Hyperbolic Reflections Research Articles

GPR investigation of the cause of persistent failure of a university road

We present the results of a multi-frequency ground-penetrating radar (GPR) survey over a university road in south-western Nigeria that has experienced persistent failures. The goal was to evaluate causes of failure to aid remediation efforts. Data was collected concurrently at 250, 500, and 1000 MHz using a UTSI electronic trivue system. Data were processed and interpreted using Reflex-Win. Visual observations of major features apparent on the road surface including failed sections were noted. Imaged features included possible bases of the surface course, base course and sub-base, subsurface projections of an outcropping and buried basement rocks, three deeply cut and back-filled sections that lie beneath sections of the road that have experienced persistent failure, and the ringing effects and rebar-associated reflection hyperbolae of two reinforced concrete drains. Indications of preferential wetting of the shallow subsurface beneath much of the failed sections suggest that failure is due to excessive moisture content in these sections. These failed sections generally correspond to regions of deep cut and backfill, and regions cut and filled for the construction of reinforced concrete drains. Apparently, the backfills at these locations have failed to prevent water influx into the subsurface and more effective remediation measures need to be deployed.

On Cemetery Hill: The legacy of burials at Clemson University, a public university in the southern USA

AbstractGround‐penetrating radar (GPR) was used to map anomalies characteristic of unmarked graves on the grounds of the modern Woodland Cemetery on the campus of Clemson University. Hundreds of these anomalies are believed to represent newly discovered unmarked graves belonging to African Americans including enslaved people, convicted laborers, sharecroppers, domestic workers, tenant farmers and wage workers, who contributed to the wealth of the Fort Hill Plantation or to building and maintaining the university. These burials appear to be in an organized arrangement indicating the presence of a burial ground where the graves would have been marked at the time of internment. Analyses of reflections from the bottom of the grave shaft detected horizontal bases as well as possible chambered and vaulted burials, a common vernacular burial type among African Americans in the 19th and early 20th centuries. A fewer number of graves showed hyperbolic reflections that can be produced by graves that contain coffins or a large artefact. This may indicate burial practices that changed over time or the status of the interred individual. The estimated length of the grave shaft in GPR grid data suggests that small adults or adolescents made up most of the burials (58%), then adults (28%) and infants and children (13%). In 1924, Woodland Cemetery was developed on Cemetery Hill, which had its first recorded burial in 1837. Plots were then gifted to prominent University leaders, faculty, staff and their families. The unmarked burials were found juxtaposed among these modern graves requiring modification of the current protocol for the operating cemetery to preserve the sacred space and to prevent destruction of these burials. This work affirms ongoing efforts by this public university to address its origins from a plantation and segregation in the American South.

An Experimental Study of GPR Near-Field Problem in Depth Ranging of Buried Objects

We evaluate the often neglected ranging (or cover depth) error of an object located within the Fresnel Region (or called radiating near-field) and reactive near-field region in ground penetrating radar (GPR). The experiments were conducted in concrete specimens with various rebar cover depths from 10 to 80 mm, which imitates any object imaged by GPR from reactive near-field, Fresnel region to far-field region. Velocities of each individual data point of the hyperbolic reflections of the embedded reinforcement in radargram are calculated by developed algorithms based on common offset antenna and multiple trilaterated ray paths. Two different velocity algorithms, based on semi- and full-trilaterated ray paths, were applied to estimate the wave travelling velocity as a prerequisite of cover depth measurement. The algorithms were firstly validated using a high-frequency 2-GHz antenna to verify the travelling speed of radar waves in air, which is equal to the speed of light. Then, the same antenna was used to estimate the cover depth by measuring the time of flight and velocity based on the two velocity algorithms. The results reveal that the ranging accuracy is highly in doubt in reactive near-field and Fresnel regions but is largely improved when the object locates in far-field region where GPR wave propagation becomes plane-type. The measurements, riding on accurate modelling of ray-path’s trilateration models, provide evidence that the normal linear scale of GPR time-to-depth conversion overlooks the effects of near-field/Fresnel region. We therefore suggest that the GPR near-field/Fresnel region and far-field boundary must be taken into account before any attempt of time-to-depth conversion and depth estimation of objects by GPR are carried out.

