Ahmad A. Behroozmand

A Review of the Principles and Applications of the NMR Technique for Near-Surface Characterization

Abstract This paper presents a comprehensive review of the recent advances in nuclear magnetic resonance (NMR) measurements for near-surface characterization using laboratory, borehole, and field technologies. During the last decade, NMR has become increasingly popular in near-surface geophysics due to substantial improvements in instrumentation, data processing, forward modeling, inversion, and measurement techniques. This paper starts with a description of the principal theory and applications of NMR. It presents a basic overview of near-surface NMR theory in terms of its physical background and discusses how NMR relaxation times are related to different relaxation processes occurring in porous media. As a next step, the recent and seminal near-surface NMR developments at each scale are discussed, and the limitations and challenges of the measurement are examined. To represent the growth of applications of near-surface NMR, case studies in a variety of different near-surface environments are reviewed and, as examples, two recent case studies are discussed in detail. Finally, this review demonstrates that there is a need for continued research in near-surface NMR and highlights necessary directions for future research. These recommendations include improving the signal-to-noise ratio, reducing the effective measurement dead time, and improving production rate of surface NMR (SNMR), reducing the minimum echo time of borehole NMR (BNMR) measurements, improving petrophysical NMR models of hydraulic conductivity and vadose zone parameters, and understanding the scale dependency of NMR properties.

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. We present an overview of a mature and general algorithm for inversion of most electromagnetic and geoelectrical data, ground-based and airborne. The implementation uses a 1D formulation for electromagnetics and MRS responses, geoelectric responses are 1D and 2D, and the 3D sheet’s response implements an overburden of varying thickness and resistivity.

Joint inversion of aquifer test, MRS, and TEM data

This paper presents two methods for joint inversion of aquifer test data, magnetic resonance sounding (MRS) data, and transient electromagnetic data acquired from a multilayer hydrogeological system. The link between the MRS model and the groundwater model is created by tying hydraulic conductivities (k) derived from MRS parameters to those of the groundwater model. Method 1 applies k estimated from MRS directly in the groundwater model, during the inversion. Method 2 on the other hand uses the petrophysical relation as a regularization constraint that only enforces k estimated for the groundwater model to be equal to MRS derived k to the extent that data can be fitted. Both methodologies can jointly calibrate parameters pertaining to the individual models as well as a parameter pertaining to the petrophysical relation. This allows the petrophysical relation to adapt to the local conditions during the inversion. The methods are tested using a synthetic data set as well as a field data set. In combination, the two case studies show that the joint methods can constrain the inversion to achieve estimates of k, decay times, and water contents for a leaky confined aquifer system. We show that the geophysical data can assist in determining otherwise insensitive k, and vice versa. Based on our experiments and results, we mainly advocate the future application of method 2 since this seems to produce the most reliable results, has a faster inversion runtime, and is applicable also for linking k of 3-D groundwater flow models to multiple MRS soundings.

A comprehensive study of parameter determination in a joint MRS and TEM data analysis scheme

We present a comprehensive study of the parameter determination of magnetic resonance sounding (MRS) models in a joint MRS and transient electromagnetic (TEM) data analysis scheme. The parameter determination is assessed by calculating the model parameter uncertainties based on an a posteriori model covariance matrix. An entire MRS data set, dependent on pulse moment and time gate values, together with TEM data, is used for all analyses and realistic noise levels are assigned to the data. Sensitivity analyses are studied for the determination of water content as a key parameter estimated during inversion of MRS data. We show the results for different suites of (three-layer) models, in which we investigate the effect of resistivity, water content, relaxation time, loop side length, number of pulse moments and measurement dead time on the determination of water content in a water-bearing layer. For all suites of models the effect of a top conductive and a top resistive layer are compared. Moreover, we analyse all models for a long (40 ms) and short (10 ms) measurement dead time. The effect of noise level on the parameter determination is also analysed. We conclude that, in general, the resistivity of the water-bearing layer (layer of interest, LOI) does not affect the determination of water content in the LOI but the resistivity of the top layer increases depth resolution; the water content of the LOI does not influence its determination considerably in cases where the signal has a relatively long relaxation time in the LOI; determination of the water content in the LOI is improved by increasing the relaxation time of the signal in the LOI; short measurement dead time will improve the parameter determination for signals with a relatively short relaxation time; increasing loop side length and the number of pulse moments do not necessarily improve the parameter determination.

