Low frequency loop-loop electromagnetic induction (EMI) is a widely-used geophysical measurement method to rapidly measure in situ the apparent electrical conductivity (ECa) of variably-saturated soils. Here, we couple Bayesian inversion of a quasi-two-dimensional electromagnetic (EM) model with image compression via the discrete cosine transform (DCT) for subsurface electrical conductivity (EC) imaging. The subsurface EC distributions are obtained from multi-configuration EMI data measured with a CMD-Explorer sensor along two transects in the Chicken Creek catchment (Brandenburg, Germany). Dipole-dipole electrical resistivity tomography (ERT) data are used to benchmark the inferred EC fields of both transects. We are especially concerned with the impact of the DCT truncation method on the accuracy and reliability of the inversely-estimated EC images. We contrast the results of two different truncation approaches for
model parametrization. The first scenario considers an arbitrary selection of the dominant DCT coefficients and their prior distributions (a commonly-used approach), while the second methodology benefits from geostatistical simulation of the EMI data pseudosection. This study demonstrates that DCT truncation based on geostatistical simulations facilitates a robust selection of the dominant DCT coefficients and their prior ranges, resulting in more accurate subsurface EC imaging from multi-configuration EMI data. Results based on geostatistical prior modeling present an excellent agreement between the EMI- and ERT-derived EC fields of the Chicken Creek catchment.
Edge detection is one of the most important steps in the map interpretation of potential field data. In such a dataset, it is difficult to distinguish adjacent anomalous sources due to their field superposition. In particular, the presence of overlain shallow and
deep magnetic/gravity sources leads to strong and weak anomalies. In this paper, we present an improved filter, STDR, which utilises the ratio of the second-order vertical derivative to the second-order total horizontal derivative at the tilt angle equation. The maximum
and minimum values of this filter delineate the positive and negative anomalies, respectively. This novel filtering approach normalises the intensity of strong and weak anomalies, as well as anomalies with different depths and properties. Moreover, to better
illustrate the edges, its total horizontal derivative (THD_STDR) is also used. For positive and negative anomalies, the maximum value of the THD_STDR filter shows the edges of the anomalies. The potentiality of the proposed method is examined through both
synthetic and real case scenarios and the results are compared with a number of existing edge detector filters, namely TDR, THD_TDR, Theta and TDX. Due to substantial improvements in the filtering, STDR and its total horizontal derivative allow for
more accurate estimation of anomaly edges in comparison with the other filtering techniques. As a consequence, the interpretation of the potential field data is more feasible using the STDR filtering method.
Monitoring spatiotemporal variations of soil water content (θ) is important across a range of research fields, including agricultural engineering, hydrology, meteorology and climatology. Low frequency electromagnetic induction (EMI) systems have proven to be useful tools in mapping soil apparent electrical conductivity (σa) and soil moisture. However, obtaining depth profile water content is an area that has not been fully explored using EMI. To examine this, we performed time-lapse EMI measurements using a CMD mini-Explorer sensor along a 10m transect of a maize field over a 6 day period. Reference data were measured at the end of the profile via an excavated pit using 5TE capacitance sensors. In order to derive a time-lapse, depth-specific subsurface image of electrical conductivity (σ), we applied a probabilistic sampling approach, DREAM(ZS), on the measured EMI data. The inversely estimated σ values were subsequently converted to θ using the Rhoades et al. (1976) petrophysical relationship. The uncertainties in measured σa, as well as inaccuracies in the inverted data, introduced some discrepancies between estimated σ and reference values in time and space. Moreover, the disparity between the measurement footprints of the 5TE and CMD Mini-Explorer sensors also led to differences. The obtained θ permitted an accurate monitoring of the spatiotemporal distribution and variation of soil water content due to root water uptake and evaporation. The proposed EMI measurement and modeling technique also allowed for detecting temporal root zone soil moisture variations. The time-lapse θ monitoring approach developed using
DREAM(ZS) thus appears to be a useful technique to understand spatiotemporal patterns of soil water content and provide insights into linked soil moisture vegetation processes and the dynamics of soil moisture/infiltration processes.
