Variogram modeling of broadband artifacts of a seafloor map for filtering with Factorial Kriging

Abstract

Accurate seafloor maps are critical in offshore petroleum projects. Almost all subsurface modeling workflows use these maps: for example, pore pressure models and reservoir geomechanics. These studies generally involve sums of properties along the vertical, consequently, noise or acquisition artifacts at the seafloor map tend to propagate and even amplify in the subsequent models. Seafloor maps are normally acquired by sound-sensing technology and related procedures, which expectedly introduce noise and artifacts. Moving window filters, such as average and median filters, are easy to use and fast to compute, hence they are used very often by interpreters to make geologically sound horizons. However such filters are unable to discern noise, artifacts and signal, resulting in the compromise of actual information. Filtering in the frequency domain can pose difficulties when noise, artifacts and geological information overlap in the frequency domain, as the total energy tend to concentrate in the lowest frequencies. Factorial kriging (FK) is a spatial filter that yields separate estimations, each corresponding to a variogram nested structure. FK relies on the principle that structurally complex information is a sum of independent information components while the variogram is a clear and reliable way to select the frequency ranges of each component. Hence, this method can effectively separate acquisition artifacts from seafloor information based on their different spatial structures modeled with variograms. This work investigates an application of FK for filtering of hard-edged (broadband) artifacts in post-processed interpreted seismic data. Differently from random noise, artifacts are spatially correlated information components mixed with actual geologic information. Initially, removal of the bathymetric trend makes the case stationary for a high-resolution variogram map computed in the frequency domain via fast Fourier transform (FFT), which enables a full 2D variogram modeling. Theoretical variogram surfaces are fit to the experimental variogram map, enabling the identification and modeling of a set of nested variograms. The authors envisaged search strategies to select a small number of informative samples to reduce kriging runtime and, at the same time, cover the necessary spatially correlated variability. A workflow on a large seismic-derived seafloor 2D map is demonstrated, detailing each step with emphasis on the sensitive variogram modeling step, followed by search strategy definition and choice of the geology-bearing factors for seafloor restoration. Filtering in frequency domain was performed for comparison. Results showed that broadband artifacts require a non-traditional approach to variogram modeling, which was performed in a second FK run with a wholly new variogram model. The filtering operations revealed seafloor features, which were previously unseen in the original map, and the final result was similar to that obtained with FFT. FK is a lossless filtering technique that is a highly effective method to remove acquisition footprints in final grids and volumes in which acquisition geometry information is not available. 11FFT – fast Fourier transform22FK – Factorial Kriging33KT – Kriging with a trend44TCL – Tool Command Language