Hee Joon Kim

Inequality constraint in least-squares inversion of geophysical data

This paper presents a simple, generalized parameter constraint using a priori information to obtain a stable inverse of geophysical data. In the constraint the a priori information can be expressed by two limits: lower and upper bounds. This is a kind of inequality constraint, which is usually employed in linear programming. In this paper, we have derived this parameter constraint as a generalized version of positiveness constraint of parameter, which is routinely used in the inversion of electrical and EM data. However, the two bounds are not restricted to positive values. The width of two bounds reflects the reliability of ground information, which is obtained through well logging and surface geology survey. The effectiveness and convenience of this inequality constraint is demonstrated through the smoothness-constrained inversion of synthetic magnetotelluric data.

Full-waveform inversion algorithm for interpreting crosshole radar data: a theoretical approach

Ground-penetrating radar is a useful tool for civil and environmental engineering fields because of its high resolving power and non-destructive measurements. This paper presents a method of full-waveform inversion of borehole radar data for imaging permittivity structures. The inversion algorithm is based on a conjugate gradient search for the minimum of an error functional relating to the difference between measured and predicted data. A small model perturbation in the functional can be efficiently calculated by propagating the data error back into the model in reverse time and correlating the field generated by the back-propagation with the corresponding incident field at each point. A finite difference time domain (FDTD) method is used for solving Maxwell’s equations to obtain incident electromagnetic wavefields. Back-propagated wavefields satisfy adjoint Maxwell’s equations, which are stable in reverse time and can be solved by the same FDTD scheme. The imaging scheme is applied to crosshole radar configuration, thereby demonstrating its capability to reconstruct permittivity structures. Tests on a two-dimensional synthetic model produce good images of target scatterers and show stable convergence.

High-frequency electromagnetic impedance method for subsurface imaging

This paper presents a high-frequency electromagnetic (EM) impedance method that extends the utility of conventional controlled-source audio-frequency magnetotelluric (CSAMT) method to the frequency range from 100 kHz to 100 MHz. In this frequency range diffusion and wave propagation must be considered together. In principle, both the electrical conductivity and the permittivity of the shallow subsurface can be imaged using impedance data gathered on the surface of the earth. The impedance approach has a distinct advantage in that coupling with the source is unnecessary, provided that the source can be positioned far enough away to yield plane waves at the receiver positions.At high frequencies the EM impedance is a function of the angle of incidence or the horizontal wavenumber, so the electrical properties cannot be readily extracted without eliminating the effect of horizontal wavenumber on the impedance. For this purpose, this paper considers two independent methods for accurately determining the horiz...

SVD Inversion of Zero-Offset Profiling Data Obtained in the Vadose Zone Using Cross-Borehole Radar

An artificial groundwater infiltration experiment was conducted in Nagaoka city in Japan, and time-lapse cross-borehole ground-penetrating radar (GPR) data were collected to monitor the infiltration process in the vadose zone using zero-offset profiling (ZOP) mode. The downward migration of induced water was observed as a variation of GPR travel times, which can be transformed into dielectric constant and further converted to volumetric water content. In this paper, we present an effective approach to extract accurate information about the hydrogeologic process in the vadose zone from ZOP data. This approach is based on a least squares inversion method using singular-value decomposition, in which a finite-difference time-domain forward modeling is used for computing electromagnetic wave fields on 2-D cylindrical coordinates. The inversion approach is validated using a synthetic example and applied to the field data. We can successfully estimate the variation of soil water content during infiltration in the Nagaoka site from the reconstructed dielectric constant models. The inversion results show that the saturation information is useful to assess hydrogeologic properties of the test soil zone.

Efficient Electromagnetic Imaging of an Artificial Infiltration Process in the Vadose Zone Using Cross-Borehole Radar

Cross-borehole ground-penetrating radar (GPR) has been widely used to characterize the shallow subsurface and to monitor hydrogeologic processes. To investigate an infiltration process in the vadose zone, an artificial groundwater infiltration test was conducted in Nagaoka, Japan. Time-lapse cross-borehole GPR data were collected using zero-offset profiling (ZOP) mode. The infiltration process was observed as a variation of GPR traveltimes, which can be transformed into a dielectric constant, and further converted to volumetric water content. A standard ZOP analysis, for which all first arrivals are assumed to be direct waves, results in an underestimation of the dielectric constant because of the existence of critically refracted waves. This letter presents an efficient algorithm using the maximum first-cycle amplitude to approximately determine the traveltime of direct arrival, deriving a dielectric constant model more accurately than the standard ZOP analysis from ZOP data. Tests on synthetic and real field data show that the proposed approach is effective in building accurate water content profile without iterative calculations as in the standard ZOP analysis.