High-resolution P- and S-wave reflection studies of an intraplate structure: The Azambuja fault, Portugal

The Azambuja fault is a NNE trending structure located 50 km north of Lisbon, the capital and most populous city of Portugal. The fault has been considered as a possible source for the historical, large earthquakes. Understanding this fault is a priority in seismic hazard evaluation of this region. The fault has a clear morphological signature. Miocene and Pliocene sediments are tilted eastward and cut by steeply dipping mesoscale fault segments, presenting reverse and normal offsets with a net downthrow to the east. Neotectonic studies indicate a Quaternary slip on the fault of 0.05–0.06 mm/year. However, no direct evidence of the Azambuja fault affecting the Pleistocene or Holocene sediments was found so far. Here, we present the findings from high-resolution seismic reflection studies using both P- and S-waves over the Holocene deposits. The detection of small-throw faulting in ductile sediments is a challenging task. We show that multiple signatures, like perturbations in the reflection hyperbolae visible in shot and CMP gathers, interruptions of reflectors in stacked sections, lateral seismic velocity variations obtained by horizon velocity analysis, all at coincident locations, strongly suggest that the activity of the Azambuja fault has affected the Holocene sediments in the study area. The lateral velocity variations are corroborated by wavepath eikonal traveltime tomography and velocity analysis supported by seismic modeling. By means of 2D viscoelastic modeling, we explain the absence of fault-related diffractions and negligible back-scattered energy from the fault. Using data from nearby boreholes, we find that the 15 ka old alluvium cover has indeed been disturbed by the presence of shallow fault strands. Considering the estimated vertical throws and the empirical relationships between fault length, co-seismic rupture and magnitude, a slip rate of 0.07 mm/y, slightly larger than previously thought, is expected for this fault.

THE DESYMMETRIZED PSL(2,Z) GROUP, THE ‘SQUARE BOX’ CONGRUENCE SUBGROUP, THE CONGRUENCE SUBGROUPS AND LEAKY TORI

The desymmetrized PSL(2,Z) group is considered. The congruence subgroups of the desymmetrized PSL(2,Z) group are analysed according to the hyperbolic reflections contained. The Laplace-Beltrami problem and the Hamiltonian problem associated with the Laplace-Beltrami operator are discussed according to the boundary conditions for the grouppal structures. New constructions of the leaky tori are found; in particular, they are obtained after the generators of the PSL(2,Z) group, from the desymmetrized-triangle PSL(2,Z) group, and from the ’square-box’ Γ0 congruence subgroup of the desymmetrized PSL(2,Z) group

Automatic Hyperbola Detection and Apex Extraction Using Convolutional Neural Network on GPR Data

Ground Penetrating Radar (GPR) is a non-destructive geophysical method used for subsurface mapping. It is frequently used for detecting buried cylindrical objects such as underground pipes and cables. Buried cylindrical objects show a hyperbolic signal pattern on a radargram. The typical shape of the hyperbolic reflections depends on the depth and material of the buried objects and the surrounding materials. In many cases, detecting buried cylindrical objects is quite a time-consuming task, thus limiting further interpretation procedures. In this paper, we propose a new method for automating hyperbola detection and apex extraction on radargram. Our work consists of two modules that take radargram as input in a form of images. In the first module, we used the Faster-RCNN to extract the hyperbola segments as a set of rectangular boundary boxes. The network was trained using synthetic radargram data simulated by the gprMax software. The second module is to estimate the coordinates of the hyperbola apex using an image processing technique. We had correctly detected all hyperbola on the simulated radargram from the test set. For the test on field radargram, the framework is capable of processing radargram that is similar to the simulated radargram data. The problem with the second module occurs on interference hyperbola as the searching window is disturbed by the noise. Apart from those problems, by using these two modules, the detection of buried cylindrical objects using GPR can be automated with a minimal amount of time.

Processing Radargrams to Obtain Resistivity Sections

Ground penetrating radar (GPR) is routinely used to locate the isolated elements that produce reflection hyperbolas in radargrams. However, we propose a method in this study for locating the various interfaces appearing in a medium by studying the signal attenuation to obtain resistivity sections. GPR signal decay has a strong relationship with the electromagnetic properties of the medium, particularly the electrical resistivity and permittivity. To assign values of resistivity to different layers, a relationship between the attenuation coefficient and the above parameters must be used. Moreover, there are geometric effects that affect the energy loss and, therefore, the signal amplitude, that are jointly considered for the elimination of such effects before calculating the attenuation coefficient. An envelope function of the traces previously corrected for geometric effects was created to detect interfaces in the medium and generate a local decay curve and radargram zonation. Two relationships are necessary for obtaining the resistivity values from signal decay: first, a relationship between the resistivity and relative permittivity of the medium; and second, a relationship between the attenuation coefficient and resistivity. A resistivity section obtained from the GPR data is shown with an electrical tomography section at the same location.

