unsaturated zone characterization in soil through transient wetting and drying using gpr joint time frequency analysis and grayscale images summary this paper describes an experimental method to characterize the soil s unsaturated zone by constructing a scenario in which transient downward water infiltration took place from the topsoil to the bottom soil continuously during the water infiltration gpr waveforms and side view grayscale images of the soil column were simultaneously and continuously captured the gpr wavelets associated with the wetting front were analyzed using short time fourier transform stft algorithm the downward wetting front and the stretch of unsaturated transition zone decelerated and eased the wetting front s reflection in the time domain as well as reduced the peak frequency and attenuated the frequency spectra in the frequency domain the subsequent drying process further attenuated but accelerated the wetting front s reflection in both time and frequency domains these observations were correlated with the image pixel profiles from which gpr velocity profiles at different lapsed times were generated after computation via a complex refractive index model crim the crim method is entirely non invasive and not only offers very detailed measurement of the water saturation profile of the transition zone in laboratory scale but also is potentially useful for the further study of a variety of vadose zone properties

high resolution characterization of vadose zone dynamics using cross borehole radar characterization of the dynamics of moisture migration in the unsaturated zone of aquifers is essential if reliable estimates of the transport of pollutants threatening such aquifers are to be made electrical geophysical investigation techniques such as ground penetrating radar offer suitable methods for monitoring moisture content changes in the vadose zone moreover these tools permit relatively large measurement scales appropriate for hydrological models of unsaturated processes and thus they offer a distinct advantage over conventional measurement approaches ground penetrating radar when applied in transmission mode between boreholes can provide high resolution information on lithological and hydrological features the technique may be applied in tomographic mode and in a much simpler vertical profile mode both modes of measurement have been utilized using two boreholes 5 m apart located at a field site in the uk sherwood sandstone aquifer radar transmission measurements have been used to characterize the change in moisture content in unsaturated sandstone due to controlled water tracer injection continual monitoring of cross borehole radar measurements over an 18 month period has also permitted determination of travel times of natural loading to the system and has revealed the impact of subtle contrasts in lithology on changes in moisture content over time the time series of inferred moisture contents show clearly wetting and drying fronts migrating at a rate of approximately 2 m month 1 throughout the sandstone

effects of the transition zone above a water table on the reflection of gpr waves 1 we simulate two levels of water table at 72 and 48 cm depth by injecting water in a sand box that also contains several buried objects gpr profiles acquired with a 1200 mhz antenna at the top of the sand box do not show any clear reflections from the water table this is because of the existence of a transition zone in which the velocity is a continuously decreasing function of depth the reflection coefficient in this case decreases with increasing frequency and even vanishes for a cut off frequency f0 which itself increases with decreasing transition zone thickness by modeling in the frequency domain we explain the absence of the high frequency gpr reflections from the top of the saturated zone when the wavelength is small high frequency compared to the thickness of the transition layer the reflection coefficient is negligible and hence no reflections from the water table will be observed

the turbulent oscillator a mechanism of low frequency variability of the wind driven ocean gyres intrinsic low frequency variability is studied in the idealized quasigeostrophic midlatitude wind driven ocean gyres operating at large reynolds number a robust decadal variability mode driven by the transient mesoscale eddies is found and analyzed the variability is a turbulent phenomenon which is driven by the competition between the eddy rectification process and the potential vorticity anomalies induced by changes of the intergyre transport

material transport in oceanic gyres part i phenomenology abstract material spreading and mixing by oceanic mesoscale eddies are analyzed in an idealized numerical model of the wind driven midlatitude oceanic circulation the main focus is on the regime with large reynolds number re and vigorous mesoscale eddies although brief comparisons are made with less turbulent solutions at smaller re the analyses are based on ensembles of lagrangian particle trajectories the authors find that tracer transport by mesoscale eddies differs in many ways from the commonly used model of homogeneous isotropic eddy diffusion the single particle dispersion which describes the spreading process is generally anisotropic and inhomogeneous and in most places it is not diffusive i e not linear in time during intermediate time intervals after tracer release in most of the basin and especially in the deep layers subdiffusive single particle dispersion occurs due to long time trapping of material by coherent structures such as vortices near the strong currents and planeta

