3-D Time-Domain Airborne EM Forward Modeling With IP Effect Based on Implicit Difference Discretization of Caputo Operator

We present two approaches to solving the airborne electromagnetic (AEM) problems given the induced polarization (IP) effect: with calculating the field in a polarizable medium directly in the time domain (TD) and with calculating the EM+IP field in the frequency domain (FD) followed by a transition to the time domain. The first approach is based on calculating the field at each time step given the sources that depend on the currents excited in the medium at previous time steps. This approach allows us to use any IP decay functions. The frequency domain approach is based on the Fourier series expansion of a non-stationary source and the Cole-Cole model. In order to reduce the computational cost, we use the Hermite spline interpolation. Both approaches allow modeling EM + IP processes in complex media with topography and the curved boundaries of layers containing 3D heterogeneities. 3D modeling is performed on non-conforming hexahedral meshes generated fully automatically. The analysis of computational efficiency and verification of the developed approaches are presented in comparison with the results from other researchers. Moreover, we compare the results obtained in the time and frequency domains. The results of 3D modeling the IP effects, which are obtained for some geoelectrical models typical for AEM exploration problems, are demonstrated.

Summary Induced polarization (IP) effects in airborne electromagnetic (AEM) surveys have commonly been investigated in helicopter-borne systems, leaving both a bibliographic and application gap for fixed-wing configurations. This gap partly reflects the large relative number of helicopter compared to fixed wing AEM systems, but also the geometric complexity of fixed wing platforms. In these platforms, nine geometric parameters come into play: the pitch, roll, and yaw of both transmitter and receiver, plus the three-axis offsets between the coils. Shifts in these factors can distort the measured data in ways that aren’t uniquely attributable, making it hard to pinpoint whether negative recordings truly arise from IP or from geometry-related effects. The non-fixed geometry also complicates removal of the primary field, often requiring iterative processing steps that may suppress or alter spectral content linked to IP. With advances in airborne IP understanding from helicopter-borne systems, revisiting fixed-wing platforms is both timely and necessary. Part A of this two-part study addresses this issue using the TEMPEST™ fixed-wing system connecting numerical modelling with field evidence. A suite of synthetic two-layer models with variable resistivity and chargeability parameters was developed to evaluate the system’s sensitivity to polarizable structures. The experiments demonstrate that IP effects, including negative secondary field responses, can be reliably detected in fixed-wing AEM data, both in X and Z magnetic field components. The capacity of these systems to detect IP phenomena is, however, strongly dependent on the electrical conductance of the environment. For instance, both fixed-wing and helicopter-borne systems, elevated near-surface conductance enhances the amplitude of purely electromagnetic induction currents, which in turn can dominate the recorded response and obscure the comparatively weaker polarization currents. More in general, IP detectability depends on the strength of the EM response generated by induction currents flowing elsewhere, which can dominate the small reverse current flow from a polarizable target. This highlights the critical role of near-surface conductivity in controlling the expression of IP responses and underscores the need to carefully account for these factors when interpreting survey data. The synthetic results are then connected with field-scale observations from a subset of the AusAEM dataset, over 470 000 line-km of TEMPESTTM data, where negative responses align with areas of low shallow conductance, confirming the simulation results. These finding open the way to the Part B of this study, where TEMPESTTM data are inverted taking into account IP and compared with helicopter-borne results and geological information.

We have demonstrated that the induced polarization effect in the airborne electromagnetic (AEM) data can be represented well using the generalized effective-medium theory of induced polarization (GEMTIP) model. We have also developed a novel method for 3D inversion of the airborne spectral induced polarization (SIP) data into the volume distribution of the parameters of the GEMTIP model. The results show that the SIP effect can be observed by a typical AEM system. The AEM data collected by the standard systems can be used not only for producing resistivity models of the subsurface formations, but for recovering the chargeability and other GEMTIP model parameters which can be subsequently used for mineral exploration and possibly mineral discrimination.

