Audio-Magnetotelluric Surveying for Groundwater Exploration

Reconnaissance-level Subsurface Characterization Using Geophysical Electromagnetic Sounding

By Darrel Dunn, Ph.D., PG, Hydrogeologist

(View Résumé 🔳)

Audio-Magnetotelluric Surveying

This webpage is a relatively nontechnical description of the use of the audio-magnetotelluric (AMT) geophysical method for groundwater and geothermal exploration.  Some technical information is added as parenthetical elements in the text and endnotes referenced in brackets.

Audio-magnetotelluric  surveying is a geophysical technique that uses naturally occurring electrical and magnetic fields [1] to approximate the distribution of electrical resistivity in the relatively shallow part of the Earth's subsurface.  The electrical fields and magnetic fields are components of the electromagnetic (EM) field.  Electromagnetic fields fluctuate in strength as they propagate outward from sources where the electrical current is rapidly fluctuating, so  they may be treated as waves.  The "audio" designation is misleading because sound waves are not used.  Instead "audio" refers to electromagnetic wave data in the frequency range of about 1 Hertz (Hz) to 20,000 Hz (a Hertz is one cycle per second), which happens to correspond roughly the range of sound waves (pressure waves in matter such as air) that humans can hear (about 20 Hz to 20,000 Hz).  This frequency range is mostly in the part of the electromagnetic wave spectrum classified as very low frequency (VLF).  Low frequency corresponds to long wavelength.  The wavelengths used in AMT range from  about 10 miles to more than 60 miles.  "Telluric" comes from the Latin word "tellus" which means earth both in the sense of "soil" and in the sense of "the globe."  So magnetotelluric refers to magnetic fields in the subsurface of the Earth.  However, EM waves do not need a medium  in which to propagate.  They can propagate in a vacuum.  In a vacuum the waves travel at the speed of light (983,571,056 feet per second).  In the atmosphere, they are slightly retarded.  In the materials of the Earth's crust they are significantly retarded.  The amount of retardation is expressed as the ratio of the speed in a vacuum to the speed in a medium.  The refractive index in a standard atmosphere is 1.0003.  The refractive index of water is 1.33 and most minerals have refractive indexes between 1.5 and 2.0.  The rate of propagation of EM waves in all media of interest in AMT is extremely fast.

The electrical resistivity of subsurface materials (rocks, sediment, soil) is a measure of how well the material conducts electricity.  How well the material conducts electricity is affected by its composition (lithology), porosity, water saturation and salinity [2].  Most of the electrical conduction is through pores filled with electrolytes.  A small change in porosity can cause a significant change in electrical conductivity (Roy, 2020).  Consequently, the subsurface distribution of resistivity may be interpreted to estimate the location and distribution of subsurface geologic and hydrologic features, including aquifers.  The depth of investigation varies with resistivity but ranges to greater than 6,000 feet in high resistivity areas.

AMT has been used as a reconnaissance geophysical method in groundwater and geothermal exploration.  Its use is encouraged by the following attributes:

However, it has significant limitations:

Natural Electromagnetic Waves

The electromagnetic waves used in AMT surveying are dominantly from distant lightning strokes (sferics).  The lightning that is the source is concentrated in the the tropics, especially Brazil, central Africa, and Malaysia (Roy, 2020).  The EM waves travel around the Earth in the Earth-ionosphere waveguide where waves are reflected back and forth between the Earth's surface and ionized layers in the lower part of the ionosphere (Babarinde and others, 2020) which is roughly 35 miles above the Earth's surface, but varies considerably due to variation in solar radiation (Milson andd Erikson, 2011).  The strength of the waves is at a minimum in the range of about 1 to 10 Hertz, which is called the dead-band (Roy, 2020).  The EM waves are often called signals.  The term "signal" may refer to any physical quantity that varies with time and space.  Only part of the signals traveling in the waveguide are reflected at the Earth's surface, the remainder is refracted into the earth.   Because of the resistivity contrast between the atmosphere and the much less conductive Earth, the refracted component propagates nearly vertically downward regardless of the incidence angle of the impinging wave (a result of Snell's Law).

Earth Resistivity Estimation

The apparent resistivity [4] of the subsurface beneath an audio-magnetotelluric field measuring station is (Long and Pierce, 1986):

ρa = (Ex/Hy)2/5f                   Equation 1

where:

ρa is apparent resistivity in ohm-meter (ohm/meter),

Ex is the horizontal electrical field magnitude in microvolts/meter (millivolts/km),

Hy is the horizontal magnetic field magnitude in gammas, and

f is frequency in Hertz.

