Applications of plane-wave destruction filters |

Plane-wave destruction filters with an improved finite-difference design can be a valuable tool in processing multidimensional seismic data. On several examples, I showed their good performance in such problems as fault detection, missing data interpolation, and noise attenuation. Although only 2-D examples were demonstrated, it is straightforward to extend the method to 3-D applications by considering two orthogonal plane-wave slopes.

The similarities and differences between plane-wave destructors and - prediction-error filters can be summarized as follows:

Similarities:

- Both types of filters operate in the original time-and-space domain of recorded data.
- Both filters aim to predict local plane-wave events in the data.
- In most problems, one filter type can be replaced by the other, and certain techniques, such as Claerbout's trace interpolation method, are common for both approaches.

- The design of plane-wave destructors is purely deterministic and follows the plane-wave differential equation. The design of - PEF has statistical roots in the framework of the maximum-entropy spectral analysis (Burg, 1975). In principle, - PEF can characterize more complex signals than local plane waves.
- In the case of PEF, we estimate filter coefficients. In the
case of plane-wave destructors, the estimated quantity is the local
plane-wave slope. Several important distinctions follow from that
difference:
- The filter-estimation problem is linear. The slope estimation problem, in the case of the improved filter design, is non-linear, but allows for an iterative linearization. In general, non-linearity is an undesirable feature because of local minima and the dependence on initial conditions. However, we can sometimes use it creatively. For example, it helped to avoid aliased dips in the trace interpolation example.
- Non-stationarity is handled gracefully in the local slope estimation. No local windows are required to produce a smoothly varying estimate of the local slope. This is a much more difficult issue for PEFs because of the largely under-determined problem.
- Local slope has a clearly interpretable physical meaning, which allows for easy quality control of the results. The coefficients of - PEFs are much more difficult to interpret.

- The efficiency of the two approaches is difficult to compare. Plane-wave destructors are generally more efficient to apply because of the small number of filter coefficients. However, they may require more computation at the estimation stage because of the non-linearity problem.

Applications of plane-wave destruction filters |

2014-03-29