Limited offset and depth wavenumber bandwidths

One of the main sources of amplitude error is the finite bandwidth of the depth (k_z) and offset (k_h) wavenumbers (Figure 4). We apply RTT in the Fourier domain using Equations (20). In practical terms, this transformation amounts to a horizontal stretch of k_h at constant k_z. However, since k_z and k_h are limited in range, we can correctly evaluate the angle transformation only within a finite angle range ($-\gamma_{max},+\gamma_{max}$). The maximum angles to which our transformation is correct is a function of image sampling on offset and depth (Figure 4). $\gamma_{max}$ can be evaluated from the data, but cannot be modified during processing. We simply need to be aware of it and limit our analysis to the proper angle range.

 

khband
Figure 4 Truncation of the depth and offset wavenumber bandwidths limits the range over which we can compute angle-gathers. A k_z-k_h offset-gather (left panel) is transformed by RTT to a $k_z-\gamma$ angle-gather (right panel). $\gamma_{max}$ is the maximum angle for which the RTT is not affected by truncation of the k_h bandwidth.