The ratio Ex/Hy is sometimes called the response or transfer function.

Different frequencies provide different depths of investigation in accordance with the equation:

d = 503(ρa/f)1/2          Equation 2

where:

d is depth in meters (skin depth[5]).

The skin depth is arbitrarily taken as the depth where the field magnitudes decrease to about 37 % of the surface value.  The lower the frequency, the greater the depth of investigation.  Consequently, the apparent resistivity between the depth corresponding to the frequencies analyzed can be estimated by successive calculations.  (One approach is to use logarithmically spaced frequencies for the calculations.)  The wave lengths used in AMT are greater than the corresponding skin depths, which contributes to the validity of the AMT method.

The apparent resistivity in Equation 1 is generally called Cagniard resistivity [4]. Cagniard (1953) derived this equation from Maxwell's four equations that describe the electromagnetic field [5].

Field Measurement of Electrical and Magnetic Horizontal Field Magnitude

Magnetic field components are usually measured with induction coils (amperes per meter).  The horizontal magnetic field is usually aligned in the magnetic north-south direction (Njuimbous-Kouoh and others, 2018).  Electric fields are measured as voltage difference between pairs of electrodes (volts per meter) located 10 to 100 meters apart (Simpson and Bahr, 2005).  Contact resistance and noise can be reduced by installing the electrodes in wet pits several hours or days before they are to be used to allow the electrochemical environment to stabilize.  Bentonite may be used around electrodes to minimize contact resistance between the electrodes and the ground.  The north-south and east-west horizontal components of the electric and magnetic fields may be measured at each recording site.  It is common practice for recording sites to be spaced at intervals of a few hundred feet in areas of specific interest (Vozoff, 1990).  A GPS unit can be used to record the location of the sites.

The induction coils and electrodes do not need to be deeply buried.  The magnitude of the reflected electrical filed is a very large proportion of the incident field so that there is near cancellation of the incident field by the reflected field.  The small part of the incident field that is refracted into the Earth is left to be measured (Jiracek, G. R. and others, 1995).  This refracted signal is the basis of the MT surveying method.

The duration of the recording at a field station depends on the depth of investigation desired.  Meaningful statistical average of the data requires 25 to 50 samples of the wave forms.  So greater depths require longer records, because greater depths correspond to low frequencies and long periods (Equation 2).

Processing of Electromagnetic Field Measurements 

The time series of electrical and magnetic data are transformed to frequencies and amplitudes (Fourier analysis).  The resulting frequency data is processed using Equation 1 and Equation 2 or more complex analytical methods.   The more complex methods may yield more information on the configuration of subsurface resistivities.

Endnotes for Audio-Magnetotelluric Surveying

[1] Electromagnetic Fields

A field is a physical quantity that has a value at every point is space.  Electrical and magnetic fields are force fields.  Their value at every point is a vector.  A vector is a value that has both magnitude and direction.  It is often represented graphically as an arrow whose length corresponds to magnitude.  The magnetic field is measured in Teslas or gammas.   Magnetic field components are usually measured with induction coils (Vossof, 1990).

[2] Archie's Law

There is great overlap in resistivities that have been measured for common rock types (Vozoff, 1990).   This overlap may be because the resistivity is primarily due to the water content in accordance with Archie's law.  Archie's law is an empirical formula which states that the rock conductivity is approximately equal to the water conductivity multiplied by the square of the porosity.  Conductivity is the inverse of resistivity.

[3]  Cultural Noise

The AMT function data used to calculate the electrical resistivity of the subsurface (Cagniard resistivity [4]) must be from planar EM waves.   Planar EM waves are at far-field distances from the source.  Far-field distances vary with wavelength and the characteristics of the source.  For VLF, a general rule of thumb for the far-field distance is to multiply the wavelength by three.  This rule suggests cultural sources that are within 30 miles of an AMT survey may be near-field and the EM waves they produce at a survey site may be non-planar.  EM waves from cultural sources are referred to as noise.  Good practice is to locate EM surveys as far as possible from sources of cultural noise, and to try to identify and reduce cultural noise in the data.  Local lightning strikes also produce non-planar waves.

