Spectral Fusion: a tool to merge low and high frequency datasets
Authors: Deplante Christian 
Published: March 2015

Abstract
"Spectral Fusion" is a new tool designed to combine different seismic datasets covering the same surveyed area, with different but overlapping bandwidths resulting for instance from various source/receiver depths for marine streamer data. By combining data with overlapping spectra a larger bandwidth can be recovered, with the benefit of using all of the available information in the overlapping frequency domain without requiring any wave shaping or predefined filters, and therefore better preserving the individual phase and amplitude character of the input data.
Driven by a real data application featuring a conventional streamer survey and a high-resolution field-oriented survey, it was developed as an alternate solution to a more complex inversion workflow. On the real data application presented, Spectral Fusion is shown to directly enable the bridging of the low-frequency gap in the high-resolution survey using the lower frequency data, allowing favorable comparison with a more complex inversion-based technique. It is also shown to bring an improvement in the quality of the resulting images as well as in the seismic well tie.

Introduction
The motivation for an amplitude-preserving non-destructive combination of partially overlapping low and high frequency datasets arose from a practical case of a specific field. The area was first covered by an exploration 3D survey with conventional acquisition parameters, and then several years later, though still before production started, by a dedicated survey whose parameters were tuned towards significantly higher frequencies. This last survey resulted in spectacular high-resolution reflectivity, but also had a lack of energy below 20 Hz. This lack of low frequencies became more obvious when the high frequency dataset was inverted for impedances. One can think of seismic inversion as a method to move from seismic reflectivities to absolute impedance. It requires bringing in the low frequencies missing in the seismic data using a background model, and finding an appropriate way to combine the relative seismic impedances with those from the background model. In this case, as is usual, the upper limit of the low frequencies brought in by the initial model is hardly more than a few Hertz, and the resulting low-frequency gap generated unacceptable secondary lobes in the inversion results.
To circumvent this issue, the first idea was to solve the problem at the inversion level. Pillet et al. (2007) presented a specific application of pre-stack inversion aimed at using the low-frequency dataset in a first inversion in order to bridge the frequency gap in a second target inversion of the high-frequency seismic.
In parallel to this workflow, which was carried forward to be used in operations, the geophysical research team at Total's Geosciences Research Center in Aberdeen took a different route and restated the problem directly from the seismic side. The method proposed does not use complementary low-pass and high-pass filters, which would be a simple way to recombine both datasets (Carter et al, 2009), but would not be appropriate for several reasons. The main drawback of this category of methods is the canceling of the large amount of redundant information in the common bandwidth whilst another is that they typically rely on pre-determined crossover filters and are therefore not self-adaptative.