Deterioration Mapping of RC Bridge Elements Based on Automated Analysis of GPR Images

Ground-Penetrating Radar (GPR) is a popular non-destructive technique for evaluating RC bridge elements as it can identify major subsurface defects within a short span of time. The data interpretation of the GPR profiles based on existing amplitude-based approaches is not completely reliable when compared to the actual condition of concrete with destructive measures. An alternative image-based analysis considers GPR as an imaging tool wherein an experienced analyst marks attenuated areas and generates deterioration maps with greater accuracy. However, this approach is prone to human errors and is highly subjective. The proposed model aims to improve it through automated detection of hyperbolas in GPR profiles and classification based on mathematical modeling. Firstly, GPR profiles are pre-processed, and hyperbolic reflections were detected in them based on a trained classifier using the Viola–Jones Algorithm. The false positives are eliminated, and missing regions are identified automatically across the top/bottom layer of reinforcement based on user-interactive regional comparison and statistical analysis. Subsequently, entropy, a textural factor, is evaluated to differentiate the detected regions closely equivalent to the human visual system. These detected regions are finally clustered based on entropy values using the K-means algorithm and a deterioration map is generated which is robust, reliable, and corresponds to the in situ state of concrete. A case study of a parking lot demonstrated good correspondence of deterioration maps generated by the developed model when compared with both amplitude- and image-based analysis. These maps can facilitate structural inspectors to locally identify deteriorated zones within structural elements that require immediate attention for repair and rehabilitation.

Prestack diffraction separation by parameterizing the reflection local slope

Diffracted waves provide an opportunity to detect small-scale subsurface structures because they give wide illumination direction of geologic discontinuities, such as faults, pinch outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometric amplitude losses and are generally weaker than reflections. To retain more diffracted waves, we have developed a prestack diffraction separation method based on the local slope pattern and plane-wave destruction (PWD) method. In general, it is difficult to distinguish between hyperbolic reflections and hyperbolic diffractions using data-driven local slope estimation in the shot domain. Therefore, we transfer slope estimation in the shot domain to velocity analysis in the common-midpoint domain and ray parameter calculation in the stack domain. The connection between local slope and the normal moveout velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the PWD method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of our prestack diffraction separation method.

GPR uncertainty modelling and analysis of object depth based on constrained least squares

The development of ground penetrating radar (GPR) in recent decades has promoted the role of this popular near-surface geophysical detection method. A step further involves its transition from use as a prospecting tool aimed at estimating the approximate location of buried objects to its application as an accurate piece of survey equipment [1], which then requires an understanding of measurement errors/uncertainties. This paper firstly discusses the sources of uncertainty affecting an object’s depth measurement with respect to host material, instrumentation, data collection method and signal processing. These error sources were modelled by formulating computation sets based on the application of a constrained least squares algorithm to hyperbolic reflections produced by buried objects. Based on the computation, uncertainty analysis was performed (1) through identification of errors on measurements of hyperbolic reflections and (2) by conducting error propagation to evaluate the combined uncertainty of the surveyed depth. At a geophysical test site at IFSTTAR, Nantes, France, sets of controlled experiments were conducted to validate the proposed uncertainty analysis method and to investigate the correlation between the evaluated uncertainty and the factors of host material, antenna centre frequency, target depth and the horizontal and vertical resolution in the radargram. Based on the experiments, it was possible to draw two main conclusions. Firstly, a centimetre-order of uncertainty can be achieved in the survey results for depth estimation of objects at several metres deep with a 95% confidence level at ± 2 standard deviations. Secondly, errors of time zero location at different GPR centre frequencies dominate the evaluation of uncertainty, whereas the resolution of radargrams and scattering noise do not explicitly affect the evaluated uncertainty.

Detection of road cavities in urban cities by 3D ground-penetrating radar

Cavities under urban roads have increasingly become a great threat to traffic safety in many cities. As a quick, effective, and high-resolution geophysical method, ground-penetrating radar (GPR) has been widely used to detect and image near-surface objects. However, the interpretation of field GPR data remains challenging. For example, it is hard to distinguish reflections caused by road cavities or other urban utilities with a conventional 2D GPR survey. The superiority of 3D GPR in data interpretation is demonstrated by a laboratory experiment. Two pipes and a glass-made cavity buried in a sandpit show similar hyperbolic reflections in the 2D GPR profiles; thus, they are difficult to discriminate. In contrast, their geometric shapes and dimensions are readily identified in the 3D image reconstructed from the synthetic 3D GPR data set. Based on these ideas, we have developed a car-mounted 3D GPR system with two antenna arrays oriented in different polarization directions and have detected more than 100 cavities in three Chinese cities over the past year. The field data of two such cavities are presented. As a result, the cavity depth, horizontal size, and height can be accurately estimated from the 3D GPR data set. Laboratory and field experimental results indicate that 3D GPR possesses potential in the detection and recognition of road cavities and utilities in the complex urban environment.