In densly populated areas the noise may be several times the natural signal.  Much research on identification and elimination of cultural noise is reported in the literature.  Methods include stacking,  identification and elimination of cultural noise frequencies, measuring signals at remote reference sites (perhaps 30 miles away), and statistical data analysis (Junge, 1996).  Stacking involves adding signals together so that random noise tends to cancel out.

Sources of cultural noise include but are not limited to the following:

[4]  Cagniard Resistivity

Cagniard Resistivity is a frequency dependent apparent resistivity calculated from values of electric E-field and magnetic H-field data.  It is based on Maxwell's EM equations [5] and planar EM waves which are transverse waves orthogonal to each other and to the direction of propagation  (Figure 1).  The direction of propagation is vertically downward into the earth because the EM waves are partially deflected in accordance with the large resistivity difference between the atmosphere in the Earth-ionosphere waveguide and the Earth material.


Figure 1.  The plane wave solution of Maxwell’s equations.  Maxwell assigned B to the magnetic field and E to the electric field.  This notation is now conventional.  (From LibreTexts.)

[5] Maxwell's Equations

James Maxwell summarized the relationship between electricity and magnetism into what are now referred to as "Maxwell's Equations."  Maxwell's Equations combine four equations made by Gauss (also Coulomb), Faraday, and Ampere, and add a term to Ampere's equation:

1. Gauss's law for static electric fields,

2. Gauss's law for static magnetic fields,

3. Faraday's law which says a magnetic field changing with time produces an electric field, 

4. Ampere-Maxwell's law which says an electric field changing with time produces a magnetic field.

These equations may be expressed by vector calculus and manipulated to produce the equation for Cagniard resistivity (Nguimbous-Kouoh, 2018).  The resistivity comes from the fourth equation, Ampere-Maxwell's law.

[6] Skin Depth

Skin depth is defined as the depth at which the amplitude of the signal has attenuated to 1/e (1/2.718) of its magnitude at the surface (Flanigan and Zablocki, 1984).  It is used as an approximate measure of the depth of investigation at the given frequency.

[7] Electromagnetism and Groundwater

Another webpage on this website discusses electromagnetism and groundwater.


References for Audio-Magnetotelluric Surveying

Babarinde, BT and L. Nwankwo (2020): A Review of the Application of Telluric and Magnetoteluric Methods in Geophysical Exploration; Tropical Journal of Science and Technology, Volume 1.  🔗

Cagniard, L. (1953): Basic Theory of Magnetotelluric Method of Geophysical Prospecting; Geophysics, Volume 18.  🔗

Flanigan, V. J. and C. J. Zablocki (1984): An Evaluation of the Applicability of the Telluric-Electric and Audio-Mangnetotelluric Mithods to Mineral Assessment on the Arabian Shield, Kingdom of Saudi Arabia; U.S. Geological Survey Open-File Report 84-425.  🔗

Hoover, D. B. and C. L. Long (1976): Audio-Magnetotelluric methods in reconnaissance geothermal exploration; United States Geological Survey Conference Paper.  🔗 

Jiracek, G. R., and others (1995): Practical Magnetotellurics in a Continental Rift Environment; in K. H. Olsen, ed., Continental Rifts: Evolution, Structure and Tectonics, Elsevier.  🔗

Junge, A (1996):  Characterization and Correction for Cultural Noise; Surveys in Geophysics, Volume 17.  🔗

Long, C. and H. A. Pierce (1986): BASIC Program to Reduce audio-magnetotelluric Data and Calculate Apparent Resistivity; U.S. Geological Survey Open-File Report 86-200.  🔗

Milsom, J. and A. Erikson (2011): Field Geophysics, Fourth Edition; Wiley.  🔗

Nguimbous-Kouoh. J. J., and others (2018): Audio-Frequency Magnetotelluric Prospecting in the Mamfe Sedimentary Basin of Southwestern Cameroon; International Journal of Earth Science and Geophysics, 4:020.  🔗

Roy, K. K. (2020): Natural Electromagnetic Fields in Pure and Applied Geophysics; Springer.   🔗 

Simpson, F. and K. Bahr (2005: Practical Magnetotellurics; Cambridge University Press.

Vozoff, K. (1990): Magnetotellurics: Principles and Practice; Proceedings of Indian Academy of Science, Volume 99, Number 4.  🔗

Zhou, Cong, and others (2021): Audio-frequency spectra of passive source electromagnetic fields under a cultural background: A case study from the middle and lower reaches of the Yangtze River, China; Journal of Applied Geopyysics, Volume 194.  🔗

Posted August 12, 2024