<p>The way I imagine this phenomenon is illustrated in the picture below. I have to warn you that it lacks scientific accuracy and is <strong>just a simple way to imagine</strong> the effects we observe on a reflective boundary. However, it can be useful as a simple model you can easily imagine.<br>
In the upper picture you can see an illustration of a <a href="http://en.wikipedia.org/wiki/Reflection_seismology#Reflection_and_transmission_at_non-normal_incidence" rel="nofollow noreferrer">reflection event</a> at a horizontal boundary.<br>
The lower picture illustrates how the vector of particle motion in a down-going P-wave is 'decomposed' into two vectors. First component is a vector of particle motion in an up-going S-wave, the second corresponds to particle motion in an up-going P-wave.</p>

<p>Once again, <strong>this is not how the rays exactly behave</strong> in a reflection event. Here we do not take into account transmitted waves and lots of other factors. Nevertheless, sometimes you can use this 'approximation' because it satisfies two conditions:</p>

<ul>
<li>At normal incidence, there is no mode conversion (shear wave does not appear)</li>
<li>As the incident angle increases, the amount of shear-wave energy increases too.    </li>
</ul>

<p>These effects are also observed in real life.<br>
Exact description of a reflection event on a plane boundary, as <a href="https://earthscience.stackexchange.com/users/70/kwinkunks">kwinkunks</a> has  mentioned above, is given by Zoeppritz equations. They take into account all details and are widely-used. No doubt, they are much more difficult (but physically correct!) than a simple sketch I suggest.</p>

<p><img src="https://i.sstatic.net/QkMAl.png" alt="a very simple illustration of mode conversion">. </p>

CC BY-SA 3.0
2015-04-03T18:08:03.313Z
Modelling shear-wave conversion does not show a monotonous increase of conversion energy as you can see [here](https://i.sstatic.net/wBlkT.gif) which is taken from [Crewes](http://www.crewes.org/ResearchLinks/ConvertedWaves/page1.php).
Jesper
CC BY-SA 3.0
2015-04-23T14:03:02.540Z
Yes, thank you @WayoftheGeophysicist for your comment. As I have mentioned, Zoeppritz equations should be used for precise calculations. A useful and intuitive tool can be found here: [CREWES Zoeppritz Explorer](http://www.crewes.org/ResearchLinks/ExplorerPrograms/ZE/ZEcrewes.html). However, as you probably may have noticed, conversion energy always increases (by its absolute value) at small incidence angles and is equal to zero at normal incidence. And just to clarify: I do not propose an accurate model of reflection event, but rather a way to imagine this phenomenon.
antongrin
CC BY-SA 3.0
2015-03-30T09:36:54.050Z
2015-03-31T23:05:00.530Z
2017-04-13T12:50:30.540Z
antongrin
<p>With the increase of incidence angle, a portion of a P-wave converts into a S-wave, how does this behaviour occur?</p>

CC BY-SA 3.0
2015-03-23T17:22:12.660Z
@SabreTooth This phenomenon, known as **mode conversion**, is described by the [Zoeppritz equations](http://en.wikipedia.org/wiki/Zoeppritz_equations), which are solutions to the [wave equation](http://en.wikipedia.org/wiki/Wave_equation). [Here's a nice demo video.](https://www.youtube.com/watch?v=ilDqQCezFFA) *How* this happens is, I think, rather a tricky question to answer without a lot of arm-waving.
Matt Hall
<geophysics><seismology>
Why does part of the P-wave convert into a S-wave with an increase of incidence angle?
Jony
# Why does part of the P-wave convert into a S-wave with an increase of incidence angle?

(Asked by: username_0 on 2015-03-23)

With the increase of incidence angle, a portion of a P-wave converts into a S-wave, how does this behaviour occur?

**Tags:** geophysics, seismology

> **Comments:**
> **username_1**: @SabreTooth This phenomenon, known as **mode conversion**, is described by the [Zoeppritz equations](http://en.wikipedia.org/wiki/Zoeppritz_equations), which are solutions to the [wave equation](http://en.wikipedia.org/wiki/Wave_equation). [Here's a nice demo video.](https://www.youtube.com/watch?v=ilDqQCezFFA) *How* this happens is, I think, rather a tricky question to answer without a lot of arm-waving.  

---

## 1 answers

### Answer by username_2 on 2015-03-30. Score: 2

The way I imagine this phenomenon is illustrated in the picture below. I have to warn you that it lacks scientific accuracy and is **just a simple way to imagine** the effects we observe on a reflective boundary. However, it can be useful as a simple model you can easily imagine.  
In the upper picture you can see an illustration of a [reflection event](http://en.wikipedia.org/wiki/Reflection_seismology#Reflection_and_transmission_at_non-normal_incidence) at a horizontal boundary.  
The lower picture illustrates how the vector of particle motion in a down-going P-wave is 'decomposed' into two vectors. First component is a vector of particle motion in an up-going S-wave, the second corresponds to particle motion in an up-going P-wave.

Once again, **this is not how the rays exactly behave** in a reflection event. Here we do not take into account transmitted waves and lots of other factors. Nevertheless, sometimes you can use this 'approximation' because it satisfies two conditions:

* At normal incidence, there is no mode conversion (shear wave does not appear)
* As the incident angle increases, the amount of shear-wave energy increases too.

These effects are also observed in real life.  
Exact description of a reflection event on a plane boundary, as [kwinkunks](https://earthscience.stackexchange.com/users/70/kwinkunks) has mentioned above, is given by Zoeppritz equations. They take into account all details and are widely-used. No doubt, they are much more difficult (but physically correct!) than a simple sketch I suggest.

![a very simple illustration of mode conversion](https://i.sstatic.net/QkMAl.png).

> **Comments:**
> **username_3**: Modelling shear-wave conversion does not show a monotonous increase of conversion energy as you can see [here](https://i.sstatic.net/wBlkT.gif) which is taken from [Crewes](http://www.crewes.org/ResearchLinks/ConvertedWaves/page1.php).  
> **username_2**: Yes, thank you @WayoftheGeophysicist for your comment. As I have mentioned, Zoeppritz equations should be used for precise calculations. A useful and intuitive tool can be found here: [CREWES Zoeppritz Explorer](http://www.crewes.org/ResearchLinks/ExplorerPrograms/ZE/ZEcrewes.html). However, as you probably may have noticed, conversion energy always increases (by its absolute value) at small incidence angles and is equal to zero at normal incidence. And just to clarify: I do not propose an accurate model of reflection event, but rather a way to imagine this phenomenon.  

---