hydrologic trajectories in transient ground penetrating radar reflection data a variable rate infiltration experiment was conducted in a sandbox to demonstrate that distinctive patterns are produced in transient ground penetrating radar gpr data collected during wetting and drying events the observed gpr response was found to be very consistent with the results of numerical simulations performed using finite difference time domain modeling of gpr coupled with a 1d unsaturated flow model hydrus 1d for which the sand hydraulic properties were determined independently using core samples despite this agreement few methods are available that can efficiently analyze transient gpr data to make a quantitative link between observed responses and the hydraulic properties of soils to address this problem a computationally efficient method is proposed that is analogous to coherency analysis used in multioffset surveys the new method isbased on the calculation of semblance along trajectories through transient gpr data each trajectory represents a specific gpr arrival e g the groun

soil moisture content estimation using ground penetrating radar reflection data abstract ground penetrating radar gpr reflection travel time data were used to estimate changes in soil water content under a range of soil saturation conditions throughout the growing season at a california winery data were collected during three data acquisition campaigns over an 80 by 180 m area using 100 mhz surface gpr antennas gpr reflections were associated with a thin low permeability clay layer located 0 8 1 3 m below the ground surface that was identified from borehole information and mapped across the study area field infiltration tests and neutron probe logs suggest that the thin clay layer inhibited vertical water flow and was coincident with high volumetric water content vwc values the gpr reflection two way travel time and the depth of the reflector at the borehole locations were used to calculate an average dielectric constant for soils above the reflector a site specific relationship between the dielectric constant and vwc was then used to estimate the depth averaged vwc of the soils above the reflector compared to average vwc measurements from calibrated neutron probe logs over the same depth interval the average vwc estimates obtained from gpr reflections had an rms error of 0 018 m3 m 3 these results suggested that the two way travel time to a gpr reflection associated with a geological surface could be used under natural conditions to obtain estimates of average water content when borehole control is available and the reflection strength is sufficient the gpr reflection method therefore has potential for monitoring soil water content over large areas and under variable hydrological conditions

stochastic boundary conditions for coastal flow modeling 1 recent high resolution radar data of surface velocity between the florida current and the coast allow us for the first time to deduce coastal boundary conditions for ocean models based on observations a stochastic model is found to be a better choice for simulating properties of the observed vorticity than a model with deterministic boundary conditions a stochastic model parameterizing boundary conditions is developed and embedded in a simple quasigeostrophic ocean model comparison of numerical simulations of western boundary flow with stochastic boundary conditions against simulations with traditional no slip and free slip conditions reveals significant differences in the formation of coherent mesoscale structures and the energetics of the western boundary current coherent structures such as dipoles and submesoscale vortices can be generated using stochastic boundary conditions the boundary current variability becomes more energetic and episodic than quasi periodic circulation features in the simulations using the conventional boundary conditions

the non invasive characterization of pumping induced dewatering using ground penetrating radar abstract ground penetrating radar gpr profiling is a non invasive geophysical technique that has been used by endres et al ground water 38 2000 566 to successfully image pumping induced drainage in an unconfined aquifer however the drained water volume calculated from the gpr data was significantly less than the actual pumped volume to investigate the reasons for this discrepancy a seven day pumping test and five day recovery test was performed at canadian forces base borden in ontario canada a dense spatial coverage of gpr profiles was used to better quantify variations in drainage due to small scale aquifer heterogeneity in addition a neutron moisture content probe was used to directly observe drainage and the soil moisture profile at a sealed well near the pumping well neutron logging indicated that the transition zone translated downward during pumping without undergoing significant extension comparison of the gpr and neutron derived transition zone drawdowns show nearly equal responses both of these observations support the hypothesis that the behaviour of the gpr reflection is an accurate measure of the transition zone response in contrast transition zone drawdown obtained from both gpr and neutron logging are significantly delayed relative to potentiometric drawdown resulting in an extended capillary fringe the drained water volume was determined from the gpr derived transition zone drawdown data using a number of different approaches methods that incorporated information about spatial variations in drainage gave larger estimates of drained water volume however those estimates were still lower than the actual pumped volume the unaccountable volume of water could be a result of several factors aquifer heterogeneity may still not be adequately represented by the increased gpr coverage and or leakage from the underlying aquitard may be providing a significant volume of water

