The wavelet is the link between seismic and stratigraphy as well as the rock properties of the subsurface.
The basic model for the seismic trace is referred to as the convolutional model, which states that the seismic trace is simply the convolution of the earth's reflectivity with a seismic source function with the addition of a noise component.
S (t) = w (t) * r (t) + n (t)
Where *implies convolution, s(t) is the seismic trace as a function of time t, w is the wavelet vector, r is the reflectivity series and n is noise.
There are at least three key methods of seismic wavelet estimation: the statistical method, the full wavelet method, and the constant phase method, which may give different results due to the influences of algorithms and data types on wavelet estimation. The best method needs to be determined for the dataset that you have, both, the seismic dataset and the well or wells relative position (according to geological structural features in focus). In my own experience in seismic reservoir characterization by inversion and AVO, just it is my paradigm, the best way to estimate the wavelet is the statistical method, to be tested by trial and error.
In the seismic inversion workflow, the extraction of statistical wavelet has two main roles: first, to correlate the wells and seismic and second, in the inversion analysis step.
Please, check the document that I attach such as a simple example, from my daily routine work in Reservoir Characterization by seismic inversion and AVO analysis.