Common Offset Data Research Articles

Reanalysis of Polythermal Glacier Thermal Structure Using Radar Diffraction Focusing

AbstractGround‐penetrating radar (GPR) is widely used on polythermal glaciers to image bed topography and detect internal scatter due to water inclusions in temperate ice. The glaciological importance of this is twofold: bed topography is a primary component for modeling the long‐term evolution of glaciers and ice sheets, and the presence of temperate ice and associated englacial water significantly reduces overall ice viscosity. Englacial water has a direct influence on radar velocity, which can result in incorrect observations of bed topography due to errors in depth conversion. Assessment of radar velocities often requires multi‐offset surveys, yet these are logistically challenging and time consuming to acquire, hence techniques to extract velocity from common‐offset data are required. We calculate englacial radar velocity from common offset GPR data collected on Von Postbreen, a polythermal glacier in Svalbard. We first separate and enhance the diffracted wavefield by systematically assessing data coherence. We then use the focusing metric of negative entropy to deduce a migration velocity field and produce a velocity model which varies spatially across the glacier. We show that this velocity field successfully differentiates between areas of cold and temperate ice and can detect lateral variations in radar velocity close to the glacier bed. This velocity field results in consistently lower ice depths relative to those derived from a commonly assumed constant velocity, with an average difference of 4.9 ± 2.5% of local ice depth. This indicates that diffraction focusing and velocity estimation are crucial in retrieving correct bed topography in the presence of temperate ice.

Percolation monitoring and water content estimation by Ground Penetrating Radar in a controlled environment

We investigated the percolation of water within a controlled environment in order to recover the EM properties and the internal structure of the materials, and to better understand the drainage processes involved. We implemented an analogue model that accurately replicates a green roof, from the construction materials to the geometry. We acquired several common offset GPR data sets on the entire surface of the model, both before and during different irrigation tests. We separately analyzed variations in the reflected amplitudes and in the EM velocities, the latter of which were calculated by combining the measured thickness of the model with the arrival times of the recorded reflections. The signal amplitudes obtained before and during irrigation are compared in order to estimate the attenuation factor at the different stages of the irrigation process. We use the attenuation factor and the EM velocities to estimate the relative permittivity of the topsoil mixture, from which we then calculate the water content, the porosity, and the relative electrical permittivity of the solid matrix by applying well known empirical formulas. The results were validated by comparing them with independent direct measurements.

Three dimensional reverse time migration on common offset GPR data for void imaging

Three dimensional (3D) Reverse time migration (RTM), as an indispensable imaging technique, has been widely applied to the observed seismic data imaging. However, the RTM of Ground Penetrating radar (GPR) is usually implemented in its two-dimensional (2D) from. This paper proposes a 3D RTM algorithm on common offset GPR data for void imaging. In this algorithm, the 3D finite difference time domain (FDTD) method is applied to calculate the backward extrapolation of electromagnetic fields. And the time zero imaging condition is applied to obtain the final RTM results. Comparisons of the imaging results of 3D and 2D RTM demonstrated that the 3D RTM imaging results were superior to those of 2D RTM. And 3D spatial distribution of Void can be imaged by the proposed 3D RTM algorithm with high accuracy, which can help the subsequent interpretation of GPR profile.

Ground-penetrating radar refraction imaging with stacked refraction convolution section method

We have evaluated a technique initially developed for the seismic refraction imaging, the stacked refraction convolution section (SRCS), which we have properly adapted to process ground-penetrating radar (GPR) refraction data. Through a mute operation, the subsurface refracting signals, recorded by the receiver from two reciprocal sources, are selected. Following that, a velocity analysis by means of the crosscorrelation of the refracted signals and the convolution of resulting traces is performed. The refraction image in intercept times is successively derived from three main steps, namely: (1) the convolution of the subsurface refracted signals, (2) the crosscorrelation of convolved trace with the reciprocal refracted signal, and (3) the stacking of crosscorrelated traces over all source couples. The technique is not only suitable for the processing of GPR data acquired with two or more reciprocal common source profiles but it is also convenient for its low acquisition cost in addition to the simplicity of software implementation and short processing times. We have evaluated the technique on a real GPR data set to characterize a near-surface morphostructure associated with a deep-seated gravitational slope deformation affecting Mt. Watles (Upper Venosta Valley, Italy). Results of the SRCS technique were validated against the direct trenching log data up to approximately 3 m in depth and complemented by the reflection processing outputs of common-source and common-offset data acquired along the line. The SRCS and common-midpoint processing provide the best reconstruction of the subsurface morphology of a shallow basement (approximately [Formula: see text] depth), characterized by a velocity range of [Formula: see text] and made of strongly to moderately weathered paragneiss. The full-wave modeling response of the reconstructed model demonstrates good agreement with the recorded signals.