A novel method for GPR imaging based on neural networks and dictionary learning

In this paper, we propose a novel framework to reconstruct image of a buried object from the ground-penetrating radar (GPR) reflection hyperbolas. The first reflection hyperbola of a buried object determines its relative permittivity and shape class (circle, rectangle, and triangle). The first two reflections are used to reconstruct image of a homogeneous buried object. After five preprocessing steps to extract region of interest of b-scan corresponding to a buried object, a Convolutional Neural Network (CNN) estimates the relative permittivity value of the buried object. Then, two novel schemes, including CNN and Dictionary Learning (DL) methods are proposed to reconstruct 2D image of the buried object. Image reconstructors are trained with a dataset containing buried objects with different shapes, sizes, and reference relative permittivity. Since two objects having the same size but different materials lead to different hyperbola reflections in their B-scans, we propose a novel transformation to convert the reflection scans from the estimated relative permittivity to a reference relative permittivity so that the image reconstructors can be used to rebuild images. The results reveal that the DL method outperforms the CNN method on noisy measurements, while the CNN method performs better when dealing with fewer traces.

GEOPHYSICAL INVESTIGATIONS OF A POTENTIAL LANDSLIDE AREA IN MAYOON, HUNZA DISTRICT, GILGIT-BALTISTAN, PAKISTAN

The Mayoon landslide in the Hunza District is a slowly developed, non-catastrophic landslide that has gained its importance in the last few years after its rapid activation and fast slip rate. The area is characterized by high earthquake hazards (zone 3 with a peak ground acceleration value of 2.4–3.2 m/s2) by the Building Code of Pakistan due to frequent earth quakes. The past high earthquake activity in the area has displaced the foliated rocks towards the south and is responsible for opening the bedrock joints. The head and body of the landslide are covered by unconsolidated material and have fractures of varying lengths and widths. The non-invasive geophysical techniques, including Ground Penetrating Radar (GPR) and Electrical Resistivity Soundings (ERS), are deployed to evaluate the Mayoon landslide subsurface. The subsurface is interpreted into a two-layer model. Bright reflectors and highly variable resistivity characterize the top layer (Layer-1). This layer is associated with a loose, highly heterogeneous, fragmented material deposited under glacial settings over the existing bedrock. Hyperbolic reflections and intermediate resistivity characterize the bottom layer (Layer-2). This layer is associated with foliated metamorphic bedrock. The hyperbolic reflections show faults/fractures within the bedrock. The extension of these fractures/faults with depth is uncertain due to decay in the GPR signal with depth. The intermediate resistivity shows the bedrock is weathered and foliated. Reflections within Layer-1 have disrupted directly above the fractures/faults suggesting a possible movement. A bright reflection between the two layers highlights the presence of the debonded surface. Loose material within Layer-1 coupled with debonding possesses a significant hazard to generate a landslide under unfavourable conditions, such as an intense rainstorm or earthquake activity.

Periodic plane-wave least-squares reverse time migration for diffractions

Diffraction imaging is important for high-resolution characterization of small subsurface heterogeneities. However, due to geometry limitations and noise distortion, conventional diffraction imaging methods may produce low-quality images. We have adopted a periodic plane-wave least-squares reverse time migration method for diffractions to improve the image quality of heterogeneities. The method reformulates diffraction imaging as an inverse problem using the Born modeling operator and its adjoint operator derived in the periodic plane-wave domain. The inverse problem is implemented for diffractions separated by a plane-wave destruction filter from the periodic plane-wave sections. Because the plane-wave destruction filter may fail to eliminate hyperbolic reflections and noise, we adopt a hyperbolic misfit function to minimize a weighted residual using an iteratively reweighted least-squares algorithm and thereby reduce residual reflections and noise. Synthetic and field data tests show that the adopted method can significantly improve the image quality of subsalt and deep heterogeneities. Compared with reverse time migration, it produces better images with fewer artifacts, higher resolution, and more balanced amplitude. Therefore, the adopted method can accurately characterize small heterogeneities and provide a reliable input for seismic interpretation in the prediction of hydrocarbon reservoirs.

