Magnetotellurics

Encyclopedia of Geomagnetism and Paleomagnetism 2007

Martyn Unsworth

Introduction

Magnetotellurics (MT) is the use of natural electromagnetic signals to image subsurface electrical conductivity structure through electromagnetic induction. The physical basis of the magnetotelluric method was independently discovered by Tikhonov ( 1950 ) and Cagniard ( 1953 ). After a debate over the length scale of the incident waves the technique became established as an effective exploration tool (Vozoff, 1991 ; Simpson and Bahr, 2005 ).

Basic method of magnetotellurics Electromagnetic waves are generated in the Earth's atmosphere and magnetosphere by a range of physical processes (Vozoff, 1991 ). Below a frequency of 1 Hz, most of the signals originate in the magnetosphere as periodic external fields including magnetic storms and substorms and micropulsations . These signals are normally incident on the Earth's surface. Above a frequency of 1 Hz, the majority of electromagnetic signals originate in worldwide lightning activity. These signals travel through the resistive atmosphere as waves and when they strike the surface of the Earth most of the signal is reflected. However, a small fraction is transmitted into the Earth and is refracted vertically downward, owing to the decrease in propagation velocity (Figure M168 ). The oscillating magnetic field of the wave generates electric currents in the Earth through electromagnetic induction, and the signal propagation becomes diffusive, resulting in signal attenuation with depth. The signals diffuse a distance into the Earth that is defined as the skin depth, δ, in meters by

where σ is the conductivity (S m −1 ), f is the frequency (Hz), and is the magnetic permeability. The skin depth is inversely related to the frequency and thus low frequencies will penetrate deeper into the Earth. The impedance of the Earth is defined as

where Ex is the horizontal electric field and Hy is the orthogonal, horizontal, magnetic field. From this impedance, apparent resistivity can be defined as

and the electric and magnetic field components will have a phase difference

In general, the impedance is written as a tensor, which relates the horizontal components of the electric and magnetic fields. The impedance relates the applied magnetic fields to the resulting electric fields and can be considered a transfer function . Note that the apparent resistivity depends on the ratio of the electric and magnetic field components. This makes the MT method simple to apply by combining values of Ex and Hy recorded at different times. The other useful characteristic is that the direction of the incident wave does not affect the value of apparent resistivity. The apparent resistivity can be considered an average value of the Earth's resistivity over a hemisphere of radius δ. Thus, by computing apparent resistivity as a function of frequency, the variation of resistivity with depth can be determined. This is illustrated in Figure M169 . At high frequency (1000–10 Hz) the apparent resistivity is equal to the true resistivity of the upper layer. As the frequency decreases, the skin depth increases and the MT signal penetrates further into the Earth and the apparent resistivity rises. The MT phase (Φ xy ) is the phase delay between the electric and magnetic fields at the Earth's surface. The apparent resistivity and phase are related through

where Φ xy is in degrees. Thus, when the apparent resistivity increases with decreasing frequency, the phase will be less than 45°. Similarly, a decrease in resistivity will correspond to a phase greater than 45°. At the lowest frequency, the apparent resistivity asymptotically approaches the true resistivity of the lower layer, and the phase returns to 45°. Note that the phase is sensitive to changes in subsurface resistivity with depth. For a multilayer model, MT data can reliably determine the conductance of a layer. Conductance is the vertically integrated conductivity, and for a uniform layer the conductance is the product of conductivity and thickness. A consequence of the inverse problem of electrical conductivity is that MT data cannot individually determine the conductivity and thickness of a layer. Thus layers with differing values of conductivity and thickness, but the same overall conductance cannot be distinguished with MT.

Figure M168 Propagation of electromagnetic waves from a distant lightning strike to the location where MT data is recorded. The resistive atmosphere forms a waveguide between the conductive Earth and ionosphere. The electric field ( E) and magnetic field ( H) are both orthogonal to the direction of propagation ( k). Note that the electromagnetic energy travels as a wave in the atmosphere, but diffuses in the Earth. This type of signal propagation occurs above 1 Hz.

