Andreas Hördt

A new sensitivity-controlled focusing regularization scheme for the inversion of induced polarization data based on the minimum gradient support

We present a new application of a focusing regularization scheme for the inversion of resistivity and induced polarization (IP) data that supports large resistivity magnitude and phase contrasts. Similar approaches so far have only been used for the interpretation of gravity, magnetic, or seismic data sets. Unlike methods based on smoothness constraints, the approach is able to resolve sharp boundaries of bodies and layers, and it allows slight parameter variations within them. Therefore, it can be used in hydrogeologic applications where we need focused images to resolve high-contrast aquifer boundaries. Our approach is based on the minimum gradient support, which seeks to minimize the occurrence of parameter contrasts, independent of their magnitude. We study the effects of a variable control parameter on the reweighting optimization, allowing a continuous transition from smooth to sharp images. We also take the spatially varying sensitivity into account to allow focusing even where sensitivities are small. The implemented weighting leads to increased smoothing in well-resolved areas and a decrease in regions of lower sensitivity. The opposite approach is examined as well. This gradient-dependent sensitivity weighting is basically an extension of depth-dependent sensitivity weighting. We demonstrate the effectiveness and limitations of the approach and the influence of the control parameter using different synthetic models and field data from a hydrogeophysical test site. The technique has proven particularly suitable for revealing sharp parameter contrasts.

Interpretation of 3-D effects in long‐offset transient electromagnetic (LOTEM) soundings in the Münsterland area/Germany

The interpretation of long‐offset transient electromagnetic (LOTEM) data is usually based on layered earth models. Effects of lateral conductivity variations are commonly explained qualitatively, because three‐dimensional (3-D) numerical modeling is not readily available for complex geology. One of the first quantitative 3-D interpretations of LOTEM data is carried out using measurements from the Munsterland basin in northern Germany. In this survey area, four data sets show effects of lateral variations including a sign reversal in the measured voltage curve at one site. This sign reversal is a clear indicator of two‐dimensional (2-D) or 3-D conductivity structure, and can be caused by current channeling in a near‐surface conductive body. Our interpretation strategy involves three different 3-D forward modeling programs. A thin‐sheet integral equation modeling routine used with inversion gives a first guess about the location and strike of the anomaly. A volume integral equation program allows models tha...

Understanding LOTEM data from mountainous terrain

Long‐offset transient electromagnetic (LOTEM) data from the Vesuvius volcano, in Italy, show that the EM response of the topography is a potential cause of data distortions. A modeling study was carried out to simulate the effect of mountainous terrain on vertical magnetic‐field time derivatives using a 3-D finite‐difference code. The objectives were to assess the importance of topographic effects and to help identify them in existing field data. The total effect of topography on the LOTEM response can be considered as a combination of four distortions of the corresponding responses for a flat terrain. First, the receiver is at some height above the flat surface. Second, the mountain acts as a conductive body displacing air. Third, large loop receivers are nonhorizontal and sense a combination of horizontal and vertical magnetic fields. Finally, the electromagnetic coupling between the mountain and deeper‐lying structure modifies the structure response. Each of the effects can be identified in field data ...

Case histories of hydraulic conductivity estimation with induced polarization at the field scale

