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1.
An algorithm for modelling and migrating ground penetrating radar (GPR) data in moderately heterogeneous dispersive media is presented. The method is based on wavefield extrapolation in the frequency–wavenumber (f–k) domain, from the solution of the 2D Maxwell's equations. The wavefield is extrapolated by a phase-shift technique using a constant relative permittivity K and a quality factor Q. It is then modified by a correction term to handle the lateral K and Q variations. The spatial distribution of the K and Q-factor values, representing the given model parameters, is introduced into the algorithm by a regular grid parametrization. The radar wave dispersion and attenuation, induced by relaxation processes, are taken into account by a linear frequency-dependent Q model, and expressed by a complex wavenumber in the propagation equation. A synthetic case and a field data set illustrate the potential of the method for frequencies of 300, 500 and 900 MHz. In the first case, a typical civil engineering problem is considered. The frequency dependence of the wave velocity and attenuation is well illustrated. The synthetic data are afterwards migrated using the initial model parameters. The results show the importance of using spatially varying model parameters in the migration processes. The second case concerns an application of the method to a real data set. In order to adjust the model parameters, a forward modelling sequence is performed until the best match between the measured and the synthetic data is achieved. A depth migration is then applied to the data, and the result is compared with the initial model parameters. In conclusion, we assess the contributions of the method to industrial applications, by discussing the performance of the algorithm compared with its limitations.  相似文献   

2.
GPR study of pore water content and salinity in sand   总被引：5，自引：0，他引：5  
High‐resolution studies of hydrological problems of the near‐surface zone can be better accomplished by applying ground‐probing radar (GPR) and geoelectrical techniques. We report on GPR measurements (500 and 900 MHz antennae) which were carried out on a sorted, clean sand, both in the laboratory and at outdoor experimental sites. The outdoor sites include a full‐scale model measuring 5 × 3 × 2.4 m3 and a salinity site measuring 7.0 × 1.0 × 0.9 m3 with three buried sand bodies saturated with water of various salinities. Our studies investigate the capability of GPR to determine the pore water content and to estimate the salinity. These parameters are important for quantifying and evaluating the water quality of vadose zones and aquifers. The radar technique is increasingly applied in quantifying soil moisture but is still rarely used in studying the problems of water salinity and quality. The reflection coefficient at interfaces is obtained from the amplitude spectrum in the frequency and time domains and is confirmed by 1D wavelet modelling. In addition, the GPR velocity to a target at a known depth is determined using techniques of two‐way traveltime, CMP semblance analysis and fitting an asymptotic diffraction curve. The results demonstrate that the reflection coefficient increases with increasing salinity of the moisture. These results may open up a new approach for applications in environmental problems and groundwater prospecting, e.g. mapping and monitoring of contamination and evaluating of aquifer salinity, especially in coastal areas with a time‐varying fresh‐water lens. In addition, the relationship between GPR velocity and water content is established for the sand. Using this relationship, a subsurface velocity distribution for a full‐scale model of this sand is deduced and applied for migrated radargrams. Well‐focused diffractions separate single small targets (diameter of 2–3 cm, at a depth of 20–180 cm and a vertical interval of 20 cm). The results underscore the high potential of GPR for determining moisture content and its variation, flow processes and water quality, and even very small bodies inside the sand or soil.  相似文献   

3.
In rough geologic media such as alluvial gravels, glacial tills, talus or colluvium, the grain sizes may span the range of GPR in situ wavelengths. Here we experimentally and numerically modeled the scattering loss from both rough-surface and subsurface dielectric scatterers. The combination of the selected radar frequency and the dimension of the scatterers placed the scattering within the Mie regime. We compared the GPR signal amplitude and waveform reflected from the metal sheet on the bottom of a large box filled with boulders with the numerically computed response from a discrete random medium (DRM) model. The DRM consists of a collection of densely packed ellipsoids. The size and orientation of the ellipsoids are randomized; the size has a Gaussian distribution similar to the physical experiment. The dielectric permittivity of the ellipsoids is constant and their electric conductivity is negligible. The starting in situ dominant pulse wavelength at 900 MHz was about 17 cm, as was about the average rock dimension. Experimentally, the 900-MHz radar pulse underwent most dispersion within the first in situ wavelength of depth, and then, at 500–700 MHz dominant frequency, the pulses underwent a near inverse range dependency loss rate, as if the media were a pure dielectric. The numerical model agrees well with the experimental data. Both experimental and numerical results support a significant scattering loss in Mie regime. Besides the scattering attenuation loss, velocity dispersion has also been observed from both observation and simulation. However, the scattering attenuation and dispersion cannot be fit by the Kramers–Kronig relation that is commonly found in intrinsic attenuation and worth further theoretical investigations.  相似文献   

