Noise and Multiple Exercises
Exercise 6-1. Prove that a hyperbola in the offset domain (x, t) maps onto an ellipse in the slant-stack domain (τ, p).
Exercise 6-2. Refer to Figure 6.E-1. What would the t − x domains look like?
Exercise 6-3. Consider constructing the slant-stack gather from offset data that consists of a reflection hyperbola. Does equal increment in p, the ray parameter, cause undersampling or oversampling of the steep dips? Of the gentle dips? What happens when an equal increment in 1/p is used? What happens when an equal increment in θ is used, where θ is related to p by p = sin θ/v?
Exercise 6-4. Identify event E in Figure 6.2-1.
Exercise 6-5. What procedure does CMP stacking correspond to in the f − k domain?
Figure 6.2-1 (a) Composite field record obtained from a walk-away noise test. Trace spacing = 10 m, A = ground roll, B = a backscattered component of A, C = dispersive guided waves, D = primary reflection. Event E is referred to in Exercise 6-4. (b) The f − k spectrum of this field record, (c) The f − k spectrum of the field record after rejecting ground roll energy A. Compare this with the f − k spectrum (b) of the original record. For display purposes, each spectrum is normalized with respect to its own maximum. (d) Dip-filtered field record whose f − k spectrum is shown in (c). Compare this record with the original in (a). (Data courtesy Turkish Petroleum Corp.)
- Introduction to noise and multiple attenuation
- Multiple attenuation in the CMP domain
- Frequency-wavenumber filtering
- The slant-stack transform
- The Radon transform
- Linear uncorrelated noise attenuation
- Multichannel filtering techniques for noise and multiple attenuation