the dynamics of a simple baroclinic model of the wind driven circulation the authors study the dynamics of a two layer approximation to the steadily forced baroclinic circulation in a closed ocean basin with the aim of understanding its temporal variability and the onset of low frequency variability it is found that for a range of dissipation that includes values used in a number of ocean modeling studies in the past five years if one waits a sufficient length of time the asymptotic behavior of the system is characterized by only a very small number of degrees of freedom by varying the dissipation as a control parameter the authors identify abrupt transitions in the form of the long term circulation exhibited by the model one type of transition from a time varying circulation dominated by two frequencies to a chaotic circulation is accompanied by the appearance of low frequency variability this constitutes an internal mechanism for the production of variability at climatological timescales the model used is a two layer quasigeostrophic model forced by a steady wind stress with a uniform cyclonic curl dissipation is modeled by a lateral diffusion of momentum with a uniform eddy viscosity in two sets of experiments with two internal deformation radii and layer depth ratios the eddy viscosity is varied and the types of circulation that result are reported the stable steady circulation seen in the viscous limit gives way to time dependent circulations of increasing temporal complexity spatially the circulations fall into two types those dominated by large recirculating gyres in the western part of the basin and those with a strong and strongly meandering peripheral current reminiscent of that seen in the black sea from an examination of the linear eigenmodes of the steady circulation the initial transition to time dependence may be characterized as a baroclinic instability of the western recirculation gyre

role of the south china sea in regulating the north pacific double gyre system abstractthe role of the south china sea scs in regulating the north pacific circulation is investigated using a two layer quasigeostrophic qg model the double gyre circulations in the north pacific with and without the scs are compared and analyzed it is found that the scs acts as a sink of both potential vorticity pv and energy in the pacific scs system for the mean state consequently the kuroshio and the upstream kuroshio extension ke are weaker in the presence of the scs moreover the eddy activity is also lower in the north pacific ocean because the barotropic instability is suppressed for a weaker circulation in terms of low frequency variations at interannual to decadal time scale the presence of the scs is found to enhance the variability of the latitudinal position and intensity of the ke jet this is explained by a positive feedback process that is associated with the negative correlation between the inertia of the kuroshio and its intrusion into the scs

transport of the north atlantic deep western boundary current about 39 n 70 w 2004 2008 abstract begun in spring 2004 a sustained measurement program line w is returning high resolution observations of the north atlantic s deep western boundary current dwbc southeast of new england the study focuses on the cold limb of the atlantic meridional overturning circulation near the boundary between the subpolar and subtropical gyres the field study consists of a 6 element continental slope spanning moored array on a line underlying an altimeter satellite ground track and periodic reoccupations of a full depth hydrographic section along the line extending from the continental shelf towards bermuda here data from the first 4 years of the array may 10 2004 april 9 2008 are analyzed along with 9 realizations of the section the array a mix of moored profiler and discrete fixed depth instrument moorings returned temperature salinity and horizontal velocity data with various temporal and depth resolutions after averaging to filter inertial tidal and other high frequency motions the combined moored data set was binned to the lowest common temporal resolution of 5 days the nominal burst sample interval of the moored profilers and interpolated to 2 dbar vertical resolution temperature salinity dissolved oxygen tracer chemical concentrations and direct velocity data were acquired on the hydrographic cruises the present work focuses on the 4 year mean and time varying meridional transport in 4 layers bounded by neutral density surfaces upper and classical labrador sea waters iceland scotland overflow waters and denmark strait overflow waters the 5 d 4 layer summed meridional transport estimates range between 3 5 and 79 9 sv with a record mean average transport of 25 1 sv and standard deviation of 12 5 sv bias adjustment to account for the finite width of the moored array increases the 4 layer mean transport estimate to 28 7 sv at time scales longer than about 1 month the variations in equatorward dwbc transport appear correlated with meridional position of the gulf stream north wall with stronger transport observed when the stream is displaced south

linear instability of a current flowing along a bottom slope using a three layer model abstract a quasi geostrophic model of a three layer fluid on an f plane is employed to study instability of a current flowing over a uniform bottom slope with isobaths parallel to the current the model has a basic flow only in the uppermost layer but no basic motion in the middle or lowest layer or no relative motion between the two lower layers the two lower layers representing a lower ocean have a relatively small density difference which is not considered in traditional two layer models in addition to a deep baroclinic mode which is nearly homogeneous in the two lower layers a surface intensified baroclinic mode whose amplitude in the lowest layer is negligible grows in the case of a realistic slope the jet like basic flow whose half width is comparable to a deformation radius also supports a barotropically unstable mode maintained by a horizontal shear in the basic flow this mode becomes less active as the jet width increase or as the jet approaches a vertical side boundary modeled after a st

