Trans‐dimensional Bayesian inversion of controlled‐source electromagnetic data in the German North Sea

Abstract

This paper presents the first controlled‐source electromagnetic survey carried out in the German North Sea with a recently developed seafloor‐towed electrical dipole–dipole system, i.e., HYDRA II. Controlled‐source electromagnetic data are measured, processed, and inverted in the time domain to estimate an electrical resistivity model of the sub‐seafloor. The controlled‐source electromagnetic survey targeted a shallow, phase‐reversed, seismic reflector, which potentially indicates free gas. To compare the resistivity model to reflection seismic data and draw a combined interpretation, we apply a trans‐dimensional Bayesian inversion that estimates model parameters and uncertainties, and samples probabilistically over the number of layers of the resistivity model. The controlled‐source electromagnetic data errors show time‐varying correlations, and we therefore apply a non‐Toeplitz data covariance matrix in the inversion that is estimated from residual analysis. The geological interpretation drawn from controlled‐source electromagnetic inversion results and borehole and reflection seismic data yield resistivities of ∼1 Ωm at the seafloor, which are typical for fine‐grained marine deposits, whereas resistivities below ∼20 mbsf increase to 2–4 Ωm and can be related to a transition from fine‐grained (Holocene age) to unsorted, coarse‐grained, and compacted glacial sediments (Pleistocene age). Interface depths from controlled‐source electromagnetic inversion generally match the seismic reflector related to the contrast between the different depositional environments. Resistivities decrease again at greater depths to ∼1 Ωm with a minimum resistivity at ∼300 mbsf where a seismic reflector (that marks a major flooding surface of late Miocene age) correlates with an increased gamma‐ray count, indicating an increased amount of fine‐grained sediments. We suggest that the grain size may have a major impact on the electrical resistivity of the sediment with lower resistivities for fine‐grained sediments. Concerning the phase‐reversed seismic reflector that was targeted by the survey, controlled‐source electromagnetic inversion results yield no indication for free gas below it as resistivities are generally elevated above the reflector. We suggest that the elevated resistivities are caused by an overall decrease in porosity in the glacial sediments and that the seismic reflector could be caused by an impedance contrast at a thin low‐velocity layer. Controlled‐source electromagnetic interface depths near the reflector are quite uncertain and variable. We conclude that the seismic interface cannot be resolved with the controlled‐source electromagnetic data, but the thickness of the corresponding resistive layer follows the trend of the reflector that is inclined towards the west.

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

“…The rjMCMC was first applied in geophysics in 2000 in an inversion study of zero-offset vertical seismic profiles (Malinverno, 2000;Malinverno and Leaney, 2000). Since then, it has been utilized in a variety of geophysical inverse problems, including earthquake seismology and tomography Agostinetti and Malinverno, 2010;Bodin et al, 2012a,b;Young et al, 2013;Zulfakriza et al, 2014;Kolb and Lekić, 2014;Galetti et al, 2015), geoacoustic inversion (Dettmer et al, 2010;Dettmer and Dosso, 2012;Steininger et al, 2013;Dettmer et al, 2013;Dosso et al, 2014), and electrical and magnetotelluric geophysics (Malinverno, 2002;Minsley, 2011;Brodie and Sambridge, 2012;Ray and Key, 2012;JafarGandomi and Binley, 2013;Ray et al, 2014;Gehrmann et al, 2015). Dadi (2014) and Dadi et al (2015) used rjMCMC for seismic impedance inversion, uncertainty estimation and well log upscaling.…”

Bayesian inversion of marine controlled source electromagnetic data offshore Vancouver Island, Canada

“…The width of the CIs for the 2-layer model may underestimate the actual range of resistivities in the subseafloor, because we do not include uncertainty on the number of layers. Recent studies which include the number of layers as an unknown in the inversion (trans-dimensional CSEM inversion, Ray & Key 2012;Gehrmann et al 2015) show uncertainties that generally increase quickly with depth.…”

“…For example, LWD resistivities from drilling extend the inferred credibility interval for resistivities at greater depth (see Figs 8 and 15) but they generally match the inferred resistivity trend. Alternatively, the number of subsurface layers can be included within a trans-dimensional inversion such as implemented for marine CSEM data by Ray & Key (2012) and Gehrmann et al (2015) to better estimate uncertainties (especially in greater depth). Trans-dimensional inversion has advantages in that it requires less user intervention and accounts for the uncertainty in the parametrization in the parameter uncertainty estimates.…”

“…Too many unknowns cause the problem to be underdetermined and spurious structure might be introduced, while including too few parameters into the inversion may cause model structure to stay unresolved, and uncertainties to be underestimated. Recently, Ray & Key (2012) and Gehrmann et al (2015) have implemented a trans-dimensional Bayesian inversion for marine CSEM data where the number of layers that can be resolved with the data is an unknown in the inversion. Alternatively, Gunning et al (2010) considered effective correlation lengths, a Bayesian smoothing similar to regularization in linearized methods and the Laplace approximation to the Bayesian evidence to estimate the maximum a posteriori model (which maximizes the posterior probability density, PPD, and represents the most probable model).…”

“…Dosso & Dettmer 2011), which has been shown to be appropriate for CSEM data inversion (e.g. Ray et al 2013b;Gehrmann et al 2015).…”