We have carried out spectral induced polarization (IP) measurements at three different hydrogeological test sites (Hasloh, Ludingworth and Kappelen) and estimated hydraulic conductivity using empirical equations previously derived from laboratory measurements. We also reviewed previously published data from another site (Krauthausen). The intention was to explore the potential and practical limitations when applying the method at the field scale. The test sites cover a lithological spectrum from gravel to silt, with a variation in hydraulic conductivity ( K ) over three orders of magnitude. At each site, hydraulic conductivity was estimated from the real and imaginary conductivity resulting from 2D inversion. We applied the constant phase angle model, where only one frequency, typically around 1 Hz is being used. The uncertainty in K -estimates arising from inversion ambiguity was assessed by exploring the model space with a control parameter that permits a transition from smooth to blocky models and by using different starting models. At the Kappelen site, this uncertainty is larger than four orders of magnitude but a reasonable lower limit for K can be obtained. At the other three sites, the uncertainties are typically one order of magnitude. The IP-based hydraulic conductivity estimates were compared with K -values obtained from grain size analyses and pumping tests. At the Hasloh and Ludingworth sites the results agree within one order of magnitude and at the Kappelen site the derived lower boundary for K is consistent with grain size information. At the Krauthausen site, the difference between IP-based data and the values derived from grain size and pumping tests is significantly larger than the estimated uncertainties, which is probably due to the non-uniform grain size distribution. The overall results indicate that order of magnitude K -estimates from IP data at the field scale are realistic targets. However, sites with significant deviations from the empirical equations can exist, emphasizing the recommendation to use a priori information whenever possible.

The influence on sample preparation on spectral induced polarization of unconsolidated sediments

Spectral induced polarization (SIP) measurements in the laboratory are in many cases intended to provide representative and comparable results of complex electrical conductivity. This is not invariably the case when using unconsolidated sediments, as the sample preparation influences several SIP-relevant properties of the samples, including the pore geometry. The pore space is supposed to control the polarization effect and therefore a change in the pore space will change the measured parameters. We analysed the influence of the sample preparation on SIP measurements by testing various filling methods, each defined by a sequence of particular steps, with regard to the reproducibility of the spectra. The measurements were performed on three different sample materials. Variations of the spectra due to different filling methods were obtained, indicating the importance of considering the sample preparation. Methods that improved the reproducibility compared to loose packing of the samples were found, but the most suitable packing procedure depended on the material properties. The mean relaxation times and normalized chargeabilities were obtained from a Debye decomposition. Although unidentified processes caused scattering of the measured parameters, a relation of the IP-parameters to the porosities was present. A decrease of the porosity reduced both the relaxation times and the normalized chargeabilities.

Reorientation of three-component borehole magnetic data

Three-component borehole magnetics provide important additional information compared to total field or horizontal and vertical measurements. These data can be used for several tasks such as the localization of ferromagnetic objects, the determination of apparent polar wander curves and the computation of the magnetization of rock units. However, the crucial point in three-component borehole magnetics is the reorientation of the measured data from the tool’s frame to the geographic reference frame North, East and Downwards. For this purpose, our tool, the G¨ ottinger Borehole Magnetometer, comprises three orthogonally aligned fibre optic gyros along with three fluxgate sensors. With these sensors, the vector of the magnetic field along with the tool rotation can be recorded continuously during the measurement. Using the high–precision gyro data, we can compute the vector of the magnetic anomaly with respect to the Earth’s reference frame. Based on the comparison of several logs measured in the Outokumpu Deep Drill Hole (OKU R2500, Finland), the repeatability of the magnetic field vector is 0.8◦ in azimuthal direction, 0.08◦ in inclination and 71 nT in magnitude.

Magnetic susceptibility measurements of seafloor massive sulphide mini-core samples for deep-sea mining applications

Seafloor massive sulphide (SMS) deposits, found at water depths to 3600 m, are products of high-temperature hydrothermal activity associated with seafloor volcanism. Dissolved metals in the hydrothermal fluids precipitate when the fluids are expelled. Metal sulphides also accumulate as chimney-like structures. SMS are considered for future commercial exploitation because of the presence of metals such as Cu, Zn, Au and Ag. Physical parameters (geotechnical and geophysical) of SMS are important for mining purposes, to allow estimation of both the size of the deposits and the amount of ore. This paper investigates the magnetic susceptibility of 40 mini-core samples with respect to the possible discrimination of ore from host rock in the cores immediately after the drilling operations. The unmineralized host rock samples in general have higher susceptibilities compared with the mineralized samples. However, the analysis of the electrical resistivity allows a unique discrimination for our set of samples, as the mineralized and unmineralized samples fall into distinct groups without overlap when both susceptibility and resistivity are considered. The imaginary conductivity, a parameter that quantifies induced polarization, further enhances discrimination between the mineralized and non-mineralized groups.

