Kalman Filters in Improving the Signal to Noise Ratio of Full Tensor Gravity Gradiometry Data

Abstract:

We have applied several extensions and optimal smoothing approaches of the Kalman filter, one of the best known recursive data processing techniques, on the Full Tensor Gradiometry (FTG) data acquired by Bell Geospace over the Vinton salt dome located in southwest Louisiana. We used the filter to improve the signal-to-noise ratio of gravity gradiometry components. We tested the standard Kalman filter and Fading memory and Constrained Kalman filter extensions with Fixed-lag and Forward-Backward smoothing methods to maintain symmetry. Our most meaningful results were obtained through the Kalman filter with the constraint of Laplace’s equation combined with the Forward-Backward filter operations. Laplace’s equation constraint was incorporated using two separate strategies: Model reduction and Perfect constraint (or Perfect measurement). In general, Kalman filter processed data have greater dynamic range than previously filtered data and also have the ability to extract signal from noisy data without having to remove a band of wavenumbers. In addition, our constrained Kalman filter also has the ability to force the Laplace’s equation constraint. These characteristics enable the Kalman filter to investigate short wavelength signals associated with near-surface lateral density variations. In analyzing two dimensional maps for geologic variations, our workflow includes leveling and decorrugation, both procedures necessary for data processed along profiles. Several previously mapped near-subsurface geologic features like faults and their continuity in the Vinton dome area are more readily apparent in our Kalman filter processed components. Since the processed data generally agree with the previously mapped and interpreted structures, the interpretation could be extended to previously unmapped areas. The use of Kalman filtering in combination with Laplace’s equation in applications such as gravity and magnetic gradiometry could be useful in determining more precisely the near-surface structural and stratigraphic variations associated with earthquake faults in addition to petroleum traps and their nature.