Summary Transient electromagnetic (TEM) is an efficient non-invasive method to map electrical conductivity distribution in the subsurface. This paper presents an inversion scheme for three-dimensional (3D) TEM time-lapse data using a generalized minimum support norm and its application to monitoring conductivity changes over time. In particular, two challenges for time-lapse TEM applications are addressed: i) the survey repetition with slightly different acquisition position, i.e. because systems are not installed; ii) non-optimal data coverage above the time-lapse anomalies, for instance, due to the presence of infrastructure that limits the acquisition layout because of coupling. To address these issues, we developed a new TEM time-lapse inversion scheme with the following features: (1) a multi-mesh approach for model definition and forward computations, which allows for seamless integration of datasets with different acquisition layouts; (2) 3D sensitivity calculation during the inversion, which allows retrieving conductivity changes in-between TEM soundings; (3) simultaneous inversion of two datasets at once, imposing time-lapse constraints defined in terms of a generalized minimum support norm, which ensures compact time-lapse changes. We assess the relevance of our implementations through a synthetic example and a field example. In the synthetic example, we study the capability of the inversion scheme to retrieve compact time-lapse changes despite slight changes in the acquisition layout and the effect of data coverage on the retrieval of time-lapse changes. Results from the synthetic tests are used for interpreting field data, which consists of two TEM datasets collected in 2019 and 2020 at the Nesjavellir high-temperature geothermal site (Iceland) within a monitoring project of H2S sequestration. Furthermore, the field example illustrates the effect of the trade-off between data misfit and time-lapse constraints in the inversion objective function, using the tuning settings of the generalized minimum support norm. Based on the results from both the synthetic and field cases, we show that our implementation of 3D time-lapse inversion has a robust performance for TEM monitoring.

Two efficient implementations of 3D and 2.5D modeling and inversion are presented to be applicable to large-scale transient electromagnetic (TEM) method explorations. The key novel features are (1) forward response and Jacobian calculations are implemented using the octree-based finite-element method, (2) a mirror approach is used to build a 2.5D inversion scheme for further efficiency, and (3) a flexible link between the forward mesh and inversion model is applied on 3D and 2.5D schemes based on the voxel formulation. We compare the performance of the new implementations with 3D modeling using tetrahedral meshes, with respect to speed and memory requirements. The 3D octree algorithm requires less than 1/3 of the computational time compared with a 3D tetrahedral scheme for equivalent accuracy. The 2.5D octree algorithm further speeds up the process by reducing the computational time by another factor of two. The inversion uses the Levenberg-Marquart approach minimizing the least-squares criterion of the objective function. We determine the utility of our inversion approach on a synthetic example and a field example. In the synthetic example, the 3D octree inversion result found superior resolution of a 3D anomaly compared with a 1D result, whereas the 2.5D inversion result was, expectedly, between the 1D and 3D results, but with favorable computational expenses compared with the full 3D solution. The field data set contained 200 soundings, and we performed a 3D inversion on the full survey. A 24-sounding section was then selected for the 2.5D inversion. The 2.5D inversion result finds resistivity features similar to the 3D inversion result at the selected profile. Hence, we conclude that the presented implementations are capable of handling fairly large TEM surveys on modern computational platforms. This could be smaller subsets of production size surveys where 2D and 3D effects are pronounced.

Recent instrument advancements in the transient electromagnetic (TEM) method enable waterborne applications as well as traditional ground-based surveys. We investigate a common framework to handle combined data sets from ground-based and waterborne TEM surveys under one model domain. The modeling complexity increases for two main reasons: (1) multidimensionality effects are unavoidable in data from settings with strong conductivity contrasts and (2) different systems have different sensitivity footprints which are challenging to integrate into a common domain. We address these challenges using a previously developed 3D inversion scheme: first, octree-based forward modeling is used to describe the multidimensional environment for more accurate field simulations. Second, a decoupling between the forward and inversion mesh offers the flexibility of modeling individual soundings to minimize computational costs, while allowing a commonly shared model domain for the inversion. We validate the method through synthetic and field case studies. The synthetic studies indicate that: (1) a careful forward mesh refinement is required for models with thin and highly conductive top layers. (2) Compared with 3D forward responses, 1D modeling has an approximate 300% error directly over the coastline decreasing to 10% error 50 m away. (3) The 3D inversion outperforms the 1D inversion by a lower data misfit and more accurate model reconstruction. The field case further underlines the better consistency of the 3D inversion, which delineates the lithologic transition from sand to clay and is verified by a better agreement with existing borehole data. Based on these experiments, we conclude that (1) 3D inversion is preferred over strong resistivity contrasts arising along a coastline, (2) careful mesh refinement and decoupling of the forward and inversion mesh is an efficient approach to handling computational challenges on forward while maintaining a common inversion mesh, and (3) more focus on optimization is required to realize a full-scale 3D inversion for integrated surveys in a coastal area.