Focused Multi-layer Inversion of Magnetic Resonance Sounding Data

We present a comparison between two different regularisation schemes for multi-layer inversion of the MRS data. The two regularizations consist of the norm (Occam’s inversion) and the support (focused inversion) of the variation of the water content and relaxation time. The focused regularization provides a sharp inversion as it minimizes the area (the support) where the variations of the model parameters occur, and not the (L2) norm of the variations. Clearly, when sharp vertical transitions of the inversion parameters are present, the focused inversion retrieves the interfaces with higher precision and reconstructs more effectively the physical property values as well. This is a quite common situation in hydrogeophysics, e.g. in correspondence with the water table and/or at the boundary between aquifers and aquitards.

Comparison of stabiliser functions for surface NMR inversions

Surface nuclear magnetic resonance is a geophysical technique providing non-invasive aquifer characterization. Two approaches are commonly used to invert surface nuclear magnetic resonance data: (1) inversions involving many depth layers of fixed thickness and (2) few-layer inversions without predetermined layer thicknesses. The advantage of the many-layer approach is that it requires little a priori knowledge. However, the many-layer inversion is extremely ill-posed and regularisation must be used to produce a reliable result. For optimal performance, the selected regularisation scheme must reflect all available a priori information. The standard regularisation scheme for many-layer surface nuclear magnetic resonance inversions employs an L2 smoothness stabiliser, which results in subsurface models with smoothly varying parameters. Such a stabiliser struggles to reproduce sharp contrasts in subsurface properties, like those present in a layered subsurface (a common near-surface hydrogeological environment). To investigate if alternative stabilisers can be used to improve the performance of the many-layer inversion in layered environments, the performance of the standard smoothness stabiliser is compared against two alternative stabilisers: (1) a stabiliser employing the L1-norm and (2) a minimum gradient support stabiliser. Synthetic results are presented to compare the performance of the many-layer inversion for different stabiliser functions. The minimum gradient support stabiliser is observed to improve the performance of the many-layer inversion for a layered subsurface, being able to reproduce both smooth and sharp vertical variations of the model parameters. Implementation of the alternative stabilisers into existing surface nuclear magnetic resonance inversion software is straightforward and requires little modification to existing codes.

Successful Sampling Strategy Advances Laboratory Studies of NMR Logging in Unconsolidated Aquifers

The nuclear magnetic resonance (NMR) technique has become popular in groundwater studies because it responds directly to the presence and mobility of water in a porous medium. There is a need to conduct laboratory experiments to aid in the development of NMR-hydraulic conductivity models, as is typically done in the petroleum industry. However, the challenge has been obtaining high-quality laboratory samples from unconsolidated aquifers. At a study site in Denmark, we employed sonic drilling, which minimizes the disturbance of the surrounding material, and extracted twelve 7.6-cm diameter samples for laboratory measurements. We present a detailed comparison of the acquired laboratory- and logging-NMR data. The agreement observed between the laboratory and logging data suggests that the methodologies proposed in this study provide good conditions for studying NMR measurements of unconsolidated near-surface aquifers. Finally, we show how laboratory sample size and condition impact the NMR measurements.

