Abstract: In this chapter, I discuss an alternative perspective on interpreting the results of joint and constrained inversions of geophysical data. Typically such inversions are performed based on inductive reasoning (i.e. we fit a limited set of observations and conclude that the resulting model is representative of the Earth). While this has seen many successes, it is less useful when, for example, the specified relationship between different physical parameters is violated in parts of the inversion domain. I argue that in these cases a hypothesis testing perspective can help to learn more about the properties of the Earth. I present joint and constrained inversion examples that show how we can use violations of the assumptions specified in the inversion to study the subsurface. In particular I focus on the combination of gravity and magnetic data with seismic constraints in the western United States. There I see that high velocity structures in the crust are associated with relatively low density anomalies, a possible indication of the presence of melt in a strong rock matrix. The concepts, however, can be applied to other types of data and other regions and offer an extra dimension of analysis to interpret the results of geophysical inversion algorithms.

Scaling on-chip Cu wiring dimensions has degraded electromigration (EM) reliability with the same metallization and rapidly increased Cu resistivity. The size effects in EM and resistivity were caused by increased contributions from EM-induced mass flow and electron scattering with interfaces and grain boundaries, respectively. The EM Cu interconnect lifetime had further degraded by the decrease in the void volume required to cause EM failure. The Cu interconnect resistance was further increased by increasing the volume fraction of barrier/liner in metal wires that were required to produce chips with good reliability. In this chapter, we review the Cu microstructure and resistivity for various CMOS technological nodes, the basic physics of the EM phenomenon addressing EM mass transport, lifetime scaling rule, and damage formation in Cu damascene line structures. This is followed with discussions on Blech short length and EM scaling rule. Several techniques developed for improving EM reliability using upper-level dummy vias, impurities, Cu surface treatments, alternated liners, and surface metal coating are discussed together with the effects of Cu microstructure, atomic layer deposition MnOx liner, and Cu/carbon nanotube composite line on EM.Finally, the EM lifetimes, failure mechanisms and activation energies through various technological nodes are presented.

Marine electromagnetic (EM) methods can be used to determine the resistivity of the subsurface, which can in turn be used to investigate bothstructure and properties of the subsurface.Natural source magnetotelluric (MT) and controlled source electromagnetic (CSEM) methods have been applied to a range of exploration and exploitation problems. In areas of complex geology where seismic can struggle to produce a clear subsurface image, both CSEM and MT have been applied to improve velocity model building and hence improve the final migrated image.In reservoir characterisation problems, CSEM derived resistivity provides a valuable complement to seismically derived acoustic and elastic properties, and has been shown to reduce interpretation ambiguity, particularly in the case of hydrocarbon saturation uncertainty.In all cases, a careful multiphysics approach, in which marine EM methods are integrated with seismic and other geophysical methods, provides the most robust result.

The development of resistivity and induced polarization (IP) methods is often attributed to the experiments and observations of Conrad Schlumberger in the 1920s. In this chapter, we trace the origins of the methods further back in time to some of the earliest geophysical studies in mineral exploration and agriculture. We provide a comprehensive historical narrative of the development of the techniques over the last 100 years, drawing from both publications and patent applications in Europe, the USA and Russia. We explain the value of electrical measurements of the near-surface Earth, being the motivation for these developments over the last century. Major transitions in the understanding of the petrophysical relationships between electrical properties and the physical and chemical properties of the subsurface are highlighted. We also identify major technological advances in the instrumentation, data-acquisition techniques and data-processing strategies. We introduce the most recent methodological developments that pave the way for a new generation of resistivity and IP imaging applications, including fully 3D imaging across complex terrain and long-term automated monitoring of environmental processes in the near-surface.

In this chapter, we explore the range of electrode configurations for measurement of resistivity and induced polarization (IP). We introduce the concept of apparent resistivity and chargeability and illustrate, for relatively simple cases, how the apparent resistivity is affected by non-uniformity of resistivity (e.g. a layered subsurface). We introduce the graphical presentation of apparent resistivity and IP measurements in a pseudosection for 2D problems. We discuss some of the practical aspects of field measurements, including choice of electrode configuration and assessment of measurement errors.Although we provide extensive coverage of the more standard ground-based electrical methods which account for a vast proportion of electrical surveying, we illustrate how measurements can be made in ‘non-standard’ settings, such as between boreholes or for imaging laboratory-scale tanks and columns, and also discuss time-lapse measurement approaches. We also illustrate how potential fields using the same four electrode configuration allows the mapping of electrical current, which has applications in the detection of fluid leaks, e.g. in landfills.

