<p><strong>We're usually not interested in the wavelet <em>per se</em>, but we need to know it in order to understand how the seismic trace relates to geological properties we are interested in.</strong></p>
<p>According to the so-called <a href="https://subsurfwiki.org/wiki/Convolutional_model" rel="nofollow noreferrer"><strong>convolutional model</strong> of seismic</a>, a trace <span class="math-container">$s(t)$</span> (the amplitude is a function of time <span class="math-container">$t$</span>) has three main components, so to speak:</p>
<p><span class="math-container">$$ s(t) = r(t) \ast w(t) + n $$</span></p>
<p>where <span class="math-container">$r$</span> is the reflectivity of the earth, <span class="math-container">$w$</span> is the wavelet, <span class="math-container">$n$</span> is random noise, and <span class="math-container">$\ast$</span> denotes a mathematical operation called <a href="https://en.wikipedia.org/wiki/Convolution" rel="nofollow noreferrer">convolution</a>.</p>
<p>The <strong>reflectivity</strong> of the earth is very useful geological information. Reflectivity is a function of the <strong>impedance contrast</strong> at a boundary (e.g. between two beds) and impedance is, in turn, a function of important rock properties, especially density and the speed of sound in the rock. Both of these properties can help us deduce the rock type, porosity, fluid type, and so on, and other related properties can tell us about thin beds and fractures and other interesting things.</p>
<p>The problem with getting at the rock property information from the seismic trace is that it's all tangled up with the wavelet via the convolutional operator (there's noise too, but we can't do much about that.)</p>
<h3>So why do we need the wavelet?</h3>
<p>Two reasons:</p>
<ul>
<li><strong>Forward modeling.</strong> With a wavelet, we can try to <strong>forward model</strong> the seismic. For example we can measure, or guess, the impedance, calculate the reflectivity, and convolve with a wavelet to have a good guess at what the seismic might look like. This will result in <strong>synthetic seismic</strong>. We can use this to, for example, try to figure out which bed in a borehole is which event in a seismic volume (we call this process 'well tying'.)</li>
<li><strong>Inversion.</strong> Or, we can use the wavelet to get at the geology from the seismic data we measured. If we can estimate the wavelet, we can try to untangle it, or <strong>deconvolve</strong> it, from the seismic trace and get at the juicy geological stuff.</li>
</ul>
<p>So, having the wavelet, or being able to make a good guess at it, is useful. There are several ways to do it, e.g. see <a href="https://wiki.seg.org/wiki/Wavelet_estimation_for_well_ties" rel="nofollow noreferrer">the SEG wiki</a>. But it's a bit of an art and can be frustrating to get right... so a lot of people give up and use a standard off-the-shelf wavelet like a <a href="https://subsurfwiki.org/wiki/Ricker_wavelet" rel="nofollow noreferrer">Ricker</a>.</p>

CC BY-SA 4.0
2022-10-30T17:41:42.497Z
Hello sir, how to calculate scale of a ricker wavelet (obtained with bruges.filter.ricker) ? Sorry for asking the question here , I just didn't find a way to reach you :(  .
Fearless_Wolf
CC BY-SA 4.0
2022-10-30T22:11:01.397Z
@Fearless_Wolf Not sure what you mean by 'scale'. But feel free to make an issue on the repo: https://github.com/agilescientific/bruges
Matt Hall
CC BY-SA 4.0
2022-08-27T15:57:26.290Z
2022-12-30T11:35:53.060Z
2022-12-30T11:35:53.060Z
Matt Hall
<p>I would love to know what exactly we can do with the extracted wavelet. What kind of information extracted wavelet can contain?</p>

CC BY-SA 4.0
2022-08-22T21:32:19.583Z
Hello Fearless, welcome to the site.  I think it may be good to explain a bit/link about what a wavelet extraction is/what directed you to use it, as that could help/draw interest to a wider audience.  As is, with Earth Science being pretty diverse subtopics, even many earth scientists may not know much about what you're talking about. :-)
JeopardyTempest
<geophysics><seismology><seismic>
What is the purpose of wavelet extraction from the seismic trace?
Fearless_Wolf
# What is the purpose of wavelet extraction from the seismic trace?

(Asked by: username_0 on 2022-08-22)

I would love to know what exactly we can do with the extracted wavelet. What kind of information extracted wavelet can contain?

**Tags:** geophysics, seismology, seismic

> **Comments:**
> **username_1**: Hello Fearless, welcome to the site.  I think it may be good to explain a bit/link about what a wavelet extraction is/what directed you to use it, as that could help/draw interest to a wider audience.  As is, with Earth Science being pretty diverse subtopics, even many earth scientists may not know much about what you're talking about. :-)  

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## 1 answers

### Answer by username_2 on 2022-08-27. Score: 6 | Accepted answer

**We're usually not interested in the wavelet *per se*, but we need to know it in order to understand how the seismic trace relates to geological properties we are interested in.**

According to the so-called [**convolutional model** of seismic](https://subsurfwiki.org/wiki/Convolutional_model), a trace $s(t)$ (the amplitude is a function of time $t$) has three main components, so to speak:

$$ s(t) = r(t) \ast w(t) + n $$

where $r$ is the reflectivity of the earth, $w$ is the wavelet, $n$ is random noise, and $\ast$ denotes a mathematical operation called [convolution](https://en.wikipedia.org/wiki/Convolution).

The **reflectivity** of the earth is very useful geological information. Reflectivity is a function of the **impedance contrast** at a boundary (e.g. between two beds) and impedance is, in turn, a function of important rock properties, especially density and the speed of sound in the rock. Both of these properties can help us deduce the rock type, porosity, fluid type, and so on, and other related properties can tell us about thin beds and fractures and other interesting things.

The problem with getting at the rock property information from the seismic trace is that it's all tangled up with the wavelet via the convolutional operator (there's noise too, but we can't do much about that.)

### So why do we need the wavelet?

Two reasons:

* **Forward modeling.** With a wavelet, we can try to **forward model** the seismic. For example we can measure, or guess, the impedance, calculate the reflectivity, and convolve with a wavelet to have a good guess at what the seismic might look like. This will result in **synthetic seismic**. We can use this to, for example, try to figure out which bed in a borehole is which event in a seismic volume (we call this process 'well tying'.)
* **Inversion.** Or, we can use the wavelet to get at the geology from the seismic data we measured. If we can estimate the wavelet, we can try to untangle it, or **deconvolve** it, from the seismic trace and get at the juicy geological stuff.

So, having the wavelet, or being able to make a good guess at it, is useful. There are several ways to do it, e.g. see [the SEG wiki](https://wiki.seg.org/wiki/Wavelet_estimation_for_well_ties). But it's a bit of an art and can be frustrating to get right... so a lot of people give up and use a standard off-the-shelf wavelet like a [Ricker](https://subsurfwiki.org/wiki/Ricker_wavelet).

> **Comments:**
> **username_0**: Hello sir, how to calculate scale of a ricker wavelet (obtained with bruges.filter.ricker) ? Sorry for asking the question here , I just didn't find a way to reach you :(  .  
> **username_2**: @username_0 Not sure what you mean by 'scale'. But feel free to make an issue on the repo: https://github.com/agilescientific/bruges  

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