ANTHROPOGENIC WETLANDS DUE TO OVER-IRRIGATION OF DESERT AREAS; A CHALLENGING HYDROGEOLOGICAL INVESTIGATION WITH EXTENSIVE GEOPHYSICAL INPUT FROM TEM AND MRS MEASUREMENTS

During the last century, many large irrigation projects were carried out in arid lands worldwide. Despite a tremendous increase in food production, a common problem when characterizing these zones is land degradation in the form of waterlogging. A clear example of this phenomenon is in the Nubariya depression in the Western Desert of Egypt. Following the reclamation of desert lands for agricultural production, an artificial brackish and contaminated pond started to develop in the late 1990s, which at present extends for about 2.5 km2. The available data provide evidence of a simultaneous general deterioration of the groundwater system. An extensive hydrogeophysical investigation was carried out in this challenging environment using magnetic resonance sounding (MRS) and ground-based time-domain electromagnetic (TEM) techniques with the following main objectives: (1) understanding the hydrological evolution of the area; (2) characterizing the hydrogeological setting; and (3) developing scenarios for artificial aquifer remediation and recharge. The integrated interpretation of the geophysical surveys provided a hydrogeological picture of the upper 100 m sedimentary setting in terms of both lithological distribution and groundwater quality. The information is then used to set up (1) a regional groundwater flow and (2) a local density-dependent flow and transport numerical model to reproduce the evolution of the aquifer system and develop a few scenarios for artificial aquifer recharge using the treated water provided by a nearby wastewater treatment plant. The research outcomes point to the hydrological challenges that emerge for the effective management of water resources in reclaimed desert areas, and they highlight the effectiveness of using advanced geophysical and modeling methodologies.

NMR for Near-surface Investigations (Development and Applications)

In porous materials, susceptibility contrasts between the matrix and the pore fluid generate pore-scale inhomogeneities in the magnetic field that are referred to as internal gradients. Internal gradients impact NMR measurements, and can cause large errors in the calculated diffusion coefficient if they are not accounted for. The magnitude of the internal gradients is determined by the susceptibility contrast, the strength of the background magnetic field, and the pore geometry. We use statistical analysis to look for correlation between measured internal gradients and properties of sediment samples. The primary goal of this analysis was to identify parameters that could be used as predictors of internal gradient magnitudes. We measured internal gradients using two different NMR methods: Method 1 estimates an average effective gradient, and Method 2 calculates a distribution of effective gradients. The sediment properties that we consider are magnetic susceptibility, iron content, specific surface area, grain size, and measured NMR parameters including the mean log T2 and the T1/T2 ratio. In our preliminary analysis, conducted with data from 20 sediment samples, we observe linear trends between iron content and measured gradients, and between magnetic susceptibility and measured gradients. We also see that the mineral form of iron appears to impact the relationships between iron content, magnetic susceptibility, and internal gradients. The correlation observed between gradients measured with Method 1 and both the specific surface area and T2 could indicate that this method is biased by relaxation time; this relationship was not observed for the gradients measured with Method 2. We plan to collect data on more sediment samples to better understand these relationships and develop a model for the estimation of internal gradients. Such a model will enable us to include internal gradient values in diffusion coefficient calculations for a range of nearsurface applications.

MRS Parameter Estimation – Improvement by Joint and Laterally Constrained Inversion of MRS and TEM Data

We present a new scheme for joint and laterally constrained inversion (LCI) of magnetic resonance sounding (MRS) data and transient electromagnetic (TEM) data, which greatly improves the estimation of the MRS model parameters. MRS is a non-invasive geophysical technique which directly quantifies the water content distribution from surface measurements. The resistivity information of the subsurface is obtained from a complementary geophysical method such as TEM or DC resistivity methods. The conventional inversion of MRS data assumes the resulting resistivity structure to be true and considers a constant MRS kernel through the inversion. We show that this assumption may introduce an error to the forward modeling and consequently result in erroneous parameter estimations. We discuss the advantage of TEM for the joint inversion compared to DC resistivity. A fast and numerically efficient MRS forward routine makes it possible to invert the MRS and TEM data sets simultaneously along profiles. As results, a more reliable and robust estimation of all parameters is achieved. We examine the approach through a field example in Denmark where good agreement with borehole data is demonstrated with clear correlation between the relaxation time T_2^* and the grain size distribution of a sandy aquifer.