In this chapter, we introduce the concepts of forward and inverse modelling of resistivity and induced polarization (IP) measurements.We provide a comprehensive account of the elements that form the majority of modern techniques for resistivity and IP modelling. 1D forward modelling is discussed, building on analytical approaches presented in Chapter 4.For 2D and 3D forward modelling, numerical (discrete) approaches are required, typically adopting finite difference or finite element methods. Inverse modelling, which provides the spatial (or spatio-temporal) variation of a property of interest, is essential for interpretation of resistivity and IP data.We detail various inverse modelling approaches for resistivity and IP data. We illustrate how a priori information can be used to enhance an inverse model and show how data errors can impact on the computed model of electrical properties. Extension of the inverse modelling to treat time-lapse data is explained.Various methods for inverse model appraisal (including model uncertainty) are presented. We illustrate alternative inverse modelling approaches that are based on probabilistic approaches. The inverse modelling of spectral IP data for recovery of relaxation parameters is also discussed.

The sensitivity of electrical properties to the physical, chemical and, possibly, microbiological properties of the subsurface has motivated the application of resistivity and induced polarization measurements to image a remarkably diverse range of subsurface structures and processes. Traditional applications of the technologies have focused on static imaging of lithology, but time-lapse monitoring of fluid and solute transport processes in the earth is rapidly growing in popularity. Using a variety of laboratory and field-based case studies, we illustrate some of these applications of resistivity and IP measurements. Our selected case studies highlight some of the key concepts described in earlier chapters of the book, including handling of errors and choice of regularization methods when inverting resistivity and IP datasets. The selected case studies draw from a diverse range of fields, including geology, archaeology, hydrology, engineering and biology. We pay particular attention to recent case studies that illustrate the application of resistivity and IP measurements to issues of high societal relevance, including climate change, food security and environmental restoration.

The acquisition of accurate resistivity and induced polarization (IP) measurements requires dedicated laboratory and field-scale instrumentation. Although resistivity measurements are relatively straightforward, IP measurements require sensitive instrumentation and procedures that minimize errors resulting from the sample holder design in the laboratory and from the cables and electrodes in the field. We discuss the basic principles of a laboratory resistivity measurement and then describe the implementation of resistivity measurements at the field-scale, focusing on modern resistivity imaging systems designed to rapidly acquire thousands of measurements on distributed arrays or grids of electrodes. Specific characteristics of the transmitting and receiving electronics, electrodes and cabling are discussed. We address the additional factors that must be considered in the acquisition of meaningful IP measurements. In laboratory measurements, we focus on the critical issue of sample holder design and in the field we focus on strategies to reduce coupling effects between the wiring and the ground. The different ways to quantify the IP effect, commonly termed ‘time domain’ and ‘frequency domain’ measurements, are introduced and derivatives discussed. We also establish the link between the different measures of the IP effect provided by the instrumentation and the intrinsic electrical properties described in Chapter 2.

In this chapter, we offer some final remarks on areas of potential future development, targeting: petrophysics, instrumentation and modelling. We discuss how new modelling approaches, e.g. using pore-networks, are emerging to improve interpretation of electrical phenomena in porous media.We highlight some aspects of ambiguity in induced polarization (IP) properties and call for improvements in mechanistic petrophysical models of IP processes.New developments in instrumentation are discussed, highlighting the potential for time-lapse (monitoring) studies and the imaging of complex terrains using distributed measurement systems. Growth in the use of parallel computation for large-scale modelling problems is discussed.The emergence of machine learning methods is also highlighted.The need for improved methods for (and more adoption of) uncertainty estimation in inverse models is discussed.We close by recognizing the immense value and likely longevity of simple, more traditional, approaches for modelling resistivity and IP data.

The electrical properties of the near-surface Earth depend on the chemical properties of the fluids filling pores, grain size, the geometry of the interconnected pore network and mineralogy of the solids. We first describe how electrical resistivity depends on the ionic composition of an electrolyte. We next discuss the controls on the resistivity of a porous medium. We start with Archie’s laws and summarize the development of the parallel conduction model used to incorporate surface conduction at the solid–fluid interface. We describe how the induced polarization (IP) effect in the case of a non-electronically conducting matrix is incorporated into the parallel conduction model through a complex surface conductivity. Models to describe the frequency dependence of resistivity in terms of a distribution of polarization length-scales, e.g. grain sizes or pore sizes, are reviewed. We discuss models to describe the mechanisms causing the large polarization enhancement observed in the presence of electronically conducting minerals and show how IP parameters are, in this case, related to the volume and size of the electronically conducting particles. We finish by considering the role of contaminants in modifying electrical properties of near surface materials and briefly consider the possibility of non-linear effects in measurements.