A Full Waveforminversion Algorithm for Interpreting Crosshole Radar Data

Ground-penetrating radar (GPR) is a useful tool for civil and environmental engineering fields because of its high resolving power and non-destructive measurements. This paper presents a method of full-waveform inversion of borehole GPR data for imaging permittivity structures. The inversion algorithm is based on a conjugate gradient search for the minimum of an error functional relating to the difference between measured and predicted data. A small model perturbation in the functional can be efficiently calculated by propagating the data error back into the model in reverse time and correlating the field generated by the back-propagation with the corresponding incident field at each point. A finite difference time domain (FDTD) method is used for solving Maxwells equations to obtain incident electromag-netic wavefields. Back-propagated wavefields satisfy adjoint Maxwells equations, which are stable in reverse time and can be solved by the same FDTD scheme. The imaging scheme is applied to crosshole radar configuration, thereby demonstrating its capability to reconstruct permittivity structures. Tests on a two-dimensional synthetic model produce good images of target scatterers and show stable convergence.

An integral equation representation of wide‐band electromagnetic scattering by thin sheets

An efficient, accurate numerical modeling scheme has been developed, based on the integral equation solution to compute electromagnetic (EM) responses of thin sheets over a wide frequency band. The thin‐sheet approach is useful for simulating the EM response of a fracture system in the earth. The focus of this development has been the accuracy of the numerical solution over a wide‐band frequency range of up to 100 MHz. The effect of displacement currents is included to correctly evaluate high‐frequency EM scattering.Currently, EM responses of two thin sheets with different geometrical and electrical properties embedded in a three‐layer earth can be modeled over a frequency band of 10−3 to 108 Hz. The layered earth and the sheets can be electrically dispersive, an important feature that allows analysis of frequency‐dependent characteristics of the model under investigation. The source field can be generated by a remote or local electric or magnetic dipole located on the surface or in a borehole. A plane‐wa...

Three-dimensional inversion of in-line resistivity data for monitoring a groundwater recharge experiment in a pyroclastic plateau

An artificial groundwater recharge experiment was conducted in a pyroclastic plateau in Kagoshima Prefecture in Japan, and time-lapse electrical resistivity data were collected to monitor the recharge process. In the experiment, time-efficient in-line resistivity surveys were performed along four intersecting lines, because a large amount of water was released from two recharge areas and a relatively fast migration of water into the vadose zone was expected. The migration of recharged water may be estimated from changes in electrical resistivity because resistivity in the vadose zone is largely controlled by water saturation variations there. The geological setting at the experiment site was interpreted from the resistivity distribution inverted from the in-line survey data, which were obtained before the recharge experiment. The resistivity distribution showed an approximately layered structure, which could be correlated with four borehole logs in the area. Three-dimensional (3D) distributions of the resistivity change ratio were derived through constrained nonlinear ratio inversion. Three-dimensional inversion of the in-line resistivity data was more suitable than two-dimensional inversion to describe the 3D phenomena associated with groundwater recharge. During the recharge experiment, the zones of decreased resistivity shifted with time, indicating non-uniform penetration of water from the recharge areas into the ground and a horizontal flow of the recharged water, especially in the secondary Shirasu layer, which comprises lacustrine or marine sediments of pyroclastic origin. These interpretations agree with the variation in water content observed in a borehole. An artificial groundwater recharge experiment was conducted in a pyroclastic plateau in Kagoshima Prefecture in Japan, and time-efficient in-line resistivity surveys were performed along four intersecting lines. The zones of decreased resistivity shifted with time, indicating non-uniform penetration of water from the recharge areas and a horizontal flow of the recharged water.

A fast inversion method for interpreting borehole electromagnetic data

A fast and stable inversion scheme has been developed using the localized nonlinear (LN) approximation to analyze electromagnetic fields obtained in a borehole. The medium is assumed to be cylindrically symmetric about the borehole, and to maintain the symmetry a vertical magnetic dipole is used as a source. The efficiency and robustness of an inversion scheme is very much dependent on the proper use of Lagrange multiplier, which is often provided manually to achieve a desired convergence. We utilize an automatic Lagrange multiplier selection scheme, which enhances the utility of the inversion scheme in handling field data. In this selection scheme, the integral equation (IE) method is quite attractive in speed because Green’s functions, the most time consuming part in IE methods, are repeatedly re-usable throughout the selection procedure. The inversion scheme using the LN approximation has been tested to show its stability and efficiency using synthetic and field data. The inverted result from the field data is successfully compared with induction logging data measured in the same borehole.

The potential of fracture imaging using high-frequency, single-hole electromagnetic data

This paper presents an inversion scheme for high‐frequency electromagnetic (EM) data from a single borehole for detection and characterization of fluid‐filled fractures. Water in the fracture zone may be characterized by its high electrical permittivity and, if saline, by high electrical conductivity. High electrical conductivity results in increased attenuation of EM fields, whereas high electrical permittivity reduces the phase velocity of propagating EM fields. Taking advantage of these effects, we use high‐frequency EM fields to detect and characterize fluid‐filled fractures. To demonstrate the feasibility of single‐hole EM imaging, we develop a three‐step inversion scheme to map a fluid‐filled fracture near the borehole and to evaluate its electrical conductivity and permittivity.We assume that a fluid‐filled fracture can be simulated by a conductive thin sheet. To test our inversion scheme, we generated synthetic data using the thin‐sheet integral equation method. A vertical magnetic dipole was used...