Based on the spatial structure correlation in different geophysical parameters, we propose a new 3-D joint inversion method for frequency-domain airborne electromagnetic (AEM) and airborne magnetic (AirMag) data by incorporating a local Pearson correlation constraint (LPCC). For each iteration, the entire model is separated into multiple subdomains and the Pearson correlation coefficients of resistivity and magnetization in the subdomain are employed as the additional regularization term to do the joint constraint. This new regularization term is continuously updated in the inversion process to ensure that the resistivity and magnetization models in two separated inversions converge to a similar spatial structure. As a statistics technology, the LPCC-based joint inversion scheme not only has the advantages of the conventional joint inversions, but also can implement the structural constraints in different scales by selecting different sizes of the subdomain. This provides the flexibility for solving multiscale problems. Synthetic examples show that the joint inversion can improve the overall inversion resolution by combining the high vertical resolution of the EM method and large exploration depth and high horizontal resolution of the magnetic method. In the application to field survey datasets, the joint inversion delivers better results than those of separate inversions, which further verifies the effectiveness of our method.

It is estimated that exposure to radon in Norwegian dwellings is responsible for as many as 300 deaths a year due to lung cancer. To address this, the authorities in Norway have developed a national action plan that has the aim of reducing exposure to radon in Norway (Norwegian Ministries, 2010). The plan includes further investigation of the relationship between radon hazard and geological conditions, and development of map-based tools for assessing the large spatial variation in radon hazard levels across Norway. The main focus of the present contribution is to describe how we generate map predictions of radon potential (RP), a measure of radon hazard, from available airborne gamma ray spectrometry (AGRS) surveys in Norway, and what impact these map predictions can be expected to have on radon protection work including land-use planning and targeted surveying. We have compiled 11 contiguous AGRS surveys centred on the most populated part of Norway around Oslo to produce an equivalent uranium map measuring 180 km × 102 km that represents the relative concentrations of radon in the near surface of the ground with a spatial resolution in the 100 s of metres. We find that this map of radon in the ground offers a far more detailed and reliable picture of the distribution of radon in the sub-surface than can be deduced from the available digital geology maps. We tested the performances of digital geology and AGRS data as predictors of RP. We find that digital geology explains approximately 40% of the observed variance in ln RP nationally, while the AGRS data in the Oslo area split into 14 bands explains approximately 70% of the variance in the same parameter. We also notice that there are too few indoor data to characterise all geological settings in Norway which leaves areas in the geology-based RP map in the Oslo area, and elsewhere, unclassified. The AGRS RP map is derived from fewer classes, all characterised by more than 30 indoor measurements, and the corresponding RP map of the Oslo area has no unclassified parts. We used statistics of proportions to add 95% confidence limits to estimates of RP on our predictive maps, offering public health strategists an objective measure of uncertainty in the model. The geological and AGRS RP maps were further compared in terms of their performances in correctly classifying local areas known to be radon affected and less affected. Both maps were accurate in their predictions; however the AGRS map out-performed the geology map in its ability to offer confident predictions of RP for all of the local areas tested. We compared the AGRS RP map with the 2015 distribution of population in the Oslo area to determine the likely impact of radon contamination on the population. 11.4% of the population currently reside in the area classified as radon affected. 34% of ground floor living spaces in this affected area are expected to exceed the maximum limit of 200 Bq/m3, while 8.4% of similar spaces outside the affected area exceed this same limit, indicating that the map is very efficient at separating areas with quite different radon contamination profiles. The usefulness of the AGRS RP map in guiding new indoor radon surveys in the Oslo area was also examined. It is shown that indoor measuring programmes targeted on elevated RP areas could be as much as 6 times more efficient at identifying ground floor living spaces above the radon action level compared with surveys based on a random sampling strategy. Also, targeted measuring using the AGRS RP map as a guide makes it practical to search for the worst affected homes in the Oslo area: 10% of the incidences of very high radon contamination in ground floor living spaces (≥800 Bq/m3) are concentrated in just 1.2% of the populated part of the area.