# Effective penetration of profiler sources

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 7 221 - 252 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 7.4a

Sieck and Self (1977) summarize “acoustic systems” as shown in Table 7.4a. For each of these systems, calculate the wavelengths and penetration depths given by Denham’s (1982) rule, that the maximum useable frequency is ${\displaystyle f_{\max }=150/t}$, where ${\displaystyle t}$ = traveltime. Reconcile your results with the stated purposes.

Table 7.4a. Acoustic systems.
System Frequency (kHz) Purposes
Fathometers 12–80 To map water bottom
Water-column bubble detectors 3–12 To locate bubble clusters, schools of fish
Side-scan sonar 38–250 To map bottom irregularities
Tuned transducers 3.5–7.0 To penetrate 30 m
Imploders 0.8–5.0 To penetrate 120 m, find gas-charged zones
Sparkers 0.04–0.15 To map 1000

### Background

Acoustic systems include several devices that use sound waves to measure distances in water. Transducers emit sound waves, usually short pulses, the travel-times of which are used to measure distances. Fathometers are transducers that emit and record high-frequency pulses (usually about 100 kHz); they determine water depth from the two-way traveltime of the sea-floor reflection. Fathometers have little penetration, but similar devices using frequencies in the range ${\displaystyle 1-10}$ kHz may penetrate as much as 30 m.

Side-scan sonar utilizes a towed transducer that emits high-frequency pulses and measures the traveltime of energy back-scattered by irregularities on the bottom.

The sparker is an energy source using the discharge of a large capacitor to create an electric arc between two electrodes in water, the sudden vaporization of the water being equivalent to an explosion.

Imploders create voids in the water and the effect of water rushing into the voids is to generate seismic waves; an example is the water gun which has two chambers, one being filled with air at high pressure, the other containing water; release of the air into the water chamber forces the water out at high velocity, thus creating voids into which the surrounding water collapses.

Denham (1982) devised an empirical rule relating the maximum useable frequency to the two-way traveltime ${\displaystyle t}$: ${\displaystyle f_{\max }=150/t}$, the useful frequency cutoff being determined by the increased absorption of higher frequencies and the background noise level. Note that high-frequency loss in water is very small, so the time is that below the seafloor.

### Solution

We assume a value 1500 m/s for the velocity of sound in water, so ${\displaystyle \lambda =1500/f}$. Taking ${\displaystyle z}$ as the depth of penetration, Denham’s rule gives ${\displaystyle z=Vt/2=112\times 10^{3}/f_{\max }}$ where ${\displaystyle f_{\max }}$ is in kilohertz. The results are given in Table 7.4b.

Table 7.4b. Calculated wavelengths and depths of penetration.
System Frequency (kHz) Wavelength (m) Penetration depth (m)
Fathometers 12–80 0.12–0.019 9–1
Bubble detectors 3–12 0.50–0.12 37–9
Side-scan sonar 38–250 0.039–0.006 3–0.4
Tuned transducers 3.5–7.0 0.43–0.021 32–16
Imploders 0.8–5.0 1.9–0.30 140–22
Sparkers 0.04–0.15 38–10 2800–750

Maximum penetration is given by the energy that the systems inject into the earth, higher frequency systems generally giving less energy. The bubble detector might locate a cluster of bubbles or a school of fish, but certainly not individual bubbles or individual fish.

## Problem 7.4b

Trade literature claims 30-cm resolution with imploders and 2–5 resolution with sparkers. How do these figures compare with the resolvable limits?

### Solution

The resolvable limit (see problem 6.18) is ${\displaystyle \lambda /4}$ and using the shorter wavelengths in Table 7.4b gives resolvable limits of 0.5 to 0.08 m for imploders and 9.5 to 2.5 m for sparkers. Thus the claims in the trade literature are reasonable.