Figure M169 Variation of apparent resistivity and phase that would be measured at the surface of a two ‐layer Earth model. Note that the depth sounding of resistivity is achieved by varying the frequency of the signal. The dip in apparent resistivity below 10 m at 1 Hz is a resonance phenomenon.

Early studies analyzed MT data in terms of a one ‐dimensional (1D) conductivity model. In this class of model, conductivity only varies with depth. This approach is sometimes valid in locations where the geoelectric structure does not change rapidly in the horizontal direction. However, it is usually necessary to consider at least a two ‐dimensional (2D) Earth model. In this case, the apparent resistivity computed from Ex and Hy will differ from that derived from Ey and Hx and the application of a 1D MT analysis can give misleading results. For a 2D Earth, Ex is dependent only on Hy and Hz, and these three field components comprise the transverse electric (TE) mode with the impedance ( Zxy ) computed from Ex and Hy. The transverse magnetic (TM) mode comprises the Hx, Ey, and Ez field components, with the impedance ( Zyx ) computed from Ey and Hx (Figure M170 ). In a 2D Earth with the x‐axis parallel to the geoelectric strike direction, the impedance tensor can be written as:

Figure M170 Geometry of electromagnetic field components over a two ‐dimensional Earth. The transverse electric (TE) mode is also called the E ‐polarization. Similarly, the transverse magnetic (TM) mode is also called the B ‐polarization.

The TE mode is most sensitive to along ‐strike conductors. In the TM mode the electric current flows across the boundaries between regions of differing resistivities, which causes electric charges to build up on interfaces. Thus the TM mode is more effective than the TE mode at locating interfaces between regions of differing resistivity.

If the subsurface structure is three ‐dimensional (3D) then all four elements of the impedance tensor are nonzero. Progress has been made in the last decade in 3D MT modeling and inversion. However, if a single profile of MT stations is available, and 3D effects can be shown to be small, then a 2D analysis can be used. If the subsurface conductivity structure exhibits electrical anisotropy , this will influence the measured impedance tensor. However, it can be difficult to convincingly distinguish heterogeneity from anisotropy in MT data. Small ‐scale, near ‐surface bodies can generate electric charges on their boundaries. If the body is small, then insignificant electromagnetic induction occurs and the only effect is galvanic distortion . This changes the magnitude of the electric field at the surface and can cause a static shift, which is a frequency ‐independent offset in the apparent resistivity curve (Jones, 1988 ). The phase curve is not affected. Static shifts are an example of spatial aliasing. A range of techniques is used to remove static shifts, and include external measurements of surface resistivity and estimation of the static shift coefficient in modeling and inversion.

Magnetotelluric data collection and time series processing

MT data are recorded in the time ‐domain, with the electric fields measured using dipoles 50–200 m in length that are connected to the ground with nonpolarizing electrodes. Audiomagnetotelluric (AMT) data (10 000–1 Hz) typically sample the upper 1–2 km and are often used in mineral exploration (see EM, industrial uses ). Magnetic fields are measured with induction coils, and in noisy environments the natural signals are supplemented with a transmitter. This modified technique is termed controlled ‐source audio magnetotellurics (CSAMT). Broadband MT data (1000–0.001 Hz) are used for sounding to midcrustal depths. Induction coils are generally used and a recording time of one day is required. In the presence of excessive cultural noise additional recording may be needed. Noise can originate in a wide range of sources, including power lines, cathodically protected pipelines, railways, water pumps, and electric fences. Long ‐period magnetotelluric (LMT) data measure very low frequencies (1– 0.0001 Hz) and are used for imaging the lower crust and upper mantle. A specialized LMT instrument is used with a fluxgate magnetometer , solar panels, and low power electronics. MT data can also be collected on the seafloor.

