We present an overview of a mature, robust and general algorithm providing a single framework for the inversion of most electromagnetic and electrical data types and instrument geometries. The implementation mainly uses a 1D earth formulation for electromagnetics and magnetic resonance sounding (MRS) responses, while the geoelectric responses are both 1D and 2D and the sheet’s response models a 3D conductive sheet in a conductive host with an overburden of varying thickness and resistivity. In all cases, the focus is placed on delivering full system forward modelling across all supported types of data. Our implementation is modular, meaning that the bulk of the algorithm is independent of data type, making it easy to add support for new types. Having implemented forward response routines and file I/O for a given data type provides access to a robust and general inversion engine. This engine includes support for mixed data types, arbitrary model parameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation. We present a review of our implementation and methodology and show four different examples illustrating the versatility of the algorithm. The first example is a laterally constrained joint inversion (LCI) of surface time domain induced polarisation (TDIP) data and borehole TDIP data. The second example shows a spatially constrained inversion (SCI) of airborne transient electromagnetic (AEM) data. The third example is an inversion and sensitivity analysis of MRS data, where the electrical structure is constrained with AEM data. The fourth example is an inversion of AEM data, where the model is described by a 3D sheet in a layered conductive host.

The surface wave method is a popular tool for geotechnical characterization because it supplies a cost-effective testing procedure capable of retrieving the shear wave velocity structure of the near-surface. Several acquisition and processing approaches have been developed to infer the Rayleigh wave dispersion curve which is then inverted. Typically, in active testing, single-component vertical receivers are used. In most cases, the inversion is carried out assuming that the experimental dispersion curve corresponds to a single mode, mostly the fundamental Rayleigh mode, unless clear evidence dictates the existence of a more complex response, e.g., in presence of low-velocity layers and inversely dispersive sites. A correct identification of the modes is essential to avoid serious errors. Here we consider the typical case of higher-mode misidentification known as “osculation” (“kissing”), where the energy peak shifts at low frequencies from the fundamental to the first higher mode. This jump occurs, with a continuous smooth transition, around a well-defined frequency where the two modes get very close to each other. Osculation happens generally in presence of strong velocity contrasts, typically with a fast bedrock underlying loose sediments. The practical limitations of the acquired active data affect the spectral and modal resolution, making it often impossible to identify the presence of two modes. In some cases, modes have a very close root and cannot be separated at the osculation point. In such cases, mode misidentification can create a large overestimation of the bedrock velocity and a large error on its depth. We examine the subsoil conditions that can generate this unwanted condition, and the common field acquisition procedures that can contribute to producing data having such deceptive Rayleigh dispersion characteristics. This mode misidentification depends strongly on the usual approach of measuring only the vertical component of ground motion, as the mode osculation is linked to the Rayleigh wave ellipticity polarization, and therefore we conclude that multicomponent data, using also horizontal receivers, can help discern the multimodal nature of surface waves. Finally, we introduce a priori detectors of subsoil conditions, based on passive microtremor measurements, that can act as warnings against the presence of mode osculation, and relate these detectors to the frequencies at which dispersion curves can be misidentified. Theoretical results are confirmed by real data acquisition tests.

Often in geophysical monitoring experiments time-lapse inversion models vary too smoothly with time, owing to the strong imprint of regularization. Several methods have been proposed for focusing the spatiotemporal changes of the model parameters. In this study, we present two generalizations of the minimum support norm, which favour compact time-lapse changes and can be adapted to the specific problem requirements. Inversion results from synthetic direct current resistivity models that mimic developing plumes show that the focusing scheme significantly improves size, shape and magnitude estimates of the time-lapse changes. Inversions of the synthetic data also illustrate that the focused inversion gives robust results and that the focusing settings are easily chosen. Inversions of full-decay time-domain induced polarization (IP) field data from a CO₂ monitoring injection experiment show that the focusing scheme performs well for field data and inversions for all four Cole–Cole polarization parameters. Our tests show that the generalized minimum support norms react in an intuitive and predictable way to the norm settings, implying that they can be used in time-lapse experiments for obtaining reliable and robust results.