On the Introduction of Canny Operator in an Advanced Imaging Algorithm for Real-Time Detection of Hyperbolas in Ground-Penetrating Radar Data

This paper focuses on the use of the Canny edge detector as the first step of an advanced imaging algorithm for automated detection of hyperbolic reflections in ground-penetrating radar (GPR) data. Since the imaging algorithm aims to work in real time; particular attention is paid to its computational efficiency. Various alternative criteria are designed and examined, to fasten the procedure by eliminating unnecessary edge pixels from Canny-processed data, before such data go through the subsequent steps of the detection algorithm. The effectiveness and reliability of the proposed methodology are tested on a wide set of synthetic and experimental radargrams with promising results. The finite-difference time-domain simulator gprMax is used to generate synthetic radargrams for the tests, while the real radargrams come from GPR surveys carried out by the authors in urban areas. The imaging algorithm is implemented in MATLAB.

Evaluating soil moisture estimation from ground‐penetrating radar hyperbola fitting with respect to a systematic time‐domain reflectometry data collection in a boreal podzolic agricultural field

AbstractThe upper 30 cm of the soil profile, which hosts the majority of the root biomass, can be considered as the shallow agricultural root zone of most temperate crops. The electromagnetic wave velocity in the soil obtained from reflection hyperbolas in ground‐penetrating radar (GPR) data can be used to estimate soil moisture (SM). Finding shallow hyperbolas in a radargram and minimizing the subjective error associated with the hyperbola fitting are the main challenges in this approach. Nevertheless, we were motivated by the recent improvements of hyperbola fitting algorithms, which can reduce the subjective error and processing time. To overcome the difficulty of finding very shallow hyperbolas, we applied the hyperbola fitting method to reflections ranging from 27‐ to 50‐cm depth using a 500‐MHz centre‐frequency GPR and compared the estimated moisture with vertically installed, 30‐cm‐long time‐domain reflectometry (TDR) sensors. We also compared TDR and GPR sample areas in a 2‐D plane using different GPR survey types and different hyperbola depths. SM measured with TDR and GPR were not significantly different according to Mann–Whitney's test. Our analyses showed that a root mean square error of 0.03 m3 m−3 was found between the two methods. In conclusion, the proposed method might be suitable to estimate SM with an acceptable accuracy within the root zone if the soil profile is fairly uniform within the application depth range.

Characterizing soil piping networks in loess‐derived soils using ground‐penetrating radar

AbstractSoil piping remains a relatively unexplored phenomenon despite its substantial impacts on water and sediment transfer at the watershed scale at numerous locations around the world. One of the main limitations regarding the study of this singular process is the characterization of the pipe networks (in terms of number, position, dimensions, and connectivity of pipes). In this context, noninvasive subsurface imaging using ground‐penetrating radar (GPR) has proven to be a promising technique. This study used two three‐dimensional (3D), high‐resolution GPR surveys performed in loess‐derived soils to characterize small pipe networks with little prior information about their location. The adopted methodology relies on high spatial resolution scanning, 3D subsurface imaging, and automated detection of reflection hyperbolas using a 200‐MHz center‐frequency antenna. Two small watersheds affected by piping were investigated at Sippenaeken and Kluisbergen (Belgium). Over the two scanned zones, results revealed significant subsurface continuous patterns. Even though the most obvious patterns corresponded to recent or past anthropic activities (e.g., artificial drainage pipes), validation tests confirmed that the chosen methodology can be used for pipe network characterization because some important continuity patterns were related to soil piping: for instance, a fairly small pipe (approximately 10–15 cm in diameter) was detected and validated for more than 100 m. Nevertheless, the high variability in size, depth, and orientation of the pipes imply that GPR may only be truly efficient when using very high spatial resolution scanning, which limits its application to specific conditions not always met in piped areas.