hydrodynamic parameters of a sandy soil determined by ground penetrating radar inside a single ring infiltrometer this study shows how mualem van genuchten m vg parameters can be obtained from gpr data acquired during water infiltration from a single ring infiltrometer in the case of a sandy soil water content profiles were generated at various time steps using hydrus 1d based on particular values of the m vg parameters and were converted to dielectric permittivity profiles using the complex refractive index method the gprmax suite of programs was used to generate radargrams and to follow the wetting front progression in depth using the arrival time of the electromagnetic waves recorded by a ground penetrating radar gpr theoretically the 1 d time convolution between reflectivity and gpr signal at any infiltration time step is related to the peak of the reflected signal recorded in the corresponding trace in the radargram we used this relationship to invert the m vg parameters for constant and falling head infiltrations using the shuffled complex evolution sce ua algorithm the method is presented on synthetic examples and on experiments carried out for a sandy soil the parameters inverted are compared with values obtained in laboratory on soil samples and with disk infiltrometer measurements

hydropedological investigations with ground penetrating radar gpr estimating water table depths and local ground water flow pattern in areas of coarse textured soils in coarse textured soils ground penetrating radar gpr can provide continuous high resolution records that chart the depth to water tables the use of this information can increase confidence in hydropedological site assessments and reduce the number of wells needed for water table depth and ground water flow determinations ground penetrating radar was used to map spatial and temporal variations in water table depths and ground water flow patterns within an unconfined aquifer located beneath an eolian landscape in northwestern indiana compared with the data collected at a limited number of wells the greater number of observations with gpr provided more comprehensive site coverage and mapped more intricate local ground water flow patterns over a 2 year period gpr revealed systematic temporal and spatial variations in water table depths and local ground water flow patterns

quasigeostrophic dynamics of the western boundary current abstract a local model is used to investigate the dynamics of the western boundary current in a midlatitude wind driven gyre this current is important for the gyre as a whole and its local instability is correlated with structural changes of the separated eastward jet and the interior gyres in particular the eastward jet can be disrupted and broadened in the regime with a strong local instability in the western boundary current such a regime occurs with a no slip lateral boundary condition alternatively in the absence of local instability the eastward jet is narrow and penetrates farther in the basin interior this behavior is typical with free slip boundary condition both the linear stability and nonlinear time dependent behavior of the western boundary current are analyzed for a wide range of parameters the current loses stability at moderate reynolds numbers and the stability threshold strongly depends upon the vertical stratification profile the nonlinear time dependent flow contains wel

ground penetrating radar for high resolution mapping of soil and rock stratigraphy ground penetrating radar is a technique which offers a new way of viewing shallow soil and rock conditions the need to better understanding overburden conditions for activities such as geochemical sampling geotechnical investigations and placer exploration as well as the factors controlling groundwater flow has generated an increasing demand for techniques which can image the subsurface with higher resolution than previously possible the areas of application for ground penetrating radar are diverse the method has been used successfully to map ice thickness water depth in lakes bedrock depth soil stratigraphy and water table depth it is also used to delineate rock fabric detect voids and identify karst features the effective application of the radar for the high resolution definition of soil stratigraphy and fractures in bedrock is highlighted the basic principles and practices involved in acquiring high quality radar data in the field are illustrated by selected case histories one example demonstrates how radar has been used to map the bedrock and delineate soil horizons to a depth of more than 20 m two case histories show how radar has been used to map fractures and changes of rock type to 40 m range from inside a mine another case history demonstrates how radar has also been used to detect and map the extent of groundwater contamination the corroboration of the radar results by borehole investigations demonstrates the power and utility of the high resolution radar method as an aid for interpolation and extrapolation of the information obtained with conventional coring programmes with the advent of new instrumentation and field procedures the routine application of the radar method is becoming economically viable and the method will see expanded use in the future

estimating the hydraulic conductivity at the south oyster site from geophysical tomographic data using bayesian techniques based on the normal linear regression model this study explores the use of ground penetrating radar gpr tomographic velocity gpr tomographic attenuation and seismic tomographic velocity for hydraulic conductivity estimation at the south oyster site using a bayesian framework since site specific relations between hydraulic conductivity and geophysical properties are often nonlinear and subject to a large degree of uncertainty such as at this site we developed a normal linear regression model that allows exploring these relationships systematically although the log conductivity displays a small variation s 2 5 0 30 and the geophysical data vary over only a small range results indicate that the geophysical data improve the estimates of the hydraulic conductivity the improvement is the most significant where prior information is limited among the geophysical data gpr and seismic velocity are more useful than gpr attenuation

