Velocity Filter Data to Remove Surface Wave Noise.

Events with a slow moveout velocity (1000-4000 ft/s) are typically unwanted noise such as surface waves. Their velocity is usually well separated from the apparent velocity of deep reflections so we can filter them out in a domain in which they are well separated from one another, namely the FK (i.e., frequency-wavenumber) domain.

As an example, assume the data d(x,t)

$$\delta(x-v_{slow}t +x_0) + \delta(x-v_{fast}t +x_0'),$$ d(x,t) = (1.8)

consist of two linear events, one moving out with a slow velocity v_slow and the other with a fast velocity v_fast. The x-intercepts are denoted by x₀ and x₀'.

In the (x,t) domain the two linear events cross one another and so it is difficult to mute one entirely from the other. However, under an FK Fourier transform the above equation becomes:

$$\tilde d(k,\omega) a \delta(kv_{slow}-\omega) + b \delta(kv_{fast}-\omega),$$ = (1.9)

where a and b are phase terms. It is clear the transformed data describe two slanted lines that do not cross each other except at the origin. Thus muting one line from the other based on their different slopes (i.e., velocities) is trivial in the FK domain.

The above procedure is called velocity filtering. As a field data example, Figure 1.15 shows a CSG before and after velocity filtering to remove the steep surface waves.

  

Figure 1.15: CSG seismograms before (LHS) and after (RHS) FK velocity filtering to eliminate surface waves.