In the sparse-layer seismic reflectivity inversion method a temporally and spatially varying wavelet estimate is used. Just as an isolated spike (with an unknown wavelet) forms the basis function in spiking deconvolution, a library of thin-bed responses comprising dipole (two-layer or thin-bed) basis functions (layer responses) are convolved with the wavelet field using a priori information and statistical assumptions. The basis functions are then fit to the data using a least-squares fit criterion. The sparse-layer inversion determines a sparse number of patterns which, when summed together, form the original seismic trace. To extend the bandwidth, we now use the same dipoles that were convolved with the original wavelet field, but now replace the original wavelet with one with an extended bandwidth. Explicitly stated, the algorithm replaces the original data with a model of dipoles convolved with the well-log generated synthetic wavelet or statistical wavelet with a wavelet of our own choosing. In this manner, the unmeasured high and low frequencies in the new extended bandwidth wavelet are consistent with the same model used to represent the original data.

The sparse-layer inversion does not directly use well data in the inversion, though well data may be used in wavelet extraction and parameter selection (such as degree of sparsity), and of course for validation. By operating on a trace-by-trace basis, this inversion yields a reflectivity series, which is then filtered to a desirable bandwidth that exhibits an optimum combination of resolution and reasonably accurate synthetic ties to wells. The output reflectivity series can also be used to derive relative acoustic impedance.

We use the 3-D seismic data from Smeaheia area in offshore Norway to demonstrate the value of sparse layer inversion, where the Smeaheia area is a candidate for CO2 storage and evaluation.

The Smeahiea area lies about 30 kilometers east of the Troll gas field (figure 1), within the Norwegian continental shelf. It is located in a fault block bounded by the Vette Fault to the west and the Øygarden Fault to the east and is raised about 300 meters relative to the Troll field. The Late Jurassic Sognefjord, Fensfjord and Krossfjord formations form the producing reservoir zones in the Troll gas field.

In the Smeaheia block, there are two four-way closure structures, the Alpha structure to the west and the Beta structure to the east. Two exploration wells, namely 32/4-1 and 32/2-1 have been drilled into these structures, and although the reservoir is good, both wells turned out to be dry, indicating that the Smeaheia area is not charged with hydrocarbons.

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