Trace Pair Filtering for Separation of Upgoing and Downgoing Waves in Vsp (Vertical Seismic Profile)

Abstract

Most multichannel algorithms used for separation of upgoing and downgoing waves in VSPs assume depth-stationarity of the signal on all the traces used in the separation filter. However, if the depth-window of the filters becomes too large (100-200 m) signal stationarity cannot be assumed. On the other hand, stationarity is a physically reasonable assumption for two neighbouring probe locations (5-20 m). A comparison is made of three algorithms used for the separation of upgoing and downgoing waves, that require only two adjacent traces and their first arrival times. They are independent of in-depth trace-spacing, provided there are no geological discontinuities between adjacent traces. The first approach (near-theoretical solution) operates in the frequency domain. A system of two equations and two unknowns is solved for every frequency within the best coherencebandwidth. The second approach (simple solution) is a delay-and-sum, and subtraction filter based on the semblance of the signals. The third approach (Wiener solution) uses a Wiener filter to predict the strongest wave, which is generally the downgoing wave. The upgoing wave is then obtained by subtracting the estimated downgoing wave from the full wave record. A second application of the Wiener filter on the upgoing waves can enhance them. The near-theoretical solution and the simple solution are narrow-pass velocity filters and are applicable to zero-offset VSPs. The simple solution is suitable for noisy data. When the signal-to-noise ratio is high, the best results are obtained using the near-theoretical solution. The velocity-filter bandwidth can be increased in the Wiener solution, so that it can also be used in case of dipping reflectors or offset VSPs. The Wiener solution is suitable for noisy data, and its effectiveness can be increased by using a reference trace. The performance of these algorithms on synthetic and field data is evaluated in terms of signal-to-noise ratio, detection of upgoing waves and sensitivity to first arrival time estimates.