Love-Wave Propagation
Your assertion is correct! See e.g. Stein &amp; 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&amp;lpg=PP1&amp;hl=de&amp;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&amp;lpg=PP1&amp;hl=de&amp;pg=PA96, which shows the dispersion curve for a layer over a halfspace.