A major impediment in the path toward airborne induced polarization (IP) is an effective method to quantify data from inductive sources, such as those used in airborne electromagnetic systems. We modeled inductive IP using a combination of Warburg and exponential decay models as a basis for fitting electromagnetic data from ground time-domain electromagnetic (TEM) and airborne versatile TEM (VTEM) surveys. Observed decays were deconvolved into electromagnetic and IP constituents by constrained least-squares fitting of basis functions modified to account for transmitter waveforms. The method was confirmed through synthetic modeling of 2D and 3D structures, and when applied to ground TEM or airborne TEM data, obtained an estimate of apparent chargeability at each station or fiducial. In the case of a VTEM survey in Africa, the apparent chargeabilities mapped graphitic sediments and provided spatially consistent indications of clay concentrations. A limitation on this airborne IP for airborne applications is motion noise, which places a lower limit on usable base frequency and begins to significantly affect the signal at the later delay times, when IP effects are most visible.

The transient electromagnetic (TEM) responses measured in areas with highly polarizable media commonly show induced polarization (IP) effects, which poses difficulties to the TEM data interpretation and inversion with conventional methods. When present, the IP effects break the monotony in TEM decay curves and can even cause sign reversals, and lead to the singularity and non-monotony of inversion method. It is therefore important to take the IP effects into account when processing those TEM data. In this paper, a new inversion method is developed to invert TEM data with IP effects. The Cole-Cole model was introduced to the forward modeling solver so that the IP effects can be accurately calculated. The regularization terms were adapted to the objective function and a global optimization method, the particle swarm optimization algorithm, was used to solve the optimization problem, which weakened the singularity and non-monotony of the inversion greatly. Field data were collected in Wulong gold mine where IP effects were detected. The data were inverted using the method developed in this paper, and the inversion results were able to identify the depth extension of NO. 163 ore-bearing quartz veins and their associated fine-grained diorite veins. The global inversion method in this paper primarily solved the inversion problem of IP-affected TEM responses, and recovered the polarization parameters, which can be used as an aid to the geological interpretation.

In recent years, there has been increasing interest in the phenomenon of induced polarization (IP) in airborne time-domain electromagnetic (ATEM) data. How to effectively extract the polarization information of the medium from the electromagnetic data containing the IP effect is a challenging problem. Most of the current studies can only recover relatively accurate resistivity information, but the recovery effect of other IP parameters is poor. In order to better extract the IP parameters of underground media, a new constrained inversion method must be sought. Using the process of z-score normalization, we define the data variance degree. Due to the correlation between IP parameters, the data difference degree is added to the multi-parameter inversion as a constraint, and a new inversion framework including the data difference degree is formed. The inversion results of synthetic data show that this method can improve the inversion results, obtain more accurate information of dielectric IP parameters, and reduce the difficulty of geological interpretation in the later stage. In order to test the stability of this constrained inversion method, we add different levels of noise for testing and obtain good inversion results. In addition, this data difference degree constraint can also be more widely used in the inversion of different geophysical methods.

Induced polarization (IP) effects are becoming more evident in time-domain helicopter airborne electromagnetic (AEM) data thanks to advances in instrumentation, mainly due to improvements in the signal-to-noise ratio and hence better data quality. Although the IP effects are often manifested as negative receiver voltage values, which are easy to detect, in some cases, IP effects can distort recovered transients in other ways so they may be less obvious and require careful data analysis and processing. These effects represent a challenge for modeling and inversion of the AEM data. For proper modeling of electromagnetic transients, the chargeability of the subsurface and other parameters describing the dispersion also need to be taken into consideration. We use the Cole-Cole model to characterize the dispersion and for modeling of the IP effects in field AEM data, collected by different airborne systems over different geologies and exploration targets, including examples from diamond, gold, and base metal exploration. We determined how multiparametric inversion techniques can simultaneously recover all four Cole-Cole parameters, including resistivity [Formula: see text], chargeability [Formula: see text], relaxation time [Formula: see text], and frequency parameter [Formula: see text]. The results obtained are in good agreement with the ancillary information available. Interpretation of the IP effects in AEM data is therefore seen by the authors as providing corrected electrical resistivity distributions, as well as additional information that could assist in mineral exploration.

During August 1982, a marine resistivity/induced polarization (IP) survey was undertaken in Prudhoe Bay, Alaska. Multi-electrode arrays with inter-electrode spacings of 10 metres and 25 metres were used to survey a total of 34 line kilometers. Apparent resistivity values were considerably higher over known granular materials. No strong IP responses were observed. The use of marine resistivity measurements in conjunction with high-resolution sub-bottom profiling can improve the chances of finding granular materials in shallow offshore waters. INTRODUCTION During late August 1982, a marine resistivity/ induced polarization (IP) survey was undertaken in Prudhoe Bay, Alaska. The purpose of the survey was to determine whether the system could be used to detect and map gravel deposits in the Bay. TECHNICAL APPROACH From measurements of resistivity made on land it is clear that the resistivity of sub-surface materials increases with increasing grain size. Thus coarse-grained materials such as sand and gravel have higher resistivities than fine-grained silts and clays. This resistivity-grain size dependence remains true even when the materials are saturated with saline water. Sub-bottom materials tend to have higher resistivities when frozen (i.e. ice-bonded) than when not frozen. The presence of permafrost in the subbottom will be observed as higher resistivities. A frozen clay could in this manner give rise to apparent resistivities comparable to those associated with unfrozen coarse-grained materials. However there is evidence (Olhoeft 1975) that frozen clays exhibit an induced polarization response which is not present in unfrozen coarsegrained materials. The IP effect can be observed as a small transient voltage which exists in a polarizable medium after interruption of electric current flow. This transient is generally two orders of magnitude lower than the voltage drop in the medium during current flow. It has time constants in the 0.1 to 10 second range. (IP effects also arise in the presence of metallic sulphides; IP measurements are frequently used in prospecting for metals). The measurement of apparent resistivity and IP effects can be expected to provide sufficient information to detect and map gravel distribution in the sub-bottom. High resistivities with no IP response would imply the presence of gravels, while high resistivities and an IP response would suggest the presence of frozen fine-grained sediments This situation is analogous to that observed on land, where measurement of electrical response is a widely-accepted means of mapping granular deposits and permafrost distribution. RESISTIVITY AND INDUCED POLARIZATION MEASUREMENT The resistivity/IP measurement system used in this survey has been developed by Hardy Associates (1978) Ltd. over the past three years. Figure 1 is a schematic illustration of the system. The system measures the electrical resistivity of sub-bottom materials by injecting electric current into the water from a pair of electrodes and measuring the resulting voltages between successive pairs of electrodes equally spaced at increasing distances from the current electrodes. The electric current is supplied by a Huntec (70) Ltd. M4 IP transmitter, capable of producing 20 amperes at power levels up to 7.5 KVA. The current waveform is an interrupted square wave with a period of 4 seconds.

3D parallel surface-borehole TEM forward modeling with multiple meshes

To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss–Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM “footprint” concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical.

This article presents a tutorial of the bases for, and problems encountered with, the resistivity and induced polarization methods in geotechnical and environmental applications. It commences with a discussion of aqueous electrolytic conduction in rocks including consideration of the effects of temperature, rock texture, rock type, geological processes, and of the presence of clay minerals. Both electrode and membrane polarization in soils and rocks are described. The elementary theory for the resistivity and induced polarization methods is introduced via formulas for electrodes on homogeneous and layered half-spaces. The notion of apparent resistivity is presented. Vertical electric sounding is described in relation to curve types, inversion, equivalence, anisotropy, and correlation. Profiling with resistivity is briefly treated while combined sounding-profiling is treated in more detail for both the resistivity and induced polarization methods. The parameters used to describe the induced polarization phenomena are introduced. A brief discourse follows on data acquisition and processing, including design considerations for transmitters and receivers, electrodes, and wire logistics. A section on arrays and the factors involved in selecting an array provokes the disclosure that while their application in geotechnical and environmental studies usually is straightforward much remains to be learned about the resistivity and induced polarization methods in general. Specific topics requiring study are comparative studies of various arrays in (a) depth of exploration in sounding and in profiling, (b) resolution of horizontal structures, (c) sensitivity to depth, (d) sensitivity to lateral effects, (e) sensitivity to buried and surface topography, and (f) the effectiveness of focused arrays. References to recent significant publications on one-, two-, and three-dimensional forward and inverse interpretation procedures follow. Problems encountered with these methods are initially treated under the section on arrays and are expanded with specific reference to geologic noise and negative induced polarization effects. The advantages of focused arrays are illustrated. The paper concludes with nine representative examples of applications.