4.
Ground penetrating radar (GPR) is currently within the scope of China's Chang-E 3 lunar mission, to study the shallow subsurface of the Moon. In this study, key factors that could affect a lunar GPR performance, such as frequency, range resolution, and antenna directivity, are discussed firstly. Geometrical optics and ray tracing techniques are used to model GPR echoes, considering the transmission, attenuation, reflection, geometrical spreading of radar waves, and the antenna directivity. The influence on A-scope GPR echoes and on the simulated radargrams for the Sinus Iridum region by surface and subsurface roughness, dielectric loss of the lunar regolith, radar frequency and bandwidth, and the distance between the transmit and receive antennas are discussed. Finally, potential scientific return about lunar subsurface properties from GPR echoes is also discussed. Simulation results suggest that subsurface structure from several to hundreds of meters can be studied from GPR echoes at P and VHF bands, and information about dielectric permittivity and thickness of subsurface layers can be estimated from GPR echoes in combination with regolith composition data.  相似文献   

5.
Previous studies of ground ice using moveout type ground-penetrating radar (GPR) surveys indicate that the dielectric permittivity can constrain the type of ground ice present in the subsurface. Due to the high-loss nature of the active layer over permafrost targets, however, the signal strength of GPR signals is often insufficient to resolve the basal boundary required for determining the dielectric permittivity of an underlying unit. We apply a non-conventional antenna orientation and post-processing method to determine the dielectric permittivity of the unit underlying the lowest resolvable boundary. We conduct moveout surveys using a 450 MHz GPR with collinear parallel oriented antennas on two adjacent ground ice formations in the region of Thomas Lee Inlet, Devon Island, Nunavut. We exploit the Brewster angle to calculate the approximate dielectric permittivity of ground ice formations below the active layer. The results agree within 1 dielectric unit with on-ice permittivity measurements made during a complementary study of the site.  相似文献   

6.
Ground-penetrating radar (GPR) is a non-destructive geophysical technique to obtain information about shallow subsurface by transmitting electromagnetic waves into the ground and registering signals reflected from objects or layers with different dielectric properties. The present GPR study was conducted in Võhmuta limestone quarry in Estonia in order to describe the relationship between GRP responses to the variations in petrophysical properties. Sub-horizontally oriented cores for petrophysical measurements were drilled from the side wall of the quarry. The GPR profiles were run at the sloped trench floor and on the top of side wall in order to correlate traceable reflections with physical properties. Based on three techniques: (i) hyperbola fitting, (ii) wide angle reflection and refraction (WARR), and (iii) topographic, a mean electromagnetic wave velocity value of 9.25 cm ns?1 (corresponding to relative dielectric permittivity of 10.5) was found to describe the sequence and was used for time-to-depth conversion. Examination of radar images against petrophysical properties revealed that major reflections appear in levels where the changes in porosity occur.  相似文献   

7.
A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant-Q (i.e. frequency-independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP-wave in the constant-Q viscoelastic anisotropic theory. For numerical simulations, the staggered-grid pseudo-spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional-order Laplacian approximation method is used to cope with spatial variable-order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant-Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional-order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.  相似文献   

8.
The travel time and amplitude of ground-penetrating radar (GPR) waves are closely related to medium parameters such as water content, porosity, and dielectric permittivity. However, conventional estimation methods, which are mostly based on wave velocity, are not suitable for real complex media because of limited resolution. Impedance inversion uses the reflection coefficient of radar waves to directly calculate GPR impedance and other parameters of subsurface media. We construct a 3D multiscale stochastic medium model and use the mixed Gaussian and exponential autocorrelation function to describe the distribution of parameters in real subsurface media. We introduce an elliptical Gaussian function to describe local random anomalies. The tapering function is also introduced to reduce calculation errors caused by the numerical simulation of discrete grids. We derive the impedance inversion workflow and test the calculation precision in complex media. Finally, we use impedance inversion to process GPR field data in a polluted site in Mongolia. The inversion results were constrained using borehole data and validated by resistivity data.  相似文献   