boundary current separation in a quasigeostrophic eddy resolving ocean circulation model abstract the response of a rectangular flat bottom eddy resolving quasigeostrophic ocean to a steady double gyre wind stress is studied to assess the sensitivity of the solutions to a partial slip lateral boundary condition in which tangential stress is proportional to tangential velocity the constant of proportionality has limiting values of zero and infinity corresponding to free slip no stress and no slip conditions respectively seven numerical solutions corresponding to the values 0 0 2 0 3 5 5 0 6 5 8 0 and 100 0 are obtained which span the free slip and no slip limits significant qualitative changes in the time mean behavior of the solutions are observed to occur with increasing these changes include a gradual retreat of the separation points of the western boundary currents in the subtropical and subpolar gyres a dramatic reduction in the basin integrated reservoirs of mean and eddy kinetic energy a weakening of bottom dissipation and its replacement by lateral dissipat

pumping induced vadose zone drainage and storage in an unconfined aquifer a comparison of analytical model predictions and field measurements summary analytical models used to analyze hydraulic head data from pumping tests incorporate boundary conditions defined along the water table to account for drainage from the overlying vadose zone although these boundary conditions do not explicitly describe the details of flow in the vadose zone they do specify a bulk vadose zone response we have quantified this response in terms of the cumulative drainage flux through the water table and undrained vadose zone storage a comparison of bulk vadose zone response predicted by analytical models and inferred from field measurements was performed using hydraulic head data and soil moisture content profiles obtained during a seven day pumping test at cfb borden ontario three different analytical models one assuming instantaneous drainage and two types of delayed drainage using exponential decay functions were used to predict the bulk vadose zone response from the hydraulic head measurements the pumping test analyses using these models gave reasonable values for aquifer parameters and the model predictions of the transient hydraulic head response replicated the observed hydraulic head data however there are significant differences between the model predictions and field observations of the bulk vadose zone response the instantaneous drainage model entirely neglected the substantial undrained storage that was observed in the vicinity of the pumping well the delayed drainage models significantly overestimated the cumulative drainage flux and underestimated the undrained storage determined from the field data the delayed drainage models predicted a relatively rapid dissipation of the undrained storage while the observed undrained storage exhibited little if any decay throughout the entire pumping test our results indicate that the water table boundary conditions used in these analytical models do not adequately replicate the mechanisms controlling the vadose zone behavior during a pumping test

geostatistical analysis of ground penetrating radar data a means of describing spatial variation in the subsurface we have investigated the use of ground penetrating radar gfr as a means of characterizing the heterogeneity of the subsurface radar data were collected at several sites in southwestern british columbia underlain by glaciodeltaic sediments a cliff face study was conducted in which geostatistical analysis of a digitized photograph of the face and the radar image of the face showed excellent agreement in the maximum correlation direction and the correlation length determined from these two data sets other two dimensional 2 d sections of radar data were divided into sedimentary architectural elements on the basis of the distinct radar appearance of these sedimentary units examples of four sedimentary units were used to obtain semivariograms from the radar data and resulted in maximum correlation lengths between 0 5 and 4 8 m a 3 d radar survey collected over a package of gravel and sand foresets was analyzed to determine the paleoflow direction a correlation length of 4 m was found in that direction

estimation of field scale soil hydraulic and dielectric parameters through joint inversion of gpr and hydrological data 1 a method is described for the joint use of time lapse ground penetrating radar gpr travel times and hydrological data to estimate field scale soil hydraulic parameters we build upon previous work to take advantage of a wide range of cross borehole gpr data acquisition configurations and to accommodate uncertainty in the petrophysical function which relates soil porosity and water saturation to the effective dielectric constant we first test the inversion methodology using synthetic examples of water injection in the vadose zone realistic errors in the petrophysical function result in substantial errors in soil hydraulic parameter estimates but such errors are minimized through simultaneous estimation of petrophysical parameters in some cases the use of a simplified gpr simulator causes systematic errors in calculated travel times simultaneous estimation of a single correction parameter sufficiently reduces the impact of these errors we also apply the method to the u s department of energy doe hanford site in washington where time lapse gpr and neutron probe np data sets were collected during an infiltration experiment we find that inclusion of gpr data in the inversion procedure allows for improved predictions of water content compared to predictions made using np data alone these examples demonstrate that the complimentary information contained in geophysical and hydrological data can be successfully extracted in a joint inversion approach moreover since the generation of tomograms is not required the amount of gpr data required for analyses is relatively low and difficulties inherent to tomography methods are alleviated finally the approach provides a means to capture the properties and system state of heterogeneous soil both of which are crucial for assessing and predicting subsurface flow and contaminant transport

