Seismic Methods

8.3.1 Seismic Method Introduction

Seismic waves are essentially elastic vibrations that propagate through soil and rock materials. Seismic waves can be introduced into the subsurface naturally, with earthquakes being a prime example. Earthquakes are seismic waves, oftentimes extremely destructive, that typically result from the energy released due to movement along large fractures (faults) in the Earth's crust. Data obtained from earthquakes have allowed seismologists to resolve the overall structure of the Earth (solid iron/nickel inner core, liquid iron/nickel outer core, mantle, and lithosphere).

Explosive, impact, vibratory, and acoustic artificial energy sources can also be used to introduce seismic waves into the ground for the purpose of investigating subsurface conditions or features. The use of active (artificial energy source) seismic geophysical methods is widespread in the petroleum and mining industries. Active seismic methods have additionally been employed for hydrological, environmental, geotechnical engineering, and archeological investigations. Although presently used very little for agricultural purposes, seismic methods are likely to find significant agricultural applications in the near future.

For seismic geophysical methods where artificial energy is supplied, the seismic waves generated are timed as they travel through the subsurface from the energy source to the sensors, which are called geophones. Incoming seismic wave amplitudes, and hence energy, are also measured at the geophones. The energy source is ordinarily positioned on the surface or at a shallow depth, and the geophones are normally inserted at the ground surface. Data on the timed arrivals and amplitudes of the seismic waves measured by the geophones are then used to gain insight on below-ground conditions or to characterize and locate subsurface features. Numerous texts provide detailed descriptions of seismic methods (Coffeen, 1978; Dobrin and Savit, 1988; Lines and Newrick, 2004; Pelton, 2005a, 2005b; Telford et al., 1976), and readers are referred to these for more information. However, some basic attributes of the seismic waves and their propagation through Earth materials along with general data collection and analysis considerations and potential seismic method agricultural applications are discussed as follows.

8.3.2 Seismic Wave Types

There are two categories of seismic waves: "surface waves" and "body waves." Surface waves, as the name implies, are seismic waves that travel only along Earth's surface. Seismic body waves, although capable of traveling along the surface directly from source to sensor, can also travel with a vertical component through soil and rock well below ground. P-waves (also called primary waves, compressional waves, and longitudinal waves) are a type of seismic body wave having an elastic back-and-forth particle motion orientation that coincides with the direction of wave propagation. P-waves can be transmitted through solid, liquid, and gas materials. P-waves are the fastest seismic waves, and their velocity, VP, within a soil or rock material is given by the following equation:

where k is the bulk modulus, ^ is the rigidity modulus (or shear modulus), and p is density. As indicated by Equation (8.1), the P-wave velocity in soil or rock depends only on elastic moduli and density of the soil or rock.

S-waves (also called secondary waves, shear waves, and traverse waves) are the second seismic body wave type and have an elastic particle motion that is perpendicular to the direction of wave propagation. There are two kinds of S-waves: the SV-wave and the SH-wave. The particle motion for an SV-wave has a vertical component. SH-waves, on the other hand, have a particle motion that is completely horizontal. S-waves are only capable of traveling through solid material, not liquids or gases. S-waves are slower than P-waves and have a velocity, VS, given by where all quantities have been previously defined. The S-wave velocity, as indicated by Equation (8.2), is governed strictly by shear stress elastic behavior and density of the soil or rock through which the S-wave travels.

There are two types of surface waves: Rayleigh waves and Love waves. Rayleigh wave particle motion is elliptical retrograde in a vertical plane oriented coincident with the direction of wave propagation. The Rayleigh wave amplitude decreases exponentially with depth. For a given soil or rock material, the Rayleigh wave velocity is approximately nine-tenths of the S-wave velocity for the same material (= 0.9VS). Love waves occur only where there is a low S-wave velocity layer at the surface that is underlain by a layer with a much higher S-wave velocity. Love waves are essentially SH-waves transmitted via multiple reflections between the top and bottom of the low seismic velocity surface layer. Accordingly, the Love wave particle motion is horizontal and perpendicular to the direction of wave propagation. The overall Love wave velocity for a particular soil or rock material is less than the S-wave velocity for the same material. Neither surface wave is capable of being transmitted through liquids, such as water.

Both surface wave types are dispersive. Dispersion occurs when different frequency components of the surface wave travel at different velocities, which causes the surface wave to become more spread out in length the farther the wave propagates. Dispersion is a result of different surface wave frequency components having different penetration depths coupled with vertical changes in soil and rock elastic moduli and density, which are the properties governing seismic wave velocity. Consequently, surface wave dispersion can provide insight as to the vertical seismic velocity structure in the shallow subsurface. (Note: The dispersion of body waves is considered to be negligible.)

8.3.3 Aspects of Seismic Wave Propagation

The seismic energy source is usually assumed for analysis purposes to occur at a point location, especially in situations where artificial energy is applied for seismic investigation of the subsurface. Again, this point source is positioned at or near the ground surface for most seismic geophysical surveys. Seismic surface waves generated at the source propagate away from the source as a continually expanding circular wavefront along Earth's surface. Seismic body waves propagate away from the source into the subsurface as a continually expanding hemispherical wavefront (Figure 8.7). Geometrical spreading of the seismic surface or body wavefront results in a decrease with time of the seismic wave amplitude, and hence energy intensity, at any point along the wavefront as it continues to expand. Basically, as the seismic waves propagate outwards, the total seismic energy generated at the source is being distributed over a greater and greater diameter circle for surface waves and over a larger and larger hemisphere for body waves. Seismic wave amplitude and energy are also reduced due to frictional dissipation of elastic energy into heat. The amount of seismic wave frictional dissipation is dependent on the nature of the soil or rock material through which the wave passes. The combined effect of geometrical spreading and frictional dissipation is called attenuation, A, and for body waves can be expressed with the following relationship:

r where A0 is the initial body wave amplitude, a is the frictional dissipation adsorption coefficient, and r is the radial distance of the wavefront from the source location (Sharma, 1997). Attenuation is frequency dependent, with the higher-frequency components of a seismic wave having been found to attenuate more rapidly with distance traveled than the lower-frequency seismic wave components.

Transformations of seismic body waves incident on a subsurface interface between two soil and rock layers are depicted in Figure 8.8. Solid and dashed arrowhead lines represent seismic wave travel paths, and the Figure 8.8 schematics are based on the assumption that Layer 2 P-wave

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