MT time series data are processed to yield frequency ‐domain estimates of apparent resistivity and phase. Modern processing schemes compute fast Fourier transforms of subsections of the time series and then utilize robust statistical techniques to average the multiple estimates of the impedance. The application of robust statistics has dramatically improved the quality of responses and allowed many types of noise to be effectively suppressed (Jones et al . 1989 ; Egbert, 1997 ). In MT data collection, time series data should be recorded simultaneously at several locations to allow for the removal of noise at the measurement location through the remote ‐reference method (Gamble et al . 1979 ). This is important even in locations with minimal cultural noise (Figure M171 ). In this example, ground motion from ocean waves caused oscillations of the magnetic sensors and resulted in the apparent resistivity being artificially low in the band 3–0.3 Hz. When the data were processed with a remote reference, the bias was removed.

Figure M171 Estimates of apparent resistivity and phase at an MT station in central California in 1999. The open circles were derived from remote reference processing, while the black circles were derived from local data only. The MT data are contaminated by magnetic noise due to ocean wave ‐induced ground motion. Note the downward bias in the apparent resistivity in the frequency band 3–0.3 Hz when local MT data processing is used.

Magnetotelluric data interpretation

Before modeling or inverting MT data, it is vital to understand the dimensionality of MT data. Tensor decomposition is a common approach and several techniques exist (Groom and Bailey, 1989 ; Bahr, 1991 ). Each method determines how well the measured MT impedance data can be fit to a 2D geoelectric model and gives an estimate of the geoelectric strike direction. It is common for a well ‐defined, consistent geoelectric strike to only be defined in a subset of an MT dataset. Decomposition can also determine if shallow conductivity structures are causing galvanic distortion of the surface electric fields. Galvanic distortion is a more general case of the process responsible for static shifts, and changes both the magnitude and direction of the electric fields. In extreme cases, near ‐surface structure can also cause distortion of the magnetic field through intense current channeling (Lezaeta and Haak, 2003 ).

Once the dimensionality has been understood, and distortion addressed, MT can be forward modeled or inverted in 1D, 2D, or 3D to recover a model of subsurface electrical conductivity. The inverse problem of electrical conductivity is nonunique (Berdichevsky and Dmitriev, 2002 ), which implies that a finite set of MT data containing noise can be reproduced by an infinite number of geoelectric models. To overcome this nonuniqueness and select a preferred model, additional constraints must be imposed on the solution. One of the most successful methods is to require that the geoelectric model derived from the inversion satisfies both the MT data and some additional requirements (regularization). In the absence of any other geoelectric information, the most common requirement is that the resistivity model should be as spatially smooth as possible in the horizontal and vertical directions (Constable et al ., 1987 ). Widely used inversion algorithms for MT data include those of Rodi and Mackie ( 2001 ) and Siripunvaraporn and Egbert ( 2000 ). The fit of the model is usually measured in term of the root ‐mean ‐square (rms) misfit of the predicted model response to the measured data. An rms misfit significantly greater than one indicates that the inversion is incapable of fitting the MT data, and usually indicates excessive noise in the data, or 3D effects that cannot be physically reproduced by a 2D inversion algorithm. A misfit significantly less than one indicates that either the error bars were too large or that the data is being over fit. In this second scenario, the resistivity model usually appears spatially rough, with the appearance of a checkerboard.

The MT method is now routinely used in both commercial exploration and in research. Commercial applications include exploration for minerals, hydrocarbons, and geothermal resources (see EM, industrial uses ). Researchers use MT to study the structure of the continents and the dynamics of plate boundaries (Brown, 1994 ) and also in EM, regional studies . MT measurements are also made on the seafloor for both commercial and academic investigations (see EM, marine controlled source ).

Cross ‐references

Anisotropy, Electrical EM Modeling, Forward EM Modeling, Inverse EM, Industrial Uses EM, Marine Controlled Source EM, Regional Studies Galvanic Distortion Magnetometers, Laboratory Periodic External Fields Storms and Substorms, Magnetic Transfer Functions

Bibliography

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