BASIC FIELD EXPERIMENT

Seismic refraction is one of the basic, classical methods of applied geophysics. Whole-earth seismology started in the late 1800’s. Perhaps the first significant small-scale work was that of Mohorovicic who analyzed earthquake records in terms of a low-velocity crust over a high-velocity mantle.

The most basic refraction experiment involves a source (earthquake, explosion, hammer blow) and a set of receivers (seismographs, geophones, hydrophones). In many cases the geophones are set out in a straight line originating at the source. The geophones respond in turn as seismic waves pass by them. The geophones are sensitive to the velocity of vertical ground motion, not to the travel velocity of the various waves.

Because of the difficulty of identifying later wiggles on the geophone traces only the "first arrival" times are used in elementary interpretations. The mathematical interpretation yields some pattern of wave velocities in the ground. Geological interpretation involves converting the velocity distribution into a geologic cross-section. In other words, what earth materials correspond to the estimated velocities?

ELEMENTS OF ELASTICITY: STRESS, STRAIN AND ELASTIC MODULI

Stretching a cylindrical rock sample leads to Hooke’s Law. Up to some elastic limit, the applied axial stress (force per unit area measured in Newtons per meter squared or Pascals) is proportional to the axial strain (fractional elongation of the rod; dimensionless). Hooke’s Law states that the stress equals the strain times Young’s Modulus (Newtons per meter squared or Pascals). This "law" holds only for small strains. In this "elastic region" strains go away when the stress is removed. The law holds for both tension and compression. For sufficiently large strains there is some form of permanent deformation or even fracture. With respect to seismic waves we experience linear (Hooke’s Law) behavior except in the immediate vicinity of the source.

If we examine our stretched rock cylinder more carefully we’ll note that it got narrower as well as longer. Poisson’s Ratio is simply the negative of the radial strain (fractional change in radius; dimensionless) divided by the axial strain. Conversely, the cylinder gets broader if it is shortened by compressive stress. Poisson’s Ratio is dimensionless (as are all ratios) and is always between zero and one half.

For our second experiment let’s subject a cube or sphere to uniform stress ("hydrostatic stress"). For small enough stresses we find that the stress is proportional to the volumetric strain (also called cubical dilation). This is just the fractional change in volume (dimensionless). The proportionality constant is called the bulk modulus (Pascals or Newtons per meter squared). In this experiment only the size of the object changes; the shape stays the same.

For a third experiment let’s apply tangential stresses (shear stresses) to the faces of a cube. We’ll note that the shape changes from a square to a rhombus. The tangent of the total angular change in an original right angle is called the shear strain (dimensionless). For the small shear strains involved in seismic wave propagation, we can equate the tangent of the angle to the angle itself. For elastic materials and behaviour the shear stress (Pascals) is proportional to the shear strain. The constant of proportionality is called the shear modulus or modulus of rigidity (Pascals).

SEISMIC WAVES

Seismic waves can be divided into two classes. "Body waves" can travel throughout a three dimensional volume. Examples of body waves are compressional waves and shear waves, "Surface waves" (in a broad sense) are restricted to travel along some interface. Ocean waves are surface waves although most ocean surface waves are not seismic waves. Love waves and Rayleigh waves on solids are examples of seismic surface waves.

Traditionally the most significant waves in seismic exploration are compressional waves (also called P-waves, primary waves and push-pull waves. P-waves are body waves and can travel through solids, liquids and gases. The waves used in echo-sounding and sonar in the sea are just P- waves as are sound waves in the air. As the name implies these are the fastest seismic waves and are the first to be picked up after an earthquake or other seismic event. The particle motion ("orbital motion") is back and forth parallel to the direction of wave travel ("ray path") and at right angles to the wavefront.

Shear waves (S-waves, secondary waves, shake waves) have traditionally been little used in exploration seismology although they always been used in earthquake seismology. This is changing rapidly with S-waves becoming more important every year. S-waves travel more slowly than P-waves and can not travel though liquids and gases. The particle motion is normal to the ray path and parallel to the wavefront. Shear waves can be polarized with horizontal, vertical or some other sense of motion.

In conventional P-wave seismology using vertical geophones we often observe very strong "ground roll" consisting of large, low-frequency waves. The waves are predominantly Rayleigh waves, one of the two major types of seismic surface waves. In the simplest case the orbits are ellipses in a vertical plane. As with other surface waves the motion dies out with depth in the ground. Unlike body waves, surface waves are dispersive. That is, the speed of travel depends on the frequency of the wave.

Love waves are another common type of seismic surface wave. Orbital motion is horizontal and normal to the ray path. Love waves die out at depth and are always dispersive. Unlike Rayleigh waves they can only travel over a layered medium. We would not expect to detect Love waves with the vertical geophones that we normally employ.

SEISMIC WAVE VELOCITIES

The text has tables of seismic velocities for common earth materials. From these tables and other observations we can draw some general conclusions. For uncompacted sediment the P-wave velocity is about the same as the velocity in the pore fluid (air or water). For S-waves the pore fluid has little influence on the velocity.

For a grab-bag of rocks the P-wave velocity increases with density. Later we’ll see that this statement needs some serious qualifications. S-wave velocities are about two-thirds of compressional wave velocities on the same rocks. Velocities increase as pressure increases. For rocks within a few km of the surface Vp and Vs may be much less than at greater depth where joints and microcracks are sealed. Near surface weathering can also lead to low velocities.

For sedimentary rocks velocities increase with cementation and compaction but decrease with porosity. Thus Vp and Vs typically increase with depth and age. Vp depends strongly on pore fluid but Vs does not.

Increase of temperature increases the velocity of waves in air, water and some sediments. In solid rocks the seismic velocities decrease as temperature increases.