Units in Geophysics

The SI (Système International) units used in this book have come into common use, but older units are still to be found, and a note on conversions may be of some value.

Electrical units

These are the least affected by the introduction of SI, which uses the same units (volt, ampere, ohm etc.) as the “practical” version of the EMU System. The only real change is that resistivity is now measured in ohm-meters (Ωm) rather than in ohm-cm or ohm-ft.

1 ohm-cm = 10‾² Ωm

1 ohm-ft ≈ 0.3 Ωm

Use of this latter conversion factor (more precisely 0.305) rather than its reciprocal in all conversions involving feet and metres makes for easy mental conversions to better than 2 per cent accuracy.

Conductivity is of course measured in mho m‾¹ or siemens (S).

Seismic velocity

The SI unit is the metre per second (m s‾¹) but seismologists commonly use the kilometre per second (km s‾¹), a unit which is conveniently also thought of as the metre per millisecond (m ms‾¹) in applied seismology.

Gravity

If a gravitational field is conceived as an acceleration, its SI unit will be the m sˉ²; if as a force per unit mass it will be measured in Newtons per kilogram (N kg‾¹), the same unit by a different name. The “gravity unit” is the µm sˉ² (or µN kg‾¹) so that

1 g.u. ≡ 10^-6 ms‾² ≡ 10^-6 N kg‾¹ ≡ 10‾¹ mGal

since the old “milligal” (mGal) unit was defined as

10‾³ cm sˉ² = 10ˉ msˉ².

The SI unit of density is the kg m‾³: the density if water is 1000 kg m‾³, and to avoid the use of large numbers it is convenient to express densities in tonnes per cubic metre (t m‾³) so that they have the same numerical value as in the old units of g cm‾³, since 1 tonne = 1000 kg.

Magnetism

There has been some confusion in the application of the SI to magnetic units, particularly in geophysics, since at least three slightly differing conventions have been in use. All these conventions are based on “rationalized” units, in which the force between two magnetic poles m _{1, m 2 in} vacuo becomes m _{1 m 2} /4πµ ₀ r² rather than m _{1 m 2} / µ ₀ r². The constant µ ₀units, known as the permeability of free space, has the value 4π•10^{-7 in SI units and unity in the old c.g.s. electromagnetic units. The factor of} 4π introduced by rationalization means that although magnetic susceptibility is a dimensionless ratio its value in SI units will be a factor of 4π larger than that appropriate to the (unrationalized) c.g.s. e.m.u. system.

In the particular (Sommerfeld) convention used in magnetizing field Fand intensity of magnetization J are both measured in amperes per meter (A m‾¹) and are related to the magnetic induction B in a magnetized medium, which is measure in teslas (T), through B= µ ₀ (F-J). The geomagnetic “field” and its anomalies are taken to be fields of the induction B rather than of F; thus outside magnetic material the normal geomagnetic field B_g= µ ₀ F_g. The intensity of magnetization J produced in a body of susceptibility k will be k F_g , but we work only with the quantity µ ₀ J= k µ ₀ F_g = k B_g and calculate from it the “B” field produced by a magnetic body. Magnetic anomaly fields are then conveniently measured in nanoteslas (nT), a unit which is the same as gamma (γ) used in the c.g.s. system, since 1γ = 10^-5 gauss and 1 tesla = 10⁴ gauss, the gauss being the unit of magnetic induction in the e.m.u. system.

(D.H. Griffiths and R.F. King “Applied Geophysics for Geologists and Engineers. The Elements of Geophysical Prospecting”. Oxford, 1981)

Date: 2016-01-14; view: 913