interpretation of drill core and georadar data of coarse gravel deposits abstract pollution in the shallow subsurface has led to an increasing need of understanding how to quantitatively characterize both the heterogeneity of gravel aquifers and the influence of heterogeneity on groundwater flow and solute transport models play an important role in decision making processes especially in the context of better characterizing and in forecasting the behavior of a given geological system the objective of the present paper is the derivation of a gradual lithofacies based interpretation of outcrop drill core and ground penetrating radar gpr or georadar data of different quality the presented method allows a probability estimation of drill core layer descriptions and radarfacies types representing defined sedimentary structure types the method includes a determination of initial structure type probabilities for grain size categories and combinations thereof described in drill core layer descriptions as well as a subsequent differentiation of these structure type probabilities in an iterative process considering additional information like main constituent quantity fraction and sorting of single grain size categories color chemical precipitation layer thickness and adjacent layer the radarfacies types are calibrated with drill cores located in the vicinity of georadar sections the calibration process consists of the assignment of the calculated structure type probabilities from the drill core layer descriptions to the corresponding radarfacies types considering the proportion in thickness between drill core layers and georadar structures the structure type probabilities can be given for points along boreholes and a grid with arbitrary mesh size along georadar sections the method is applied to field examples from the rhine wiese aquifer near basel in switzerland the resulting structure type probabilities can be used for conditioning stochastic simulations of geological models however the conditioned stochastic simulation of the rhine wiese aquifer is the topic of another paper the results show the importance of a detailed sedimentological analysis of outcrops and drill cores as well as its significance on the distinction of sedimentary structure types

hydrogeological characterization of the south oyster bacterial transport site using geophysical data a multidisciplinary research team has conducted a field scale bacterial transport study within an uncontaminated sandy pleistocene aquifer near oyster virginia the overall goal of the project was to evaluate the importance of heterogeneities in controlling the field scale transport of bacteria that are injected into the ground for remediation purposes geochemical hydrological geological and geophysical data were collected to characterize the site prior to conducting chemical and bacterial injection experiments in this paper we focus on results of a hydrogeological characterization effort using geophysical data collected across a range of spatial scales the geophysical data employed include surface ground penetrating radar radar cross hole tomography seismic cross hole tomography cone penetrometer and borehole electromagnetic flowmeter these data were used to interpret the subregional and local stratigraphy to provide high resolution hydraulic conductivity estimates and to provide information about the log conductivity spatial correlation function the information from geophysical data was used to guide and assist the field operations and to constrain the numerical bacterial transport model although more field work of this nature is necessary to validate the usefulness and cost effectiveness of including geophysical data in the characterization effort qualitative and quantitative comparisons between tomographically obtained flow and transport parameter estimates with hydraulic well bore and bromide breakthrough measurements suggest that geophysical data can provide valuable high resolution information this information traditionally only partially obtainable by performing extensive and intrusive well bore sampling may help to reduce the ambiguity associated with hydrogeological heterogeneity that is often encountered when interpreting field scale bacterial transport data

modelling of gpr waves for lossy media obeying a complex power law of frequency for dielectric permittivity the attenuation of ground penetrating radar gpr energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies absorption with increasing traveltime and causes also a distortion of wavelet phase dispersion the attenuation is often expressed by the quality factor q for gpr studies q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity we consider a complex power function of frequency for the dielectric permittivity and show that this dielectric response corresponds to a frequency independent q or simply a constant q model the phase velocity dispersion relationship and the absorption coefficient of electromagnetic waves also obey a frequency power law this approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only for example q and the phase velocity at an arbitrary reference frequency this simplicity makes it practical for any inversion technique furthermore by using the hilbert transform relating the velocity and the absorption coefficient which obeys a frequency power law we find the same dispersion relationship for the phase velocity both approaches are valid for a constant value of q over a restricted frequency bandwidth and are applicable in a material that is assumed to have no instantaneous dielectric response many gpr profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes changes in water content are believed to be the origin of this reflectivity we model the radar reflections from the bottom of a dry aeolian dune using the 1d wavelet modelling method we discuss the choice of the reference wavelet in this modelling approach a trial and error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site additionally by combining the complex refractive index method crim and or topp equations for the bulk permittivity dielectric constant of moist sandy soils with a frequency power law for the dielectric response we introduce them into the expression for the reflection coefficient using this method we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling