Generalized Error Analysis for Conventional and Remote Reference Magnetotellurics

An error analysis which applies to both conventional and remote reference magnetotelluric impedance and tipper estimates is developed based on the assumption that noise in the field measurements is governed by a complex normal distribution. Under the assumed model of noise it is shown that the theoretical expressions for the variances and covariances derived recently by Gamble et al (1979b) specifically for remote reference estimates apply to conventional estimates as well. However, calculations are biased if the impedance or tipper functions are biased. The impedance and tipper functions are calculated as ratios of two random functions of noisy field measurements. The expressions for the variances and covariances account for noise in both the numerator and denominator of the estimates. They are useful provided the probability that the magnitude of the random error in the denominator exceeds the magnitude of its expected value is small. Expressions for the bias errors of the impedance and tipper functions are obtained in order to assess the relative contributions of random and bias errors to the man squared error of the estimates. The relative magnitude of both random and bias errors depends on the noise level and on the values of the sample coherencies between various pairs of the field measurements used to compute a particular estimate

Weighted Least Squares Estimates of the Magnetotelluric Transfer Functions from Nonstationary Data

Magnetotelluric field measurements can generally be viewed as sums of signal and additive random noise components. The standard unweighted least squares estimates of the impedance and tipper functions which are usually calculated from noisy data are not optimal when the measured fields are nonstationary. The nonstationary behavior of the signals and noises should be exploited by weighting the data appropriately to reduce errors in the estimates of the impedances and tippers. Insight into the effects of noise on the estimates is gained by careful development of a statistical model, within a linear system framework, which allows for nonstationary behavior of both the signal and noise components of the measured fields. The signal components are, by definition, linearly related to each other by the impedance and tipper functions. It is therefore appropriate to treat them as deterministic parameters, rather than as random variables, when analyzing the effects of noise on the calculated impedances and tippers. From this viewpoint, weighted least squares procedures are developed to reduce the errors in impedances and tippers which are calculated from nonstationary data

Probability distributions for magnetotellurics

Estimates of the magnetotelluric transfer functions can be viewed as ratios of two complex random variables. It is assumed that the numerator and denominator are governed approximately by a joint complex normal distribution. Under this assumption, probability distributions are obtained for the magnitude, squared magnitude, logarithm of the squared magnitude, and the phase of the estimates. Normal approximations to the distributions are obtained by calculating mean values and variances from error propagation, and the distributions are plotted with their normal approximations for different percentage errors in the numerator and denominator of the estimates, ranging from 10% to 75%. The distribution of the phase is approximated well by a normal distribution for the range of errors considered, while the distribution of the logarithm of the squared magnitude is approximated by a normal distribution for a much larger range of errors than is the distribution of the squared magnitude. The distribution of the squared magnitude is most sensitive to the presence of noise in the denominator of the estimate, in which case the true distribution deviates significantly from normal behavior as the percentage errors exceed 10%. In contrast, the normal approximation to the distribution of the logarithm of the magnitude is useful for errors as large as 75%

Uplift of the central transantarctic mountains

The Transantarctic Mountains (TAM) are the world's longest rift shoulder but the source of their high elevation is enigmatic. To discriminate the importance of mechanical vs. thermal sources of support, a 550 km-long transect of magnetotelluric geophysical soundings spanning the central TAM was acquired. These data reveal a lithosphere of high electrical resistivity to at least 150 km depth, implying a cold stable state well into the upper mantle. Here we find that the central TAM most likely are elevated by a non-thermal, flexural cantilever mechanism which is perhaps the most clearly expressed example anywhere. West Antarctica in this region exhibits a low resistivity, moderately hydrated asthenosphere, and concentrated extension (rift necking) near the central TAM range front but with negligible thermal encroachment into the TAM. Broader scale heat flow of east-central West Antarctica appears moderate, on the order of 60-70mWm(-2), lower than that of the U.S. Great Basin

Author Correction: Uplift of the central transantarctic mountains

The original version of this Article incorrectly referenced the Figures in the Supplementary Information. References in the main Article to Supplementary Figure 7 through to Supplementary Figure 20 were previously incorrectly cited as Supplementary Figure 5 through to Supplementary Figure 18, respectively. This has now been corrected in both the PDF and HTML versions of the Article

Uplift of the central transantarctic mountains (vol 8, 2017)

The Transantarctic Mountains (TAM) are the world’s longest rift shoulder but the source of their high elevation is enigmatic. To discriminate the importance of mechanical vs. thermal sources of support, a 550 km-long transect of magnetotelluric geophysical soundings spanning the central TAM was acquired. These data reveal a lithosphere of high electrical resistivity to at least 150 km depth, implying a cold stable state well into the upper mantle. Here we find that the central TAM most likely are elevated by a non-thermal, flexural cantilever mechanism which is perhaps the most clearly expressed example anywhere. West Antarctica in this region exhibits a low resistivity, moderately hydrated asthenosphere, and concentrated extension (rift necking) near the central TAM range front but with negligible thermal encroachment into the TAM. Broader scale heat flow of east-central West Antarctica appears moderate, on the order of 60–70 mW m?2, lower than that of the U.S. Great Basin

Lithospheric dismemberment and magmatic processes of the Great Basin-Colorado Plateau transition, Utah, implied from magnetotellurics

To illuminate rifting processes across the Transition Zone between the extensional Great Basin and stable Colorado Plateau interior, we collected an east-west profile of 117 wideband and 30 long-period magnetotelluric (MT) soundings along latitude 38.5°N from southeastern Nevada across Utah to the Colorado border. Regularized two-dimensional inversion shows a strong lower crustal conductor below the Great Basin and its Transition Zone in the 15–35 km depth range interpreted as reflecting modern basaltic underplating, hybridization, and hydrothermal fluid release. This structure explains most of the geomagnetic variation anomaly in the region first measured in the late 1960s. Hence, the Transition Zone, while historically included with the Colorado Plateau physiographically, possesses a deep thermal regime and tectonic activity like that of the Great Basin. The deep crustal conductor is consistent with a rheological profile of a brittle upper crust over a weak lower crust, in turn on a stronger upper mantle (jelly sandwich model). Under the incipiently faulted Transition Zone, the conductor implies a vertically nonuniform mode of extension resembling early stages of continental margin formation. Colorado Plateau lithosphere begins sharply below the western boundary of Capitol Reef National Park as a resistive keel in the deep crust and upper mantle, with only a thin and weak Moho-level crustal conductor near 45 km depth. Several narrow, steep conductors connect conductive lower crust with major surface faulting, some including modern geothermal systems, and in the context of other Great Basin MT surveying suggest connections between deep magma-sourced fluids and the upper crustal meteoric regime. The MT data also suggest anisotropically interconnected melt over a broad zone in the upper mantle of the eastern Great Basin which has supplied magma to the lower crust, consistent with extensional mantle melting models and local shear wave splitting observations. We support a hypothesis that the Transition Zone location and geometry ultimately reflect the middle Proterozoic suturing between the stronger Yavapai lithosphere to the east and the somewhat weaker Mojave terrane to the west. We conclude that strength heterogeneity is the primary control on locus of deformation across the Transition Zone, with modulating force components.Philip E. Wannamaker, Derrick P. Hasterok, Jeffery M. Johnston, John A. Stodt, Darrell B. Hall, Timothy L. Sodergren, Louise Pellerin, Virginie Maris, William M. Doerner, Kim A. Groenewold, and Martyn J. Unswort