Common midpoint versus common offset acquisition geometry in seismic imaging

We compare and contrast the qualitative nature of backprojected imagesobtained in seismic imaging when common offset data are usedversus when common midpoint data are used. Our results showthat the image obtained using common midpoint data contains artifactswhich are not present with common offset data. Although there aresituations where one would still want to use common midpoint data,this result points out a shortcoming that should be kept in mind wheninterpreting the images.

Evaluation of Internal Structure, Volume and Mass of Glacial Bodies by Integrated LiDAR and Ground Penetrating Radar Surveys: The Case Study of Canin Eastern Glacieret (Julian Alps, Italy)

We propose an integrated methodology to image the internal structure, evaluate the volume and estimate the densities of different units within ice bodies, useful for more precise mass estimation of very small glaciers. The procedure encompasses light detection and ranging (LiDAR) and ground penetrating radar (GPR) common offset data. The case study is the Canin Eastern Glacieret (CEG), a very small and maritime glacier in the Eastern Alps, and one of the lowermost glaciers of the European Alps. We calculate both volumetric and mass variations of the analysed ice body by integrating GPR measurements with LiDAR surveys acquired in different years (2006 and 2011). Between 2006 and 2011, the area of the glacieret increased from 8,510 to 17,530 m2 with a gain of 9,016 m2. The observed volume increase has been estimated in 96,350 m3 (+97 %), which corresponds to a positive mass balance of 3.89 m w.e.. This quite unusual finding in the present global warming behaviour is mainly due to the above-average winter accumulation (cw) in the considered period. Moreover, the winter season 2008–2009 represented an exceptional event with a cw equal to 13.38 m, the highest of the available record. Thanks to density estimation, we infer the total mass of the CEG at the time of the geophysical surveys, comparing such results with the ones obtained with available empirical equations, observing an important mass gain in the 5 years considered.

Velocity analysis from common offset GPR data inversion: theory and application to synthetic and real data

We implemented a procedure to estimate the electromagnetic (EM) velocity using common offset ground penetrating radar (GPR) data. The technique is based on the inversion of reflection amplitudes to compute the series of reflection coefficients used to estimate the velocity in each interpreted layer. The proposed method recursively calculates the incident angles at any interface, taking into account the offset between antennas, and needs as input, in addition to the picked amplitudes values, a reference amplitude for each analysed GPR trace and a velocity value for the first (shallowest) layer. The latter two parameters can be estimated directly from the available data or can be better constrained by further dedicated GPR acquisitions or by additional direct measurements. We critically evaluated the performances for both synthetic and real data acquired with different antenna frequencies and we demonstrated that the new method can be applied in several real situations. Despite the necessary approximations and simplifying hypotheses, the velocity values calculated for each layer are consistent with direct information and with cross-validations obtained considering profiles acquired using different antennas and various path directions. Tests of the method on synthetic and real data sets show that the errors in the calculated velocity fields are quite low and comparable with more demanding velocity analysis techniques. The obtained EM velocity field is crucial in many processing steps, such as, for example, true amplitude recovery, depth conversion and imaging, and provide essential information to characterize the subsurface materials.

A new fast methodology to estimate the density of frozen materials by means of common offset GPR data

Abstract We propose a methodology to estimate the density of frozen media (snow, firn and ice) using common offset (CO) GPR data. The technique is based on reflection amplitude analysis to calculate the series of reflection coefficients used to estimate the dielectric permittivity of each layer. We determine the vertical density variations for all the GPR traces by applying an empirical equation. We are thus able to infer the nature of frozen materials, from fresh snow to firn and ice. The proposed technique is critically evaluated and validated on synthetic data and further tested on real data of the Glacier of Mt. Canin (South-Eastern Alps). Despite the simplifying hypotheses and the necessary approximations, the average values of density for different levels are calculated with acceptable accuracy. The resulting large-scale density data are fundamental to estimate the water equivalent (WE), which is an essential parameter to determine the actual water mass within a certain frozen volume. Moreover, this analysis can help to find and locate debris or moraines embedded within the ice bodies.