Geometrical constraints for membrane polarization

Membrane polarization is one process that might describe the causes of induced polarization in sediments at the pore scale. Here, we investigate the practical relevance of one particular model, which consists of two cylindrical pores with different radii r and lengths L, for which the impedance can be calculated analytically. We derive approximate equations that relate polarizabilities and relaxation times directly to r and L. Based on these relations and on a systematic exploration of the parameter space, we investigate under which conditions membrane polarization is relevant in the sense that it produces measurable phase shifts in the frequency range typically observed in the laboratory or at the field scale. In principle, a wide range of spectra can be obtained. Maximum phase shifts up to hundreds of milliradian can be simulated, and the characteristic time scales cover the entire range typically measured in the laboratory. We discuss some specific constraints in the context of results from mercury injection porosimetry and recently published laboratory data and show that the required geometries are not unrealistic, even if a moderate ratio between pore length and width is included as an additional condition. We conclude that membrane polarization as a possible mechanism is not limited to a particular frequency range. We also provide evidence that the pore length of the wide pore is likely to control the measured relaxation times in practical situations. The results encourage further attempts to combine impedances of two-pore systems to approach the simulation of real sediments, with the aim to extract pore space parameters from measured data.

Relationships between soil hydraulic parameters and induced polarization spectra

Spectral induced polarization is a promising method to estimate soil hydraulic properties relatively quickly without interfering with the subsurface. It is essential for the interpretation of the spectral induced polarization data to understand the relationships between soil hydraulic properties and the parameters obtained from spectral induced polarization measurements. Recent studies often relate to certain types of unconsolidated sediments, e.g., artificial mixtures of sand and clay, or refer to particular pairs of soil hydraulic and complex electrical parameters. In the present study, we investigated seven samples of natural soils and a pure sand sample in the laboratory by spectral induced polarization and soil hydraulic measurements. After examining single combinations of parameters that can be expected from theoretical considerations, we calculated the correlation coefficients for all available pairs of complex electrical and soil hydraulic parameters. Based on this, two new empirical relationships are proposed and discussed in more detail. First, a linear relationship between the van Genuchten–Mualem parameter α and the inverse of the normalized chargeability mn is described. Second, a power law was found to estimate the saturated hydraulic conductivity Ks from the DC resistivity ρ0, the normalized chargeability mn, and the fluid conductivity σw.

Paleomagnetic inclination and declination from three-component borehole magnetometer data—New insights from logging in the Louisville seamounts

We carried out measurements of the magnetic field vector at two sites during Integrated Ocean Drilling Program (IODP) Expedition 330 to the Louisville Seamount Chain. The aim was to impose constraints on the magnetization direction and to contribute to the reconstruction of possible hot spot motion. The measurements were conducted using the Gottingen Borehole Magnetometer (GBM). It comprises three fiber optic gyros (FOG) that can be used to reorient the magnetic field data. To improve accuracy, we are using a new algorithm that combines FOG data and data of two inclinometers. As can be evaluated by comparing downlog and uplog of the measurements, the three-dimensional magnetic field data obtained is of good quality. An interpretation of the magnetic field data using a state of the art method based on horizontal layers yields results inconsistent with measurements of the natural remanent magnetization (NRM) of drill core samples. In the following, we define the magnetization from the horizontal layer as apparent magnetization and develop a new interpretation method based on dipping layers. Our method includes a new approximate forward modeling algorithm and considerably improves the consistency of the borehole measurements and the NRM data. We show that a priori information about the geometry of a layer is required to constrain the inclination and declination of magnetization. Especially the azimuth of a layer and the declination of magnetization cannot be determined separately. Using azimuth and layer dip information from borehole images, we obtain constraints on inclination and declination for one particular layer.