Loop-loop electromagnetic induction (EMI) has proven to be efficient for fast and real-time soil apparent electrical conductivity (ECa) measurements. It is important to develop robust and accurate inversion strategies to obtain
soil electromagnetic conductivity image (EMCI) from ECa data. Moreover, obtaining an accurate nonlinear relationship between subsurface electrical conductivity (σ) and water content (θ) plays a key role for soil moisture monitoring using EMI. Here, we incorporated probabilistic inversion of multi-configuration ECa data with dimensionality reduction technique through the discrete cosine transform (DCT) using training image (TI)-based parametrization to retrieve soil EMCI. The ECa data were measured repeatedly along a 10 m transect using a CMD mini-Explorer sensor. Time-lapse reference data were collected as well to benchmark the inversion results and to find the in-situ relationship between σ and θ. To convert the inversely estimated timelapse EMCI to the soil moisture,we examined two approaches, namely, Rhoades et al. (1976) model and artificial neural network (ANN). The proposed inversion strategy estimated the soil EMCI with an excellent agreement with the reference counterpart. Moreover, the ANN approach demonstrated superiorities than the commonly used petrophysical model of Rhoades et al. (1976) to obtain spatiotemporal images of θ from time-lapse EMCI.
The results demonstrated that incorporation of the DCT-based probabilistic inversion of ECa data with the ANN approach offers a great promise for accurate characterization of the temporal wetting front and root zone soil moisture.
In recent years, probabilistic solution to the inversion of electromagnetic induction (EMI) data has been progressively developed for non-invasive subsurface characterization. However, Bayesian inversion of EMI data using forward solvers based on full solution ofMaxwell's equation is associated with computationally expensive modelings, particularly for large-scale surveys. Here, we incorporated artificial neural network (ANN) with Bayesian inference to obtain subsurface electromagnetic conductivity image (EMCI) fromEMI data down to 10mdepth. In this respect, a complex EMI forward model was replaced by a trained neural network (ANN proxy forward function) that can be evaluated comparably rapidly. The accuracy of the ANN-based forward solver was examined using different synthetic subsurface models. The proposed methodology was applied on EMI data measured with a DUALEM-421 s sensor from 10 ha study site in the Alken Enge area of Denmark. We compared the inversely estimated EMCI with the counterpart obtained from a quasi-three-dimensional (quasi-3D) spatiallyconstrained deterministic algorithm as a standard code. The network training procedure was performed within fewminutes, and once itwas trained, the ANN-based forward solver returned roughly 150,000 model responses per second. This value for the EMI forward solverwas around 400, demonstrating the computational efficiency of the ANN proxy forward function. The theoretical simulations demonstrated that the ANN-based forward solver accurately mimics the EMI response within the training range. Moreover, the proposed inversion strategy successfully delineated the subsurface EMCI from Alken Enge area. This approach thus facilitates rapid and accurate subsurface conductivity imaging using Bayesian inversion of multi-configuration EMI data, which is particularly pertinent for large-scale measurements.
Low-frequency loop–loop electromagnetic induction (EMI) offers several key advantages over many other geophysical techniques for proximal soil sensing. Yet, because of problems with the inversion of measured apparent electrical conductivity (ECa) data, application of EMI for geophysical imaging and interpretation is limited. In this study, a Bayesian inference was used to obtain electromagnetic conductivity images (EMCIs) from multiconfiguration ECa data. This approach allows analysis of highly nonlinear problems and renders an ensemble of models obtained from the posterior distribution that can be used to explore parameter uncertainty. In this respect, generalized formal likelihood function was used to more accurately describe the sensitivity of the posterior distribution to residual assumptions. Discrete cosine transform (DCT) was employed as a model compression technique to reduce the number of unknown parameters in the inversion. The DCT parameterization was performed using training image (TI)-based geostatistical simulations considering the ECa data pseudosection as a TI. The potential of the proposed approach was examined through different theoretical scenarios. The estimated subsurface EMCI shows excellent agreement with the original synthetic models subject to the appropriate choice of prior information. Moreover, DCT parameterization reduces the number of unknown parameters, increasing accuracy of the inversion with the Bayesian procedure. The proposed approach ensures accurate and high-resolution characterization of subsurface conductivity layering from measured ECa values.
