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

Approximation of the inverse Ricker wavelet

Generally, it is a complicated issue to find a good initial guess for bidirectional deconvolution. However, in most field and synthetic geophysical data the wavelet is similar to a Ricker wavelet. For example, band-limited marine seismic data with ghosts and the land response of an accelerometer are both Ricker-like. Hence Ricker-like wavelets have broad applicability. For this reason, we choose a Ricker wavelet to approximate the wavelet of the data and derive the initial filters from the inverse Ricker wavelet. If we could derive the inverse of the Ricker wavelet, it would provide a suitable initial guess.

In theory, however, Ricker wavelets do not have a stable inverse. Therefore we must find an approximate inverse to use as the initial guesses for filters $f_a$ and $f_b$ . Since we need two initial guesses, one for each filter, our approximate inverse should consist of two symmetric parts.

We have three tasks: first we must find a finite approximation for the continuous Ricker wavelet; second we must separate the approximate form into two symmetric parts; and third we must find a way to avoid the singularity problems we encounter when inverting these two parts directly in the frequency domain. Let's address these tasks one by one.

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