Detection of Soil Pipes Using Ground Penetrating Radar

Soil piping leads to land degradation in almost all morphoclimatic regions. However, the detection of soil pipes is still a methodological challenge. Therefore, this study aims at testing ground penetrating radar (GPR) to identify soil pipes and to present the complexity of soil pipe networks. The GPR surveys were conducted at three sites in the Bieszczady Mountains (SE Poland), where pipes develop in Cambisols. In total, 36 GPR profiles longitudinal and transverse to piping systems were made and used to provide spatial visualization of pipe networks. Soil pipes were identified as reflection hyperbolas on radargrams, which were verified with the surface indicators of piping, i.e., sagging of the ground and the occurrence of pipe roof collapses. Antennas of 500 MHz and 800 MHz were tested, which made possible the penetration of the subsurface up to 3.2 m and 2 m, respectively. Concerning ground properties, antenna frequencies and processing techniques, there was a potential possibility to detect pipes with a minimum diameter of 3.5 cm (using the antenna of lower frequency), and 2.2 cm (with the antenna of higher frequency). The results have proved that soil pipes meander horizontally and vertically and their networks become more complicated and extensive down the slope. GPR is a useful method to detect soil pipes, although it requires field verification and the proper selection of antenna frequency.

Distribution of cold and temperate ice in glaciers on the Nordenskiold Land, Spitsbergen, from ground-based radio-echo sounding

Data of ground-based radio-echo sounding of 16 glaciers located on the Nordenskiold Land, Spitsbergen, carried out in springs of 1999, 2007 and 2010–2013, allowed defining five glaciers as of the cold thermal type while other eleven ones were polythermal glaciers. In the last ones (polythermal) the average thickness of the upper layer of cold ice and the bottom layer of temperate ice was equal to 11-66 m and 15-96 m, respectively. The ratio of these thicknesses varies from 0.32 to 2.28, and the volume fraction of temperate ice in the total volume of the glaciers varies from 1 to 74% and changes from 0 to 50% in the ablation zone up to 80% in the accumulation zone. Thickness of cold ice was determined by measured delay time of radar reflections from cold-temperate surface (CTS) while thickness of temperate ice was derived as a difference between the total thickness of the glacier and the thickness of its cold ice. For interpretation of radar reflections from CTS we used the noticeable distinction in character of the radar reflections from the upper and lower thicknesses of glacier: absence of internal reflections (excluding reflections from buried crevasses and glacier wells) from upper cold ice layer and a great number of reflections of hyperbolic form from the lower layer related to strong scattering of radio waves by water inclusions in the temperate ice. According to the measurements, relative power of the radar reflections from CTS is by 5,5–14,2 dB smaller than those from the bedrock, that can be considered as an indicator of smaller water content at CTS; so, the repeated measurements of their relative power can be used for estimation of temporal changes in the water content at these boundaries. In layers of the temperate ice, the series of vertical hyperbolic reflections penetrating the cold ice down to CTS and further to the bedrock were detected. Such reflections are related to buried crevasses and/or the glacier wells and can serve as sources of the water permeating during the melt periods from the glacier surface down to CTS and bedrock and, thus, influencing on the ice viscosity and fluidity as well as on velocity of the bottom sliding in the polythermal glaciers. Repeated measurements of relative power of reflections from buried crevasses and wells can also be used to study processes of freezing them through and emptying during the period before start of the surface melting. Relation between volume of temperate ice and area of 16 studied glaciers was used to estimate the probability of existence of polythermal glaciers with a temperate ice core in all 202 glaciers in the Nordenskiold Land. 72 glaciers with areas exceeding 1.79 km2 may be referred to the polythermal type. The probable total volume of temperate ice in these glaciers amounts roughly to 10 km3, and with the 95% confidence it is within the interval from 8 to 33 km3. Almost 80% of the whole temperate ice may be concentrated in only five glaciers with area more than 17 km2, that makes up 2.5% of the total number of glaciers and about 30% of their total area. Data presented in this paper demonstrate more sophisticated pattern of the cold and temperate ice distribution within the glaciers than it was earlier known that should be taken into consideration when modeling and forecasting dynamics of the polythermal glaciers and investigating internal processes of the temperate ice formation in such glaciers.

Simultaneous reconstruction of seismic reflections and diffractions using a global hyperbolic Radon dictionary

We have developed a new transform with basis functions that closely resemble seismic reflections and diffractions. The new transform is an extension of the classic hyperbolic Radon transform and accounts for the apex shifts of the seismic reflection hyperbolas and the asymptote shifts of the seismic diffraction hyperbolas. The adjoint and forward operators of the proposed transform are computed using Stolt operators in the frequency domain to increase the computational efficiency of the transform. This new transform is used, in conjunction with a sparse inversion algorithm, to reconstruct common-shot gathers. Our tests indicate that this new transform is an efficient tool for interpolating coarsely sampled seismic data in cases in which one cannot use small data windows to validate the linear event assumption that is often made by Fourier-based reconstruction methods.