The velocity spectrum
The input CMP gather in Figure 3.2-9a contains a single reflection hyperbola from a flat interface. The medium velocity above the reflector is 3000 m/s. Suppose that this gather is NMO-corrected and stacked, repeatedly, using a range of constant velocities from 2000 to 4300 m/s. Figure 3.2-9b displays the resultant stack traces for each velocity side by side on a plane of velocity versus two-way zero-offset time. This is called the velocity spectrum . We have transformed the data from the offset versus two-way time domain (Figure 3.2-9a) to the stacking velocity versus two-way zero-offset time domain (Figure 3.2-9b).
The highest stacked amplitude occurs with a velocity of 3000 m/s. This is the velocity that should be used to stack the event in the input CMP gather. The low-amplitude horizontal streak on the velocity spectrum results from the contribution of small offsets, while the large-amplitude region on the spectrum is due to the contribution of the full range of offsets . Hence, we need long offsets for good resolution on the velocity spectrum. A way to minimize the streak effect of finite-cable length on the velocity-spectrum is to transform the CMP gather from offset to velocity domain by way of discrete Radon transform (the radon transform).
A CMP gather associated with a layered earth model is shown in Figure 3.2-10a. Based on the stacked amplitudes, the following picks for stacking velocity function are made from the velocity spectrum (Figure 3.2-10b): 2700, 2800, and 3000 m/s. These picks correspond to the shallow, middle, and deep events, respectively. The velocity spectrum not only can provide the stacking velocity function, but it also allows one to distinguish between primary and multiple reflections.
The quantity displayed on the velocity spectra in Figures 3.2-9b and 3.2-10b is the stacked amplitude. When the signal-to-noise ratio of the input data is poor, then the stacked amplitude may not be the best display quantity. The aim in velocity analysis is to obtain picks that correspond to the best coherency of the signal along a hyperbolic trajectory over the entire spread length of the CMP gather.  described various types of coherency measures that can be used as attributes in computing velocity spectra.
- Measure of coherency
- Factors affecting velocity estimates
- Interactive velocity analysis
- Horizon velocity analysis
- Coherency attribute stacks
- Topics in moveout and statics corrections
- Taner and Koehler, 1969, Taner, M. T. and Koehler, F., 1969, Velocity spectra — digital computer derivation and applications of velocity functions: Geophysics, 39, 859–881.
- Sherwood and Poe, 1972, Sherwood, J. W. C. and Poe, P. H., 1972, Constant velocity stack and seismic wavelet processing: Geophysics, 37, 769–787.
- Neidell and Taner (1971), Neidell, N. S. and Taner, M. T., 1971, Semblance and other coherency measures for multichannel data: Geophysics, 34, 482–497.