Interferometric Multichannel Analysis of Surface Waves (IMASW)

Abstract Refraction microtremor (ReMi) and multichannel analysis of surface waves (MASW) are effective approaches to estimate shallow shear-wave velocity ( V S ) structure often needed to estimate ground motions using recent ground motion prediction relations. Interferometric MASW (IMASW) uses slowness-frequency slant-stack analyses combined with interferometric time-domain dispersion analyses to improve resolution of lower-frequency Rayleigh-wave dispersion to better constrain V S . Cross-correlation interferometry is used to obtain deterministic correlation Green’s function (CGF) IMASW seismograms from ambient-noise and/or active-source wave fields contained in ReMi and/or MASW data. The CGFs are processed using the multiple-filter technique to estimate phase and group dispersion. In the IMASW approach, active seismic sources ensure that the stationary-phase contributions to cross correlations dominate CGF responses. In a single IMASW profile, each geophone represents a virtual source, and the IMASW approach stacks CGF common-offset data from all virtual sources to obtain a single averaged forward- and reverse-record section. CGF time-domain and slowness-frequency phase-slowness estimates are combined with CGF time-domain group slowness estimates for a consistency check on dispersion picks. A multistate Monte Carlo approach is used to estimate mean slowness depth and slowness uncertainties. IMASW is evaluated with passive ReMi data from two sites and active-source IMASW at six sites with independent downhole velocity–depth logs. Comparison of six P-S suspension log–IMASW profile pairs across the Van Norman Complex in northern San Fernando Valley shows that, on average, 30-m-depth shear-wave velocity estimates between the two methods differed by P-S suspension log measurements of V S were made at the IMASW profile midpoint, the IMASW V S depth inversions resolve 3-m thickness V S variations accurately to the bottom of one borehole at 40-m depth and to 100-m depth at a >200-m-deep borehole site.

Migration/inversion for incident waves synthesized from common-shot data gathers

Wavefield synthesis is a process for producing reflection responses from more general sources or from prescribed incident waves by combining common-shot data gathers. Synthesis can provide surveywide data sets, similar in that regard to common-offset data gathers, but with the added advantage that each synthesized data set is a solution to a single wave equation. A common-offset data set does not have this last feature. Thus, synthesized data sets can be processed by true-amplitude wave-equation migration. The output is then known to be true amplitude in the same sense as is the output of Kirchhoff inversion. That is, the peak amplitude is proportional to the ray-theoretic reflection coefficient at a determinable specular incidence angle multiplied bythe area under the frequency-domain source signature and scaled by [Formula: see text]. Alternatively, the Kirchhoff inversion of synthesized data has a Beylkin determinant that is expressed in terms of the ray-theoretic Green’s function amplitude. This is in contrast to 3D common-offset inversion, wherein the Beylkin determinant is most difficult to compute. We present a theory of data synthesis and true-amplitude migration/inversion based on the application of Green’s theorem to the ensemble of common-shot gathers and prescribed more general sources or prescribed incident waves. Specific examples include delayed-shot line sources and incident dipping plane waves at the upper surface. We also discuss two cases in which waves are prescribed at depth, back-projected to the upper surface, and then used to generate a synthesized data set.

Multi-offset ground penetrating radar data for improved imaging in areas of lateral complexity — Application at a Native American site

Multi-offset ground penetrating radar (GPR) data offers numerous imaging benefits over common offset GPR data, such as increased signal to noise ratio and depth penetration, and improved reflector continuity and dip imaging. Another relevant benefit of multi-offset data is the improved lateral imaging capabilities it provides. Neglecting lateral complexity considerations can produce an erroneous interpretation. An example from a Native American archaeological site highlights how 200 MHz multi-offset data provides a better estimate of the lateral density of possible archaeological material, as well as more accurate depth estimates. This is compared to 200 MHz common offset data, which produced an erroneous interpretation both in terms of potential archaeological material density and depth. This analysis also highlights an important caveat of multi-offset acquisition, which is having suitable near-surface conditions to realize improved data quality. Common offset reflectivity is very sensitive to changes in water saturation, and multi-offset data even more so due to the additional dependence of reflectivity on the multiple angles of investigation. A multi-offset section at the same location, but acquired under drier conditions, produced little imaging improvement over the common offset section. Even given the imaging benefits of multi-offset data, it is seldom acquired mainly due to the tedious task of single channel acquisition with bistatic GPR systems. Acquiring the multi-offset traces continuously as common source gathers while still maintaining positioning accuracy and signal quality halved the acquisition time of this multi-offset dataset.

