SEISMIC REFLECTION TECHNIQUES.

All of the geophysical techniques described in this section are founded on the same basic principles of seismic reflection. The technique operates by an acoustic wave being produced from a point source, the time interval is then recorded for this wave to reach a reflecting surface and return to a point at or near the original source. This interval is known as the two-way travel time (t) which is related to depth (D) by the simple equation:

D = 0.5Vp x t Equation 2.1)

In this equation Vp represents the compressional velocity of the transmitting medium, this quantity being determined by the values of the bulk modulus (k), the shear modulus (n) and the density (p) of the medium via the relationship:

h.

Vp = (k + 4/3n)/p Equation 2.2)

The value of Vp therefore varies between different rock and sediment types, with the simple relationship that hard rigid rock materials have relatively high compressional velocities where as soft plastic rocks have low compressional velocities. Further, the general empirical rule applies that compressional velocity increases in step with increased density in similar rock types.

If an acoustic wave encounters a boundary between two mediums of differing properties the energy of the incident wave is partitioned into transmitted and reflected waves. The relative proportions of the energy transmitted to each of these waves is determined by the contrast in acoustic impedance (Z) across the interface. Acoustic impedance is the product of the compressional velocity (Vp) and the density (p) of a medium:

Simply the greater the impedance contrast the greater proportion of the energy is apportioned to the reflected pulse and hence the stronger the returning signal. The partition of the incident wave can be expressed by the Reflection Coefficient (R) which is the ratio of the of the amplitude of the reflected wave (Ai) to the amplitude of the original incident wave (Ao). (See Figure 2.5):

Chapter 2. Field Methodology______________________________________________________ 37

R - Ai/A0 Equation 2.4)

For a normally incident wave this equation can also be expressed in terms of compressional velocity and density (z.e. acoustic impedance) from Zoeppritz’s equation (Telford etal.,

R = p2Vp2 - PiVpi/p2V„2 + piVpi Equation 2.5)

Values of R from this equation will range between -1 and 1; if R = 0 the incident energy is entirely transmitted i.e. there is no impedance contrast across the boundary, even if the compressional velocity and density of the two layers are different. If R = -1 or 1 all the incident energy is reflected this commonly occurs at the air/water interface where R = -0.9995 (Kearey & Brooks, 1991). Commonly values for R fall between ± 0.2 with the majority of the energy being transmitted. It is, however, important to understand that boundaries of strong impedance contrast need not necessarily correspond with lithological boundaries. In particular, subsurface density may vary with the liquid or gas content of a material, or indeed the degree of compaction of the sediment (Landmesser

et al., 1982; Davies et al., 1984; Hequette and Hill, 1989; N.G.T. Fannin, 1990 pers. comm.).

The degree of penetration, through a medium, achieved by an acoustic wave is proportional to the rate of energy loss. This is in turn dependent on:

z) Geometrical spreading; as the wave propagates its original energy (Eo) becomes distributed over a sphere of expanding radius. The amount of energy contained within a unit area of this sphere (Eua) can be expressed by:

Figure 2.5. Diagram Showing the Reflected and Transmitted components of an Incident Wave Striking a Boundary of High Acoustic Impedance Contrast

From Zoeppritz's equation we can calculate a value for the Reflection Coefficient (R): Assuming:

P2V2 > RVi

The majority of the orginal energy (Ao) is reflected (Ai) Note: Energy is represented by the amplitude (A) of the individual

Chapter 2. Field Methodology 38

Eua - E0/47cr2 Equation 2.6)

Consequently the energy of an individual ray will be reduced relative to r2.

zz) Internal friction losses; as energy is gradually absorbed into the medium by internal friction losses, even if an acoustic wave passed through a homogeneous medium it would still eventually disappear. The proportion of energy lost during the passage of a pulse over a single wavelength can be expressed as the absorption coefficient (a) which is measured in decibels per wavelength. The absorption coefficient can be quantitatively related to energy dissipation by:

a = 27.3/(E0ZEi) dB/A Equation 2.7)

Where Eo = original energy transmitted and Ei - energy dissipated (After McQuillin & Ardus, 1977). Common values of absorption coefficients vary between 0.25 and 0.75 dB/A and the higher the a value the more rapidly, in terms of time and distance, the wave is attenuated.

zzz) Frequency; simply lower frequency acoustic pulses achieve greater penetration than higher frequency acoustic pulses assuming the wave is travelling through a medium with constant Vp and a values. This is due to the fact that, as sound waves pass through successive layers, higher frequency pulses are absorbed more effectively than lower frequency ones. For example consider two waves, with frequencies (/) of 10 Hz and 100 Hz respectively, which are transmitted through a medium in which Vp = 2000 ms-1 and a = 0.5 dB/A. The wavelength (A) of the pulse can be calculated from the basic equation:

Vp -f A Equation 2.8)

The 100 Hz wave (A = 20 m) will be attenuated due to absorption by 5 dB over 200 m. The 10 Hz (A =200 m) by comparison will only be attenuated by 0.5 dB over the same distance. The consequences of this frequency related attenuation are even more dramatic when you consider that the decibel scale is in fact logarithmic such that a:

Chapter 2. Field Methodology 39

1 dB attenuation = 20.1ogio (Aa/Ao) Equation 2.9)

Where Aa = attenuated amplitude and Ao =. original amplitude, consequently an attenuation of 5 dB is equivalent to a reduction in amplitude of 50%; compared to only a > 10% reduction for a 0.5 dB attenuation.