An approximation of the inverse Ricker wavelet as an initial guess for bidirectional deconvolution |

We can manipulate equation 6 and decompose it into two symmetric parts. First, we shift the Ricker wavelet to the center of the axes:

ricker,ricker-freq
The fourth-order finite approximation of the Ricker wavelet: (a) in the time domain; (b) in the frequency domain.
Figure 1. |
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which rearranges to

We call one of these symmetric parts a ``half-Ricker wavelet'':

Figures 2(a) and 2(b) show this finite approximation of the Ricker wavelet in the time and frequency domains.

We denote the inverse of the half-Ricker wavelet, which is our candidate as the initial guess for both filter
and filter
, as
and
in the time domain and
and
in the Z domain:

half-ricker,half-ricker-freq
The fourth-order half-Ricker wavelet: (a) in the time domain; (b) in the frequency domain.
Figure 2. |
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An approximation of the inverse Ricker wavelet as an initial guess for bidirectional deconvolution |

2011-05-24