Theory of true-amplitude one-way wave equations and true-amplitude common-shot migration

One-way wave operators are powerful tools for forward modeling and migration. Here, we describe a recently developed true-amplitude implementation of modified one-way operators and present some numerical examples. By “true-amplitude” one-way forward modeling we mean that the solutions are dynamically correct as well as kinematically correct. That is, ray theory applied to these equations yields the upward- and downward-traveling eikonal equations of the full wave equation, and the amplitude satisfies the transport equation of the full wave equation. The solutions of these equations are used in the standard wave-equation migration imaging condition. The boundary data for the downgoing wave is also modified from the one used in the classic theory because the latter data is not consistent with a point source for the full wave equation. When the full wave-form solutions are replaced by their ray-theoretic approximations, the imaging formula reduces to the common-shot Kirchhoff inversion formula. In this sense, the migration is true amplitude as well. On the other hand, this new method retains all of the fidelity features of wave equation migration. Computer output using numerically generated data confirms the accuracy of this inversion method. However, there are practical limitations. The observed data must be a solution of the wave equation. Therefore, the data must be collected from a single common-shot experiment. Multiexperiment data, such as common-offset data, cannot be used with this method as presently formulated.

3-D Kirchhoff Migration of GPR Data to Image the Inside of a Stone Pagoda

We have chosen the GPR method for investigating the inner structure of a stone pagoda in a non-destructive way. The selection of a suitable source frequency of the GPR antenna is the key because the main frequency of its pulse controls the resolution and the depth of the investigation. Through theoretical consideration and numerical simulation, we found that 500 to 800 MHz is suitable for a field model with a foundation part of 3 to 4 m. To image the inner structure we selected 3-D Kirchhoff prestack depth migration technique used in seismic processing. We have used the modified migration algorithm for the source and receiver configurations of common offset GPR data. To verify the scheme, we calculated the synthetic data using the 3-D FDTD algorithm and applied the migration technique to it. Through these experiments, we confirmed that the 3-D Kirchhoff prestack depth migration technique is a very powerful tool to image the inside of a stone pagoda with high resolution. We have also applied the technique to the field data of the foundation of a five-story stone pagoda at Jeongnim temple site in Buyeo City, Korea. Based on the 3-D migrated images, we inferred that the structure of the foundation of this pagoda seemed to be preserved quite well and the thickness of the outer wall was about 0.5 m.

A FREEWARE PACKAGE FOR THE ANALYSIS AND INTERPRETATION OF COMMON-OFFSET GROUND PROBING RADAR DATA, BASED ON GENERAL PURPOSE COMPUTING ENGINES

The Ground Probing Radar (GPR) has become an invaluable means of exploring shallow structures for geoscientific, engineering environmental and archaeological work. At the same time, GPR analysis software is mostly proprietary and expensive. The academic freeware community has been slow to react the limited free software is usually highly focused and generally unorganized. Herein we report the beginning of an attempt to remedy this situation with a cross-platform freeware analysis and interpretation package, which can also be expandable and customizable to the requirements of a particular user with relatively little programming effort. Almost ideal platforms for the development of such a kind of software are general purpose computing engines, such as MATLAB ™ and/or OCTAVE. These provide two very similar, cross-platform and complete environments for the development of advanced analysis software. We have designed a two-layered software system. The Bottom Layer comprises a set of self-contained and self-documented functions to handle, visualize, process and interpret GPR data and is expandable with addition of a user's own functions. The Top Layer organizes these functions, automating data management and streamlining the flow of work by means of a GU Interface. At the present stage of development, this GPR analysis offers a decent and in many respects advanced means of treating and interpreting common-offset data; future releases may even become competitive, if maintained and developed by collective effort along the spirit of the GNU project.

