ALBERT

Description: Author Posting. © The Authors, 2019. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 218(3), (2019): 1822-1837, doi: 10.1093/gji/ggz253.

Description: Joint inversion of multiple electromagnetic data sets, such as controlled source electromagnetic and magnetotelluric data, has the potential to significantly reduce uncertainty in the inverted electrical resistivity when the two data sets contain complementary information about the subsurface. However, evaluating quantitatively the model uncertainty reduction is made difficult by the fact that conventional inversion methods—using gradients and model regularization—typically produce just one model, with no associated estimate of model parameter uncertainty. Bayesian inverse methods can provide quantitative estimates of inverted model parameter uncertainty by generating an ensemble of models, sampled proportional to data fit. The resulting posterior distribution represents a combination of a priori assumptions about the model parameters and information contained in field data. Bayesian inversion is therefore able to quantify the impact of jointly inverting multiple data sets by using the statistical information contained in the posterior distribution. We illustrate, for synthetic data generated from a simple 1-D model, the shape of parameter space compatible with controlled source electromagnetic and magnetotelluric data, separately and jointly. We also demonstrate that when data sets contain complementary information about the model, the region of parameter space compatible with the joint data set is less than or equal to the intersection of the regions compatible with the individual data sets. We adapt a trans-dimensional Markov chain Monte Carlo algorithm for jointly inverting multiple electromagnetic data sets for 1-D earth models and apply it to surface-towed controlled source electromagnetic and magnetotelluric data collected offshore New Jersey, USA, to evaluate the extent of a low salinity aquifer within the continental shelf. Our inversion results identify a region of high resistivity of varying depth and thickness in the upper 500 m of the continental shelf, corroborating results from a previous study that used regularized, gradient-based inversion methods. We evaluate the joint model parameter uncertainty in comparison to the uncertainty obtained from the individual data sets and demonstrate quantitatively that joint inversion offers reduced uncertainty. In addition, we show how the Bayesian model ensemble can subsequently be used to derive uncertainty estimates of pore water salinity within the low salinity aquifer.

Description: We gratefully acknowledge funding support from National Science Foundation grants 1458392 and 1459035. We thank the captain and crew of the R.V. Marcus G. Langseth for a successful cruise and the Marine EM Lab at Scripps Institution of Oceanography for providing the instrumentation. We also thank Chris Armerding, Marah Dahn, John Desanto, Jimmy Elsenbeck, Matt Folsom, Keiichi Ishizu, Jeff Pepin, Charlotte Wiman and Georgie Zelenak for participating in the cruise. We gratefully acknowledge Alberto Malinverno for the idea to use a Monte Carlo scheme to estimate the distribution of pore fluid salinity, and William Menke for many constructive conversations and suggestions.

Description: Author Posting. © The Author(s), 2019. This is the author's version of the work. It is posted here by permission of Oxford University Press for personal use, not for redistribution. The definitive version was published in Geophysical Journal International, 219(1), (2019): 464-478, doi:10.1093/gji/ggz315.

Description: The electromagnetic (EM) field generated by ocean tidal flow is readily detectable in both satellite magnetic field data, and in ocean-bottom measurements of electric and magnetic fields. The availability of accurate charts of tidal currents, constrained by assimilation of modern satellite altimetry data, opens the possibility of using tidal EM fields as a source to image mantle electrical resistivity beneath the ocean basins, as highlighted by the recent success in defining the globally averaged lithosphere–asthenosphere boundary (LAB) with satellite data. In fact, seafloor EM data would be expected to provide better constraints on the structure of resistive oceanic lithosphere, since the toroidal magnetic mode, which can constrain resistive features, is a significant component of the tidal EM field within the ocean, but is absent above the surface (in particular in satellite data). Here we consider this issue in more detail, using a combination of simplified theoretical analysis and 1-D and 3-D numerical modelling to provide a thorough discussion of the sensitivity of satellite and seafloor data to subsurface electrical structure. As part of this effort, and as a step toward 3-D inversion of seafloor tidal data, we have developed a new flexible 3-D spherical-coordinate finite difference scheme for both global and regional scale modelling, with higher resolution models nested in larger scale solutions. We use the new 3-D model, together with Monte Carlo simulations of errors in tidal current estimates, to provide a quantitative assessment of errors in the computed tidal EM signal caused by uncertainty in the tidal source. Over the open ocean this component of error is below 0.01 nT in Bz at satellite height and 0.05 nT in Bx on the seafloor, well below typical signal levels. However, as coastlines are approached error levels can increase substantially. Both analytical and 3-D modelling demonstrate that the seafloor magnetic field is most sensitive to the lithospheric resistance (the product of resistivity and thickness), and is more weakly influenced (primarily in the phase) by resistivity of the underlying asthenosphere. Satellite data, which contain only the poloidal magnetic mode, are more sensitive to the conductive asthenosphere, but have little sensitivity to lithospheric resistance. For both seafloor and satellite data’s changes due to plausible variations in Earth parameters are well above error levels associated with source uncertainty, at least in the ocean interior. Although the 3-D modelling results are qualitatively consistent with theoretical analysis, the presence of coastlines and bathymetric variations generates a complex response, confirming that quantitative interpretation of ocean tidal EM fields will require a 3-D treatment. As an illustration of the nested 3-D scheme, seafloor data at five magnetic and seven electric stations in the northeastern Pacific (41○N, 165○W) are fit with trial-and-error forward modelling of a local domain. The simulation results indicate that the lithospheric resistance is roughly 7 × 108 Ωm2. The phase of the seafloor data in this region are inconsistent with a sharp transition between the resistive lithosphere and conductive asthenosphere.

Description: This work has been supported by National Natural Science Foundation of China grants 41804072 and 41574104, and NSF grant EAR-1447109. Special thanks to Dr Benjamin Murphy who provided the conductivity-depth profile for 1-D earth model, Dr Min Ding who provided valuable discussion about the oceanic lithosphere and Dr Jeffery Love who provided comments on the stylistics of the manuscript.

Description: Author Posting. © The Authors, 2019. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 218(3), (2019): 2165-2178, doi: 10.1093/gji/ggz280.

Description: A multitaper estimator is proposed that accommodates time-series containing gaps without using any form of interpolation. In contrast with prior missing-data multitaper estimators that force standard Slepian sequences to be zero at gaps, the proposed missing-data Slepian sequences are defined only where data are present. The missing-data Slepian sequences are frequency independent, as are the eigenvalues that define the energy concentration within the resolution bandwidth, when the process bandwidth is [−1/2,1/2) for unit sampling and the sampling scheme comprises integer multiples of unity. As a consequence, one need only compute the ensuing missing-data Slepian sequences for a given sampling scheme once, and then the spectrum at an arbitrary set of frequencies can be computed using them. It is also shown that the resulting missing-data multitaper estimator can incorporate all of the optimality features (i.e. adaptive-weighting, F-test and reshaping) of the standard multitaper estimator, and can be applied to bivariate or multivariate situations in similar ways. Performance of the missing-data multitaper estimator is illustrated using length of day, seafloor pressure and Nile River low stand time-series.

Description: The length of day utilized in Section 3 are available from http://hpiers.obspm.fr. The pressure data used in Section 4 are available from https://doi.org/10.1029/2018JC014586. A Matlab function MDmwps.m to compute missing-data power spectra is available from the Mathworks file exchange website. The author thanks Jeff Park and editor F.J. Simons for thorough reviews. This work was supported by an Internal Research and Development award at WHOI, and by the Walter A. and Hope Noyes Smith Chair for Excellence in Oceanography.