Accurate determination of near surface soil electrical properties is important for agricultural and environmental management. In this respect, low frequency electromagnetic induction (EMI) has been widely used to measure soil apparent electrical conductivity. However, the potential to model soil subsurface layering has not been fully realized using EMI data. In this paper, we applied a probabilistic optimization approach, namely DREAM (ZS), on Geonics EM38 data to explore the robustness of this approach for soil subsurface conductivity mapping. The EM38 data was measured from the Ardakan region in the province of Yazd located in central Iran. Several soil sampleswere taken andwere further analyzed in a laboratory to derive soil textural and physical parameters. The probabilistic inversion was performed in a joint multi-configuration framework considering a five layered model. The estimated values are mainly in agreementwith the clay map (as the most influential factor); nevertheless, soil salinity data and inversely estimated conductivity values are poorly correlated for deeper layers due to the aridic condition and high clay content in the study area. DREAM (ZS) optimization approach appears to be promising for accurate retrieval of soil conductivity depth profile from EM38 data.
Conventional geophysical inversion techniques suffer from several limitations including computational cost, nonlinearity, non-uniqueness and dimensionality of the inverse problem. Successful inversion of geophysical data has been a major challenge for decades. Here, a novel approach based on deep learning (DL) inversion via convolutional neural network (CNN) is proposed to instantaneously estimate subsurface electrical conductivity (σ) layering from electromagnetic induction (EMI) data. In this respect, a fully convolutional network was trained on a large synthetic data set generated based on 1-D EMI forward model. The accuracy of the proposed approach was examined using several synthetic scenarios. Moreover, the trained network was used to find subsurface electromagnetic conductivity images (EMCIs) from EMI data measured along two transects from Chicken Creek catchment (Brandenburg, Germany). Dipole–dipole electrical resistivity tomography data were measured as well to obtain reference subsurface σ distributions down to a 6 m depth. The inversely estimated models were juxtaposed and compared with their counterparts obtained from a spatially constrained deterministic algorithm as a standard code. Theoretical simulations demonstrated a well performance of the algorithm even in the presence of noise in data. Moreover, application of the DL inversion for subsurface imaging from Chicken Creek catchment manifested the accuracy and robustness of the proposed approach for EMI inversion. This approach returns subsurface σ distribution directly from EMI data in a single step without any iterations. The proposed strategy simplifies considerably EMI inversion and allows for rapid and accurate estimation of subsurface EMCI from multiconfiguration EMI data.
Low frequency loop-loop electromagnetic induction (EMI) is widely used for monitoring soil electrical conductivity and water content. As a non-invasive geophysical technique, EMI allows for rapid and real-time electrical conductivity measurements. However, EMI has not yet been used much to back out the vertical (depth profile) conductivity structure due to problems with the inversion of measured apparent electrical conductivity (ECa) data. In this study, we used Bayesian inference with the MT-DREAM(ZS) algorithm to infer the electrical conductivity layering of the subsurface from EMI data.We test and evaluate our methodology using apparent electrical conductivity data measured along two transects in the Hühnerwasser catchment in Lusatia, Germany. These measurements were made using CMD-Explorer, a multi-configuration sensor with three inter-coil spacings and two antenna orientations. Three offsets and two antenna modes lead to six measurement depths. Electrical Resistivity Tomography (ERT) measurements were also carried out to provide reference conductivity values and to calibrate the EMI data. Such calibration is necessary for quantitative interpretation of the ECa values and to enable multi-layered inversion. The Discrete Cosine Transform (DCT) was used to reduce the number of unknown parameters, and different likelihood functions were used to evaluate the sensitivity of the posterior parameter distribution to residual assumptions. DCT-based inversion equates to a quasi-two-dimensional framework which incorporates all data along the profile and results in a low-dimensional over-determined optimization problem. Results demonstrated that although appropriate selection of the low frequency DCT coefficients is important, the definition of the likelihood function plays a crucial role in the estimation of parameter and predictive uncertainty. The use of a Gaussian likelihood function introduces artifacts in DCT-based inversion of EMI data. The use of a more flexible likelihood function results in more accurate results of the DCT-inversion. Integration of the DCT with the MT-DREAM(ZS) algorithm and a flexible generalized likelihood function appears promising for the inversion of low frequency loop-loop EMI data. The proposed approach promises accurate and high resolution estimation of subsurface hydrogeophysical properties from EMI data.