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I did a basic google search but, I wasn't really satisfied with the output info.
I would love to know what exactly we can do with the extracted wavelet.
What kind of information extracted wavelet can contain ?

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  • $\begingroup$ so, what did you find, why were you not satisfied. See, we're basically the same folks whose results you find using an (appropriate) google search (maybe a google scholar search, too), so it's pretty likely you'll hit the same problems as with your google results, if you don't specify what you've understood so far, and what that did not answer! $\endgroup$ Aug 22 at 10:40
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    $\begingroup$ @MarcusMüller Seismic wavelet estimation is done to deconvolve the seismic trace, tie the well log to the seismic data, design inversion operator and etc. I want to know another uses of wavelet extraction. And as I mentioned in my question : What kind of information extracted wavelet can contain ? $\endgroup$ Aug 22 at 10:50
  • $\begingroup$ See how much difference that makes? Deconvolution would probably have been the main thing an answer would have explained, and you already seem to know that. So, please edit your question to be much more precise in what you want to know (comments on here are likely to get lost) $\endgroup$ Aug 22 at 13:35

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1.- WT allows more accuracy.

If you are already familiar with the nuts and bolts of for instance ; Fourier transform, FFT, Direct Cosine Transform, .. (1D transforms for 1D signals) then the Wavelet Transform WT, quoting A.Akansu A.Haddad in

https://www.sciencedirect.com/topics/computer-science/wavelet-transforms

is

[QUOTE] " .. another mapping from L2(R) → L2(R2), but one with superior time-frequency localization as compared with the STFT .."
[END OF QUOTE]

2.- Among many literature sources mentioning WT as useful for seismic signals analysis this one may help:

Wavelets and seismic interpretation JL Larsonneur, J Morlet Wavelets, 126-131, 1990

3.- In the following page

https://uk.mathworks.com/help/wavelet/getting-started-with-wavelet-toolbox.html?s_tid=srchtitle_wavelet%20tutorial_2

Mathworks has the following tutorials that you may find useful:

Visualizing Wavelets, Wavelet Packets, and Wavelet Filters

Obtain the filters, wavelet, or wavelet packets corresponding to a particular wavelet family.

Time-Frequency Analysis and Continuous Wavelet Transform

Learn how the CWT can help you obtain a sharp time-frequency representation.

Discrete Wavelet Analysis

Analyze and denoise signals and images using discrete wavelet transform techniques.

Critically Sampled Wavelet Packet Analysis

Obtain the wavelet packet transform of a 1-D signal and a 2-D image.

Matching Pursuit : Create sensing dictionaries and perform matching pursuit on 1-D signals.

Lifting : Use lifting to design wavelet filters while performing the discrete wavelet transform.

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The term "wavelet" most probably refers here to the "seismic wavelet". It is not "a wavelet transform" as we know it today, though both terms are related (thought the work of Jean Morlet). One of the early papers is Norman Ricker's The form and nature of seismic waves and the structure of seismograms, providing a standard propagation model:

A theory is presented to account for the structure of seismograms. It is demonstrated mathematically that a sharp seismic disturbance gives rise to a traveling wavelet, of shape determined by the nature of the earth’s absorption spectrum for elastic waves, and that a seismogram is composed of a succession of these wavelets, generally overlapping but sometimes in the clear. It is further brought out that it is the center of the wavelet which travels with a velocity characteristic of the medium, and that the wavelet broadens as it moves along in accord with a definite law. Experimental support of the theory also is presented.

The wavelet is the short waveform that is "practically" propagated to the ground. What is send by seismic sources can be known, but the weathered zone, and other artefacts may distort it. Its knowledge may help deconvolution, of course. It bypasses the weathered zone. And its variation along offsets may help understand subtle properties: non-linearity, anisotropy, multiple reflections, groundroll, etc. To finally have a better geology understanding, like body boundaries, thin beds, etc. One example is the 1941 paper by N. Ricker: A note on the determination of the viscosity of shale from the measurement of wavelet breadth

From the breadth of a wavelet for a given travel time, it is possible to calculate the viscosity of the formation through which the seismic disturbance has passed. This calculation has been carried out for the Cretaceous Shale of Eastern Colorado, and the value thus found ranges from 2.7×107 to 4.9×107, with a mean value of 3.8×107 grams per cm. per second.

Internet is nice. Yet for those questions, reputable book sources are still useful. Öz Yilmaz's "Seismic data analysis" remains a useful first reference.

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