Implementation of Non-Uniform F-K and Strict F-K Filter Normalization in Seismic Downhole Processing

In fundamental geophysics, we can understand that if we hit the surface, the body and surface waves propagate into and on the soil or rock. The body waves consist of pressure waves, which are the fastest, and shear waves, which are slower. This phenomenon can be measured using the seismic downhole method to determine the velocity of P and S waves of soil layers by generating source energy at the surface and calculating the arrival time at a tri-axial sensor inside a borehole. Determining the arrival time of S waves is often tricky because the recorded S wave arrival is on the coda of the P waves and is also distracted by measurement noise. A common method to separate P and S waves is direct F-K filtering from the F-K image of the measurement data. This study modified this method by adjusting the actual source-receiver distance by implementing a non-uniform F-K transform to produce the correct velocity response. Another improvement was strict filter normalization to regain continuity, thus preventing a shadow response in the F-K image. Synthetic and real measurement data showed that our modification performed better than direct FK-filtering.