Seismic wave velocity isseismic waveThe velocity of propagation in rock is usually related to rock type, confining pressure, rock structure and other geological factors.
On October 17, 1989, when the Loma Pratt earthquake struck, I suddenly felt the house shaking at my home in Berkeley, and I began to time.After 10 seconds, the shaking suddenly becomes very severe, which means that the S wave has arrived.P waves always arrive first from the source because they travel faster than S waves along the same path.Using this characteristic of wave, I can calculate that the source of this earthquake is more than 80 kilometers away.
The actual propagation speed of P and S waves depends on the density and internal elasticity of rocks.For linear elastic materials, when the wave is independent of the running direction, the wave speed only depends on two elastic properties, called elastic modulus: bulk modulus k and shear modulus μ of rock.
When a uniform pressure is applied to the surface of a rock cube, its volume will decrease. The volume change per unit volume is used as a measure of the required pressure, which is called bulk modulus.This type of deformation occurs when P waves propagate through the earth's interior;Because it only causes volume changes, it can also occur in fluids, as it does in solids.Generally, the larger the bulk modulus, the greater the velocity of P wave.
The second type of deformation is that when the tangential force in opposite directions is applied to the two opposite faces of the rock cube, the volume cube will be sheared and deformed without volume change.Similarly, this deformation also occurs when both ends of a cylindrical core are twisted by forces of equal magnitude and opposite direction.The greater the resistance of rock to shear or torsion stress, the greater its rigidity.S-wave propagates through shearing rock, and shear modulus gives a measure of its velocity.Generally, the greater the shear modulus, the greater the S-wave velocity.
The simple formulas of P-wave and S-wave velocities are given below.These expressions are consistent with the important properties of the waves already mentioned: because the shear modulus of the fluid is 0, the velocity of the shear wave in the water is 0, and because the two elastic moduli are always positive, P waves propagate faster than S waves.
Because of the strong pressure inside the earth, the density of rock increases with depth.Since the density is on the denominator of the P-wave and S-wave velocity formulas, it seems that the wave velocity should decrease with the increase of its depth in the earth.However, the bulk modulus and shear modulus increase with depth and increase faster than rock density (but when rock melts, its shear modulus decreases to 0).In this way, the P and S seismic wave velocities in our earth's interior generally increase with depth, which will be further discussed in Chapter 6.
Although the elastic modulus of a given rock is a constant, the properties of rock in different directions can change significantly in some geological environments.This condition is called anisotropy. At this time, P wave and S wave have different velocities when propagating in different directions.The exploration of this anisotropic property can provide information about the geological conditions of the earth's interior, which is a widely studied problem today.However, the following discussion will be limited to the isotropic case, which is the case for most seismic movements.