Transient electromagnetic (TEM) data can be seriously distorted by induced polarization (IP) phenomena when a polarizable body is present. The TEM field generated by a grounded-wire source contains transverse electric (TE) and transverse magnetic (TM) modes. The IP effect is most commonly studied with the TEM total field, rather than considering the difference between TE and TM fields. To investigate the effect of IP phenomena on the TE and TM fields, we have performed a detailed analysis on IP-distorted TEM data based on numerical and field examples. We first compare the IP effect on the TE and TM fields when polarizable bodies with different polarizable parameters are present. The TM field is more severely affected by the IP effect than the TE field. Compared to a single grounded-wire source, a double-line grounded-wire source can generate a larger TM field in the horizontal electric field. We compare the IP effect on TEM data from single- and double-line grounded-wire TEM configurations, and find that the data from the double-line configuration have a higher TM/TE ratio and are more severely affected by IP phenomena than in the single-line case. Thus, it would be easier to identify and extract the IP response from field data acquired with a double-line grounded-wire source configuration. These results have been verified by a field survey of the Kalatongke copper-nickel ore district, which has predominantly layered geology, in Xinjiang, China.

For several decades, induced polarization (IP) effects on transient electromagnetic (TEM) responses have been observed. These effects can manifest as late-time negative transients or as rapidly decaying curves and are usually associated with highly polarizable bodies. If neglected, IP effects can lead to erroneous resistivity models. Recent work allows IP effects to be incorporated into the inversion of TEM data on a more routine basis. In a recent field survey in western Tanzania, strongly IP-affected TEM signals are observed using a towed-transient electromagnetic (tTEM) system. The survey have been carried out to locate drinking water resources in a weathered regolith setting. In these settings, an inversion of tTEM data using a resistivity-only forward model (i.e., IP neglected) cannot fit the data and severely limits the value of the TEM data for hydrogeologic interpretation. To account for IP effects, we have applied a modified version of the Cole-Cole model called the maximum phase angle (MPA) model to invert IP-affected tTEM data. The MPA model incorporates four inversion model parameters: resistivity ([Formula: see text]), MPA ([Formula: see text]), relaxation time ([Formula: see text]), and frequency exponent ([Formula: see text]). The MPA model fits the data well and improves the reliability of the resistivity model. In much of the surveyed region, the inverted models using MPA display a three-layer system consisting of an upper resistive laterite layer of varying thickness and an intermediate polarizable conductive unit overlying more resistive weathered basement rocks. The conductive polarizable layer is interpreted as a chemically weathered saprolite separating the surficial and deeper aquifers. Overall, tTEM inversion results provide a local understanding of groundwater systems, especially in such regions with very limited subsurface knowledge.

This paper presents the application of a novel trans-dimensional sampling approach to a time domain airborne electromagnetic (AEM) inverse problem to solve for plausible conductivities of the subsurface. Geophysical inverse field problems, such as time domain AEM, are well known to have a large degree of non-uniqueness. Common least-squares optimisation approaches fail to take this into account and provide a single solution with linearised estimates of uncertainty that can result in overly optimistic appraisal of the conductivity of the subsurface. In this new non-linear approach, the spatial complexity of a 2D profile is controlled directly by the data. By examining an ensemble of proposed conductivity profiles it accommodates non-uniqueness and provides more robust estimates of uncertainties.

This paper discusses the physical and mathematical principles of the airborne induced polarization (IP) method. The possibility of extracting information about the IP properties of rocks from airborne survey data has become a subject of active research recently. We introduce a method for the joint inversion of the airborne EM data into the electrical conductivity and IP parameters based on the generalized effective-medium theory of induced polarization (GEMTIP). We also present the results of the inversion of the airborne EM data collected over the Echum Project Area, in Northwestern Ontario, Canada, into 3D conductivity and chargeability models. Obtaining IP physical property models from an airborne geophysical survey may result in a paradigm change in mineral exploration by pulling more information and value from airborne EM surveys.