9.
王洪华  王敏玲  张智  刘海 《地球物理学报》2018,61(10):4136-4147
针对Cole-Cole频散介质中的复介电常数是jω的分数次幂函数,传统的时域有限元法难以离散及计算时间域分数阶导数,本文采用Pade逼近算法将含有时间分数阶导数的Cole-Cole频散介质电磁波方程推导为一组整数阶辅助微分方程,提出了一种适用于Cole-Cole频散介质的GPR有限元正演模拟算法.在复数伸展坐标系下,通过在频率域Cole-Cole频散介质电磁波方程中引入2个中间变量,并将其变换到时间域,从而以变分形式将PML边界条件加载到Cole-Cole频散介质GPR有限元方程组中,并给出了详细的求解公式.在此基础上,编制了基于Pade逼近的Cole-Cole频散介质GPR有限元正演程序,利用该程序对均匀模型进行计算,并与解析解进行对比,验证了本文构建的GPR有限元正演算法的正确性和有效性.设计了一个复杂Cole-Cole频散介质GPR模型,利用本文构建的GPR有限元正演算法进行模拟并与非频散介质模型的模拟结果进行对比,分析了电磁波在Cole-Cole频散介质中传播衰减增强、子波延伸,分辨率降低等传播规律,有助于实测雷达资料更可靠、更准确的解释.模拟结果表明,基于Pade逼近的GPR有限元正演算法可用于复杂Cole-Cole频散介质结构模拟,且具有较高的计算精度.  相似文献   

10.
The dielectric permittivity of fiery spoil tips (Shakhty town, Rostov Region) is studied with the use of a GROT 12E remote-controlled ground-penetrating radar (GPR). An anomalous zone in a combustion source is shown to be clearly pronounced in GPR data due to the temperature dependence of the dielectric permittivity of these spoil tips. To substantiate this statement, the GPR data are compared with direct measurements of soil temperatures at depths from 1.5 to 2.5 m. The experimental results are compared with the variable spectral range of a GPR sounding pulse. GPR is shown to be a promising tool for the mapping of temperature-contrast underground objects.  相似文献   

11.
Multiple scattering from cracks is considered in the two-dimensional plane-strain condition. It is assumed that identical cracks are distributed uniformly in space and that the effective waves propagate normal to the crack surfaces. Then, the apparent dispersion and attenuation are calculated as functions of frequency for three independent modes of wave propagation: SV, P and SH.The calculated results show that, in each case, the attenuation coefficient Q?1 takes a peak value when the wavelength is nearly twice the crack width, while phase velocity has a maximum deviation from the intrinsic value at a frequency lower than the peak frequency for Q?1.  相似文献   

12.
Ground penetrating radar （GPR） is one of the promising technologies that can be used to detect landmines. Many factors may affect the ability of GPR to detect landmines. Among those factors are： 1） the type of landmine material （metallic or plastic）, 2） conditions of the host soil （soil texture and soil moisture）, and 3） the radar frequency utilized. The impact of these factors on the ability of GPR to detect landmines is investigated by studying their effect on the dielectric permittivity contrast between the landmine and the host soil, as well as on the attenuation of the radar waves. The impact of each factor was theoretically reviewed and modeled using the Matlab and Mathcad software packages. Results of the computer modeling were correlated with GPR data acquired for metallic and plastic landmine types. It was found that the ability of GPR to detect landmines depends to a great extent on the landmine type, water content of the host soil, utilized radar frequency, and soil texture. The landmines are much easier to detect than plastic landmines for any soil conditions and any radar frequency. Increasing the soil＇s moisture content, regardless of soil texture, eases the detection of the plastic landmine and worsens the detection of the metallic mines. Increasing the percentage of clay in the soil causes the same effect as the moisture content. However, higher radar frequency delivers better results for landmine detection as long as the percentage of clay and the moisture content in the soil remains low. The results of this study are expected to help in selecting optimum radar antennae and data acquisition parameters depending on the landmine type and environmental conditions.  相似文献   

13.
The subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement. Q values are required for most of conventional Q-compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non-stationary sparse reflectivity inversion, we evaluate a series of methods for Q-compensation with/without knowing Q and with/without knowing wavelet. We demonstrate that if Q-compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two-phase Q-compensation method in the frequency domain to eliminate Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of Q-filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and Q and solve an over-determined equation to obtain the final reflectivity series and Q values, where both the amplitude and phase information are utilized to estimate the Q values. The evaluated inversion-based Q estimation method handles the wave-interference effects better than conventional spectral-ratio-based methods. For Q-compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of Q-compensation without knowing Q but with wavelet given.  相似文献   

