Texture of land data: near-surface problems

Reflection seismic data recorded on land frequently displays randomness because of the irregularity of the soil layer. Often it is so disruptive that the seismic energy sources are deeply buried (at much cost). The geophones are too many for burial. For most land reflection data, the texture caused by these near-surface irregularities exceeds the texture resulting from the reflecting layers.

To clarify our thinking, an ideal mathematical model will be proposed. Let the reflecting layers be flat with no texture. Let the geophones suffer random time delays of several time points. Time delays of this type are called statics. Let the shots have random strengths. For this movie, let the data frames be common-midpoint gathers, that is, let each frame show data in (h,t)-space at a fixed midpoint y. Successive frames will show successive midpoints. The study of Figure 1 should convince you that the travel-time irregularities associated with the geophones should move leftward, while the amplitude irregularities associated with the shots should move rightward. In real life, both amplitude and time anomalies are associated with both shots and geophones.

EXERCISES:

1. Note that Figure 1 is drawn for a shot interval $\Delta s$ equal to half the geophone interval $\Delta g$.Redraw Figure 1 for $\Delta s = \Delta g$.Common-midpoint gathers now come in two types. Suggest two possible definitions for ``near-offset section.''
2. Modify the program of Figure 5 to produce a movie of synthetic midpoint gathers with random shot amplitudes and random geophone time delays.
    

   cube Figure 5

   

   Observing this movie you will note the perceptual problem of being able to see the leftward motion along with the rightward motion. Try to adjust anomaly strengths so that both left-moving and right-moving patterns are visible. Your mind will often see only one, blocking out the other, similar to the way you perceive a 3-D cube, from a 2-D projection of its edges.

3. Define recursive dip filters to pass and reject the various textures of shot, geophone, and midpoint.