<p>Your assertion is correct! See e.g. Stein &amp; Wysession <em>An Introduction to Seismology, Earthquakes, and Earth Structure</em> (2003) p. 90 ,section 2.7.3: Love waves in a layer over a halfspace (<a href="https://books.google.ch/books?id=-z80yrwFsqoC&amp;lpg=PP1&amp;hl=de&amp;pg=PA90" rel="nofollow noreferrer">https://books.google.ch/books?id=-z80yrwFsqoC&amp;lpg=PP1&amp;hl=de&amp;pg=PA90</a>). In particular, for any particular frequency/period, Love waves can only have certain horizontal apparent velocities/wavenumbers. Hence, different frequencies have different apparent velocities, which is what we refer to as dispersion. See for example also the figure 2.8-2 from the book, <a href="https://books.google.ch/books?id=-z80yrwFsqoC&amp;lpg=PP1&amp;hl=de&amp;pg=PA96" rel="nofollow noreferrer">https://books.google.ch/books?id=-z80yrwFsqoC&amp;lpg=PP1&amp;hl=de&amp;pg=PA96</a>, which shows the dispersion curve for a layer over a halfspace.</p>

CC BY-SA 4.0
2019-03-12T13:26:54.353Z
2019-03-12T13:26:54.353Z
Erik
<p>Love-waves cannot exist in a half-space. Layering must be present and there also must be accompanied impedance contrasts associated with the layering.</p>

<p>Because layering naturally induces seismic dispersion (in certain frequency ranges) and layering must be present for Love-wave generation, does that - as a corollary - indicate that Love-waves are <em>naturally</em> and always dispersive?</p>

<p>Note that the motivation for this question primarily comes from the idea that Rayleigh-waves - which <em>can</em> exist in a half-space - are <strong>not</strong> dispersive when layering is not present.</p>

<geophysics><seismology><seismic>
Love-Wave Propagation
nate
# Love-Wave Propagation

(Asked by: username_0 on 2019-03-11)

Love-waves cannot exist in a half-space. Layering must be present and there also must be accompanied impedance contrasts associated with the layering.

Because layering naturally induces seismic dispersion (in certain frequency ranges) and layering must be present for Love-wave generation, does that - as a corollary - indicate that Love-waves are *naturally* and always dispersive?

Note that the motivation for this question primarily comes from the idea that Rayleigh-waves - which *can* exist in a half-space - are **not** dispersive when layering is not present.

**Tags:** geophysics, seismology, seismic


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## 1 answers

### Answer by username_1 on 2019-03-12. Score: 2 | Accepted answer

Your assertion is correct! See e.g. Stein & Wysession *An Introduction to Seismology, Earthquakes, and Earth Structure* (2003) p. 90 ,section 2.7.3: Love waves in a layer over a halfspace (<https://books.google.ch/books?id=-z80yrwFsqoC&lpg=PP1&hl=de&pg=PA90>). In particular, for any particular frequency/period, Love waves can only have certain horizontal apparent velocities/wavenumbers. Hence, different frequencies have different apparent velocities, which is what we refer to as dispersion. See for example also the figure 2.8-2 from the book, <https://books.google.ch/books?id=-z80yrwFsqoC&lpg=PP1&hl=de&pg=PA96>, which shows the dispersion curve for a layer over a halfspace.


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