14.
Wavefield depth extrapolation and prestack depth migration in complex anelastic media are studied. Kjartansson's frequency‐independent Q law is used to describe the absorption of seismic energy. The macromodel used is analogous to the macromodel used for current migration schemes except that an additional frequency‐independent Q macromodel needs to be provided. Absorption in the forward one‐way propagator is introduced by assuming a complex phase velocity, and the inverse one‐way propagator is obtained using the reciprocity theorem for one‐way wavefields in dissipative media. The stability of the inverse propagator is achieved by limiting the angle of propagation of wavefields. A table‐driven explicit operator scheme for imaging complex 2D anelastic media is presented. High‐accuracy, short convolution operators are designed by the weighted least‐squares method, and two kinds of imaging conditions are proposed. Numerical examples of depth extrapolation in laterally varying media, the migration of a spatial impulse with dispersion as well as shot record depth migration demonstrate the potential of the proposed explicit forward operator, the explicit inverse operator and the prestack depth migration scheme, respectively.  相似文献   

15.
The WKB-method is used for the derivation of both the complex dispersion relation and displacement functions for Love channel-waves that propagate in a coal seam of varying thickness. The constant Q-model is used to describe the anelastic friction. With numerical solutions of the absorption-dispersion relation, the influence of thickness changes on the phase velocity and absorption coefficient of Love seam-waves is analysed at various frequencies. It is shown that the changes in the seam thickness can be optimally detected around the average Airy-phase frequency. An equivalence is pointed out between the wave guide structures: homogeneous with varying seam thickness and horizontally inhomogeneous with constant seam thickness.  相似文献   

16.
We investigate the early time induced polarization (IP) phenomenon in frozen unconsolidated rocks and its association with transient electromagnetic (TEM) signals measured in northern regions. The distinguishing feature of these signals is the distortion of the monotony or sign reversals in the time range from a few tens to a few hundreds of microseconds. In simulating TEM data, the IP effects in frozen ground were attributed to the dielectric relaxation phenomenon rather than to the frequency‐dependent conductivity. This enabled us to use laboratory experimental data available in the literature on dielectric spectroscopy of frozen rocks. In our studies we focused on simulating the transient response of a coincident‐loop configuration in three simple models: (i) a homogeneous frozen earth (half‐space); (ii) a two‐layered earth with the upper layer frozen; (iii) a two‐layered earth with the upper layer unfrozen. The conductivities of both frozen and unfrozen ground were assumed to exhibit no frequency dispersion, whereas the dielectric permittivity of frozen ground was assumed to be described by the Debye model. To simplify the presentation and the comparison analysis of the synthetic data, the TEM response of a frozen polarizable earth was normalized to that of a non‐polarizable earth having the same structure and resistivities as the polarizable earth. The effect of the dielectric relaxation on a TEM signal is marked by a clearly defined minimum. Its time coordinate tmin is approximately three times larger than the dielectric relaxation time constant τ. This suggests the use of tmin for direct estimation of τ, which, in turn, is closely associated with the temperature of frozen unconsolidated rock. The ordinate of the minimum is directly proportional to the static dielectric permittivity of frozen earth. Increasing the resistivity of a frozen earth and/or decreasing the loop size results in a progressively stronger effect of the dielectric relaxation on the TEM signal. In the case of unfrozen earth, seasonal freezing is not likely to have an appreciable effect on the TEM signal. However, for the frozen earth, seasonal thawing of a near‐surface layer may result in a noticeable attenuation of the TEM signal features associated with dielectric relaxation in a frozen half‐space. Forward calculations show that the dielectric relaxation of frozen unconsolidated rocks may significantly affect the transient response of a horizontal loop laid on the ground. This conclusion is in agreement with a practical example of inversion of the TEM data measured over the permafrost.  相似文献   

17.
Velocity as well as attenuation factorQ –1 ofP-wave in a dry granitic rock sample under uniaxial compressions were measured in the range of frequency between 100 kHz and 710 kHz by using the pulse transmission technique. Above the stress of 0.5 f , where f is the fracture stress, theP-wave velocity decreases with increasing axial stress, whereasQ –1 increases. Particularly, the change ofQ –1 is greater for high frequency than for low frequency. At a given stress level, the higher the frequency, the higher theP-wave velocity and the largerQ –1. This result means that the velocity decrease with increasing stress is smaller for higher frequency. Because of this frequency-dependence of velocity decrease, theP-wave in the rock under dilatant state shows dispersion. The body wave dispersion is more remarkable at higher stress, and is not found in a homogeneous material with no cracks. Thus the disperison is attributed to the generation of cracks. When the frequency-dependence ofQ –1 is approximated asf n in the present frequency range, the exponentn takes a value from 0.63 to 0.77.  相似文献   

