Quantitative imaging of water, ice and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data

Abstract

SUMMARY Quantitative estimation of pore fractions filled with liquid water, ice and air is crucial for a process-based understanding of permafrost and its hazard potential upon climate-induced degradation. Geophysical methods offer opportunities to image distributions of permafrost constituents in a non-invasive manner. We present a method to jointly estimate the volumetric fractions of liquid water, ice, air and the rock matrix from seismic refraction and electrical resistivity data. Existing approaches rely on conventional inversions of both data sets and a suitable a priori estimate of the porosity distribution to transform velocity and resistivity models into estimates for the four-phase system, often leading to non-physical results. Based on two synthetic experiments and a field data set from an Alpine permafrost site (Schilthorn, Bernese Alps and Switzerland), it is demonstrated that the developed petrophysical joint inversion provides physically plausible solutions, even in the absence of prior porosity estimates. An assessment of the model covariance matrix for the coupled inverse problem reveals remaining petrophysical ambiguities, in particular between ice and rock matrix. Incorporation of petrophysical a priori information is demonstrated by penalizing ice occurrence within the first two meters of the subsurface where the measured borehole temperatures are positive. Joint inversion of the field data set reveals a shallow air-rich layer with high porosity on top of a lower-porosity subsurface with laterally varying ice and liquid water contents. Non-physical values (e.g. negative saturations) do not occur and estimated ice saturations of 0–50 per cent as well as liquid water saturations of 15–75 per cent are in agreement with the relatively warm borehole temperatures between −0.5 and 3 ° C. The presented method helps to improve quantification of water, ice and air from geophysical observations.

Petrophysical Joint Inversion Applied to Alpine Permafrost Field Sites to Image Subsurface Ice, Water, Air, and Rock Contents

“…FIGURE 1 | Schematic on the estimation of water, ice, and air from electrical resistivity and refraction seismic data (modified after Wagner et al, 2019). (A) Conventional inversion of both datasets with subsequent petrophysical transformation.…”

“…These shortcomings led to the recent development of a joint inversion code to fully use the complementarity of independent geophysical data (Wagner et al, 2019). Figures 1A,B highlight the conceptual differences of both inversion approaches.…”

“…Their values are considered constant and equal to values found in the literature (e.g., Hauck et al, 2011). Archie's law (Archie, 1942) is used in the original 4PM and also for the PJI study by Wagner et al (2019), although other relationships were tested within the conventional 4PM (e.g., unpublished Master thesis, Python, 2015). The electrical resistivity ρ (or conductivity σ ) combines the contribution of three conduction mechanisms: particle conduction, surface conduction, and electrolytic conduction (e.g., Klein and Santamarina, 2003).…”

“…To improve the characterization of the composition of frozen ground, Wagner et al (2019) developed a PJI framework to quantify water, ice, and air contents from geophysical datasets based on the 4PM approach (Hauck et al, 2011). The approach was successfully validated on synthetic datasets and a proof-ofconcept field application (Schilthorn field site).…”

“…The objectives of this contribution are to (i) apply and extend the algorithm developed by Wagner et al (2019) by testing different petrophysical relations and apply them to several field sites, which represent a high diversity of mountain permafrost landforms, from ice-poor to ice-rich grounds, (ii) analyse the influence of the regularization parameters, and (iii) validate the results with borehole data (temperature and direct or indirect measurements of ice content data). Different equations linking the electrical resistivity to water content (taking into account the electrolytic conduction, the surface conduction, or both) are explored.…”