## Seismic Notes

Basis of the seismic method is the timing of artificially generated pulses of elastic wave energy that propagates through the ground. These pulses of elastic wave energy or seismic waves are detected using electromagnetic transducers called geophones.

The two parameters which affect the elapse time of transmission of a pulse from its source to the detector are:

• Propagation velocity or velocities of the seismic wave;
• Geometry of the propagation path;

Propagation velocity depends on the elastic moduli and the density of the material through which the seismic wave travels.

Geometry of the propagation path is determined by the nature of the interface between two layers of differing velocities and the angle at which the wave strikes that interface.

To understand what occurs at a boundary, we must understand:

1. Huygens' Principle
2. Fermats Principle
3. Snell's Law

Remember: Elastic wave energy spreads out from a point source as an expanding sphere of energy.

Huygen's Principle states that every point on an advancing wave front of elastic wave energy is the source of new elastic wave energy that also travels out as an expanding sphere of energy. Only those wave fronts that add constructively continue on. Lines perpendicular to wave fronts define ray paths which can be though as pencils of elastic wave energy.

Fermat's Principle states the first arrival of elastic wave energy (at a geophone) travels the shortest time path.

Snell's Law describes how elastic waves are reflected and refracted across a boundary separating layers of differing velocity.

Derivation of Snell's Law; (Part1); (Part 2)

Snell's Law for incident P-wave

Snell's Law for incident S-wave

Amplitudes at an interface

How the energy of an incident wave is proportioned (i.e. reflected -vs- refracted) depends on the acoustic impedance of the two layers (z = acoustic impedance = V) and the angle of incidence

The relationships are described by the use of Zoeppritz or Shuey's equations which are rather involved,
but ...

For normal P-wave incidence, the ratio of the reflected "P-wave" energy to the incident "P-wave" energy is given by:

• ER / EI = (2V2 - 1V1)2 / (2V2 + 1V1)2

The square root of this equation is known as the reflection coefficient (R.C.)

• R.C. = (2V2 - 1V1) / (2V2 + 1V1)

The amount of energy transmitted is

• T.C. = (21V1) / (2V2 + 1V1)

When:
R.C. = 0 all the incident energy is transmitted
R.C. = ±1 all the incident energy is reflected
R.C. = ±.2 most of the incident energy is transmitted

EXAMPLE: bright spots and AVO (amplitude verses offset)
gas saturated sands have a lower velocity than adjacent H20 or oil filled sands