18.
Analysis of quality factors for Rayleigh channel waves   总被引：3，自引：1，他引：2  
To facilitate investigation of the effect of imperfect elastic dissipation on thepropagation of Rayleigh-type channel waves and use of their quality factors in investigationsof the properties of coal seams, a simple method for calculating the quality factor QR isproposed in this paper. Introduction of complex velocities into the dispersion function allowscalculation of the dispersion function of Rayleigh-type channel waves in coal seams. By thecontrol variable method, we analyzed changes in QR with changes in coal seam thickness andP- and S-wave Q-factors within the coal seam and adjacent rock layers. The numerical resultsshow that the trend of the QR curve is consistent with the group velocity curve. The minimumQR value occurs at the Airy phase frequency; the Airy phase frequency decreases as coal seamthickness increases. The value of QR increases with increasing Qs2 （quality factor for S wavein coal seam）. We can compensate for the absorption of Rayleigh-type channel waves usingthe computed QR curve. Inversion of the QR curve can also be used to predict the thicknessesand litholoeies of coal seams.  相似文献   

19.
AVO investigations of shallow marine sediments   总被引：2，自引：0，他引：2  
Amplitude‐variation‐with‐offset (AVO) analysis is based on the Zoeppritz equations, which enable the computation of reflection and transmission coefficients as a function of offset or angle of incidence. High‐frequency (up to 700 Hz) AVO studies, presented here, have been used to determine the physical properties of sediments in a shallow marine environment (20 m water depth). The properties that can be constrained are P‐ and S‐wave velocities, bulk density and acoustic attenuation. The use of higher frequencies requires special analysis including careful geometry and source and receiver directivity corrections. In the past, marine sediments have been modelled as elastic materials. However, viscoelastic models which include absorption are more realistic. At angles of incidence greater than 40°, AVO functions derived from viscoelastic models differ from those with purely elastic properties in the absence of a critical angle of incidence. The influence of S‐wave velocity on the reflection coefficient is small (especially for low S‐wave velocities encountered at the sea‐floor). Thus, it is difficult to extract the S‐wave parameter from AVO trends. On the other hand, P‐wave velocity and density show a considerably stronger effect. Attenuation (described by the quality factor Q) influences the reflection coefficient but could not be determined uniquely from the AVO functions. In order to measure the reflection coefficient in a seismogram, the amplitudes of the direct wave and the sea‐floor reflection in a common‐midpoint (CMP) gather are determined and corrected for spherical divergence as well as source and streamer directivity. At CMP locations showing the different AVO characteristics of a mud and a boulder clay, the sediment physical properties are determined by using a sequential‐quadratic‐programming (SQP) inversion technique. The inverted sediment physical properties for the mud are: P‐wave velocity α=1450±25 m/s, S‐wave velocity β=90±35 m/s, density ρ=1220±45 kg/m3, quality factor for P‐wave QP=15±200, quality factor for S‐wave QS=10±30. The inverted sediment physical properties for the boulder clay are: α=1620±45 m/s,β=360±200 m/s,ρ=1380±85 kg/m3,QP=790±660,QS=25±10.  相似文献   

20.
While seismic reflection amplitudes are generally determined by real acoustical impedance contrasts, there has been recent interest in reflections due to contrasts in seismic‐Q. Herein we compare theoretical and modelled seismic reflection amplitudes for two different cases of material contrasts. In case A, we examine reflections from material interfaces that have a large contrast in real‐valued impedance () with virtually no contrast in seismic‐Q. In case B, we examine reflections from material interfaces that have virtually no contrast in but that have very large seismic‐Q contrasts. The complex‐valued reflection coefficient formula predicts non‐zero seismic reflection amplitudes for both cases. We choose physical materials that typify the physics of both case A and case B. Physical modelling experiments show significantly large reflections for both cases – with the reflections in the two cases being phase shifted with respect to each other, as predicted theoretically. While these modelling experiments show the existence of reflections that are predicted by theory, there are still intriguing questions regarding the size of the Q‐contrast reflections, the existence of large Q‐contrast reflections in reservoir rocks and the possible application of Q‐reflection analysis to viscosity estimation in heavy oilfields.  相似文献   

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