Spatially Constrained Inversion Research Articles

Spatially constrained inversion of semi-airborne transient electromagnetic data based on a mixed norm

The interpretation of semi-airborne transient electromagnetic data is mainly based on a one-dimensional inversion algorithm. The continuity of the resistivity profile is generally poor when the data noise is strong because the resistivity is laterally unconstrained, and the constraint between the resistivity in the vertical distribution is usually taken as the L2 norm regular term. However, the main disadvantage of this regularization constraint is that it over-smoothens the model and cannot effectively describe the interface information of an abrupt electrical change. To address these issues, this paper proposes a mixed norm spatially constrained inversion (SCI) algorithm that adopts the L1 norm regularization term for the vertical spatial constraint and the L2 norm regularization term for the lateral spatial constraint. The Gauss-Newton iterative method is used to solve the objective function. Fixed and adaptive strategies are proposed for the regularization factors, and a parameter is used to adjust the weights of the two constraints. The influence of different constraint weights on the results is analyzed. The inversion of noisy synthetic data verifies that the proposed SCI algorithm has a higher resolution for electrical interfaces and better noise suppression effect than the L2 norm SCI algorithm. The inversion of field data shows a good effect and practicability.

3D interpretation of helicopter-borne frequency-domain electromagnetic (HEM) data from Rams\xe5 Basin and adjacent areas at And\xf8ya, Norway

The Ramså Basin is situated on the strandflat on the northeastern side of Andøya between Ramså and Skarstein. It is the only known Mesozoic sedimentary basin onshore Norway and therefore represents an easily accessible analogue to study the setting and development of the offshore Mesozoic basins along the Norwegian continental shelf. Basement rocks (100–10,000 Ωm) and sedimentary rocks (5–1000 Ωm) have distinct ranges of the electrical resistivity. Resistivity of the subsurface can be investigated by electric and electromagnetic (EM) methods to delineate the extent of the sedimentary basin. This paper presents the interpretation of helicopter-borne frequency-domain electromagnetic (HEM) data and their correlation with data obtained from borehole logging and two-dimensional (2D) electrical resistivity tomography (ERT). Resistivity data obtained from these methods show a good agreement. Spatially constrained inversion (SCI) of HEM presents a three-dimensional (3D) subsurface resistivity image of a larger area in comparison to what could have been drawn from few ERT lines and borehole logging. HEM interpretation together with other ERT and borehole resistivity data indicates the extent of Ramså Basin beyond the presently mapped boundary. This extension is also supported by interpretation of earlier collected gravity, magnetic and seismic data. The Ramså sedimentary basin shows a wide range of electrical resistivity between ca. 10 and 600 Ωm at different depths. Two highly conductive areas are newly identified by HEM data interpretation. In one of these areas, outcropping graphite and sulfide minerals were found by field observations.

Exploration of the Aquifer of San Felipe Geothermal Area (Mexico) by Spatially Constrained Inversion of Transient Electromagnetic Data

We present an updated description of the San Felipe-Punta Estrella aquifer in Mexico by using new Transient Electromagnetic (TEM) measurements. A total of 17 TEM soundings were acquired with a 50 × 50 m2 single-loop configuration. The one-dimensional inversion of TEM data is performed by using Occam and Marquardt inversion techniques. A three-layer model, where a resistive layer is embedded by conductive ones, is sufficient to fit the data. The second and third layer are associated with the aquifer. We also applied Spatially Constrained Inversion (SCI) to the TEM data in order to derive a pseudo-3D model. A resistive layer extends from 10–100 m and is correlated to the permeable unit of the aquifer. The lowest conductive layer is associated to the semipermeable unit and starts appearing at a depth of 100 m. A high salinity in the permeable unit is detected at TEM stations near the shoreline, suggesting a saltwater intrusion. The TEM 1D inversion and SCI results confirm what a previous Vertical Electrical Sounding (VES) survey campaign has detected using electrode spacing up to 1,000 m. The bedrock of the aquifer structure could not be detected by the applied TEM configuration.

Examples of Improved Inversion of Different Airborne Electromagnetic Datasets Via Sharp Regularization

Large geophysical datasets are produced routinely during airborne surveys. The Spatially Constrained Inversion (SCI) is capable of inverting these datasets in an efficient and effective way by using a 1D forward modeling and, at the same time, enforcing smoothness constraints between the model parameters. The smoothness constraints act both vertically within each 1D model discretizing the investigated volume and laterally between the adjacent soundings. Even if the traditional, smooth SCI has been proven to be very successful in reconstructing complex structures, sometimes it generates results where the formation boundaries are blurred and poorly match the real, abrupt changes in the underlying geology. Recently, to overcome this problem, the original (smooth) SCI algorithm has been extended to include sharp boundary reconstruction capabilities based on the Minimum Support regularization. By means of minimization of the volume where, the spatial model variation is non-vanishing (i.e., the support of the variation), sharp-SCI promotes the reconstruction of blocky solutions. In this paper, we apply the novel sharp-SCI method to different types of airborne electromagnetic datasets and, by comparing the models against other geophysical and geological evidences, demonstrate the improved capabilities of in reconstructing sharp features.

Joint inversions of two VTEM surveys using quasi-3D TDEM and 3D magnetic inversion algorithms

In the current paper, we present results of a joint quasi-three-dimensional (quasi-3D) inversion of two versatile time domain electromagnetic (VTEM) datasets, as well as a joint 3D inversion of associated aeromagnetic datasets, from two surveys flown six years apart from one another (2007 and 2013) over a volcanogenic massive sulphide gold (VMS-Au) prospect in northern Ontario, Canada. The time domain electromagnetic (TDEM) data were inverted jointly using the spatially constrained inversion (SCI) approach. In order to increase the coherency in the model space, a calibration parameter was added. This was followed by a joint inversion of the total magnetic intensity (TMI) data extracted from the two surveys. The results of the inversions have been studied and matched with the known geology, adding some new valuable information to the ongoing mineral exploration initiative.

An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data

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.

Surface water–groundwater exchange in transitional coastal environments by airborne electromagnetics: The Venice Lagoon example

A comprehensive investigation of the mixing between salt/fresh surficial water and groundwater in transitional environments is an issue of paramount importance considering the ecological, cultural, and socio‐economic relevance of coastal zones. Acquiring information, which can improve the process understanding, is often logistically challenging, and generally expensive and slow in these areas. Here we investigate the capability of airborne electromagnetics (AEM) at the margin of the Venice Lagoon, Italy. The quasi‐3D interpretation of the AEM outcome by the spatially constrained inversion (SCI) methodology allows us to accurately distinguish several hydrogeological features down to a depth of about 200 m. For example, the extent of the saltwater intrusion in coastal aquifers and the transition between the upper salt saturated and the underlying fresher sediments below the lagoon bottom are detected. The research highlights the AEM capability to improve the hydrogeological characterization of subsurface processes in worldwide lagoons, wetlands, deltas.

Spatially constrained inversion for quasi 3D modelling of airborne electromagnetic data – an application for environmental assessment in the Lower Murray Region of South Australia

We present an application of spatially constrained inversion (SCI) of SkyTEM (airborne electromagnetic) data for defining spatial patterns of salinisation in the Bookpurnong irrigation area located in the lower Murray Basin of South Australia. SCI uses Delaunay triangulation to set 3D constraints between neighbouring soundings, taking advantage of the spatial coherency that may be present in the dataset. Conductivity information for individual soundings is linked through the spatial constraints, from well determined parameters to locally poorly determined parameters. For the survey presented here, SCI generated maps detail the spatial variability of floodplain salinisation, the extent of floodplain sediments influenced by lateral recharge and flushing along stretches of the Murray River, and the variable quality of groundwater in deeper semi-confined aquifers of the Murray Group. Available borehole and other ancillary information, such as vegetation density and health patterns, match the observed conductivity variations seen in the SCI results, even at the very near surface (≈2m depth). The SCI provides more accurate and spatially consistent results compared with those from single site inversions. They are also more uniform and detailed than maps obtained with single point Layered Earth Inversions or a laterally constrained inversion. In this example, the SCI provided reliable quasi 3D modelling, that confirmed and improved the hydrogeological knowledge of the area, indicating that the technique would have application with helicopter electromagnetic data in similar settings throughout the lower Murray Basin of Australia.

Quasi-3D modeling of airborne TEM data by spatially constrained inversion

We present a new methodology, spatially constrained inversion (SCI), that produces quasi-3D conductivity modeling of electromagnetic (EM) data using a 1D forward solution. Spatial constraints are set between the model parameters of nearest neighboring soundings. Data sets, models, and spatial constraints are inverted as one system. The constraints are built using Delaunay triangulation, which ensures automatic adaptation to data density variations. Model parameter information migrates horizontally through spatial constraints, increasing the resolution of layers that would be poorly resolved locally. SCI produces laterally smooth results with sharp layer boundaries that respect the 3D geological variations of sedimentary settings. SCI also suppresses the elongated artifacts commonly seen in interpretation results of profile-oriented data sets. In this study, SCI is applied to airborne time-domain EM data, but it can also be implemented with other ground-based or airborne data types.

Spatially Constrained Inversion for Quasi 3-D Modelling of AEM Data

The spatially constrained inversion (SCI) produces quasi-3D modelling of geoelectrical and EM data of varying spatial density, using a 1D forward solution. Information migrate horizontally through spatial constraints and allow resolution of layers that would be locally poorly resolved. The constraints are built using the Delaunay triangulation, which ensures automatic adaptation to data density variations. It also allows creation of subsets suitable for parallel computing. In this study the SCI was applied to airborne time domain EM soundings (SkyTEM data from the Island of Lolland, Denmark), but it can be implemented also with all other data types. The field case study proves that the SCI produces laterally c onsistent results that respect the 3D geological variations of the sedimentary settings. The resolution of near surface tills and water bearing sand and gravel layers is greatly enhanced and so is the boarder of the saline groundwater intrusion beneath the island. The SCI also suppresses the elongated artifacts commonly seen in profile oriented data sets.