## Rayleigh wave

Seismic waves can be classified into body wave that travel through the Earth's interior, and surface waves that travel along the surface. Surface waves are classified into Rayleigh waves with volume change and Love waves, which oscillate horizontally. This page will discuss Rayleigh waves.

First of all, let's see how the Rayleigh wave propagetes (Figure 1). The circles are markers in the ground to identify the movements. The figure shows e ground is wavy shapeprotruding. If you move the cursor over the image and press "s" on your keyboard, the Rayleigh waves will start to propagate in the right direction. If you look at the circle, you can see that the Rayleigh wave is spinning around.

Let's look at the movement near the ground surface in more detail. If you look at the circles, you can see that it is rotating in a counterclockwise direction. At the depth of about 1/3 of the depth (the color change from red to blue), you can see that the rotation changes into clockwise direction.

Note the white circle near the center of the ground surface. The vertical and horizontal components are plotted in green and orange, respectively (the lower left panel). As this record shows, the seismometer captures the movement of the ground at a single point. The trajectory of the white circle (i.e., polariztion of ground motion) is plotted in the lower right panel. You can see that it rotates around in a counterclockwise direction.

### A little more detailed (technical) explanation

Press 1 on the keyboard. The absolute value of volumetric strain is shown in red and shear strain in blue. Near the ground surface, volumetric strain (red) increases due to the free boundary surface. There are regions of high shear strain on either side of the surface.

Press 2 on your keyboard to display the absolute value of σzz in red and σxz in blue. You can see that near the surface they are both zero, as they satisfy the free boundary surface, and that the color of the circles is black.

Here is a rough explanation. Let's consider a situation where Sv waves propagate in an infinite medium to the right. Then we cut it off in the middle and make it a semi-infinite medium. Then the ground surface will bulge to satisfy the zero-stress boundary condition (large volume strain). This causes a large deformation and the propagation speed becomes slower than that of S-waves.

### Figure 1

• Common
• Pause and restart: press "s" key
• Reset: press "r" key
• Particle trajectory (press "0" key)
• Plot the circles that rotate counterclockwise in red
• Clockwise circles are plotted in blue
• Strain (press "1" key)
• The absolute value of volume strain is plotted in red
• Shear strain is plotted in blue
• Stress (press "2" key)
• σzz plotted in red
• Plot σxz in blue