True amplitude wave equation migration arising from true amplitude one-waywave equations

One-way wave operators are powerful tools for use in forward modelling andinversion. Their implementation, however, involves introduction of the square rootof an operator as a pseudo-differential operator. Furthermore, a simple factoringof the wave operator produces one-way wave equations that yield the same traveltimes as the full wave equation, but do not yield accurate amplitudes except forhomogeneous media and for almost all points in heterogeneous media. Here, wepresent augmented one-way wave equations. We show that these equations yieldsolutions for which the leading order asymptotic amplitude as well as thetravel time satisfy the same differential equations as the correspondingfunctions for the full wave equation. Exact representations of the square-rootoperator appearing in these differential equations are elusive, except incases in which the heterogeneity of the medium is independent of thetransverse spatial variables. Here, we address the fully heterogeneous case.Singling out depth as the preferred direction of propagation, we introduce arepresentation of the square-root operator as an integral in which a rationalfunction of the transverse Laplacian appears in the integrand. This allows usto carry out explicit asymptotic analysis of the resulting one-way waveequations. To do this, we introduce an auxiliary function that satisfies a lowerdimensional wave equation in transverse spatial variables only. We prove thatray theory for these one-way wave equations leads to one-way eikonalequations and the correct leading order transport equation for the full waveequation. We then introduce appropriate boundary conditions at z = 0 togenerate waves at depth whose quotient leads to a reflector map and an estimateof the ray theoretical reflection coefficient on the reflector. Thus, these trueamplitude one-way wave equations lead to a ‘true amplitude wave equationmigration’ (WEM) method. In fact, we prove that applying the WEMimaging condition to these newly defined wavefields in heterogeneous medialeads to the Kirchhoff inversion formula for common-shot data when theone-way wavefields are replaced by their ray theoretic approximations.This extension enhances the original WEM method. The objective ofthat technique was a reflector map, only. The underlying theory did notaddress amplitude issues. Computer output obtained using numericallygenerated data confirms the accuracy of this inversion method. However, thereare practical limitations. The observed data must be a solution of thewave equation. Therefore, the data over the entire survey area must becollected from a single common-shot experiment. Multi-experiment data, suchas common-offset data, cannot be used with this method as currentlyformulated. Research on extending the method is ongoing at this time.

Numerical Integration for Kirchhoff Migration

In 3D seismic surveys, common offset data often involve an irregular distribution of midpoints. In such a situation, common offset Kirchhoff migration cannot be correctly performed by means of a mere discrete diffraction stack algorithm. Such an algorithm indeed corresponds to an inconsistent numerical integration formula. To overcome this difficulty, genuine numerical integration formulas (yielding a consistent approximation of the continuous diffraction stack) have to be used, e.g. numerical integration formulas based on polynomials leading to the so-called Lagrange or Hermite interpolations. A numerical integration formula based on Lagrange interpolation can cope with irregularly sampled midpoints provided that the density of midpoints involved in the common offset gather is sufficient. Besides, Hermite interpolation, more accurate in theory than the former, also provides relative improvement in the images at the vicinity of the migrated event,. Both techniques can be implemented by means of a simple preprocessing (adequate scaling) of the data. Thus they are quite easy to implement in any existing diffraction stack code. In addition, they can be used in combination with filters to prevent aliasing of the migration operator. The additional computation cost is negligible compared with the cost of running the diffraction stack itself.

Influence of Data Irregularities on 3d Common Offset Migration

In 3D seismics offset is a vector characterized by the source-receiver distance and azimuth. Due to irregularities in the acquisition (for instance streamer feathering in marine acquisition) common offset data are not available and, in turn, 3D common offset migration does not make sense any longer. We then introduce the concept of migration by offset class: it is a straightforward extension of common offset migration in which we migrate all traces that belong to a given offset class, namely all traces with offset close to a given one. The result of such a migration depends of course on how the offset class is constructed or, in other words, on what is meant with close . The aim of this paper is to investigate by means of a 3D numerical study how to design offset classes so as to obtain migrated images that can be interpreted without trouble (such an interpretation is a key element for a successful migration velocity analysis). We have to find a trade-off between two extremes:- a too loose offset class that would mix heterogeneous offsets (in particular mixing substantially different azimuths can be dangerous); - a too narrow offset class that would result in sparse seismic traces with, in turn, an inadequate coverage of the reflector. The regularity, within an offset class, of the offset variation as well as the one of the distribution of midpoints are parameters that can have a drastic influence on the quality of the migrated image. It is shown that migration by offset class appears as a robust procedure all the more than the offset varies slowly with the midpoint coordinate within an offset class. Besides, the smaller the mean offset norm, the lower is the contamination of the image due to the mixing of azimuths within an offset class.

Archaeological investigation in Sendai Castle using ground-penetrating radar

Ground-penetrating radar (GPR) was applied to the 400-year-old Sendai Castle in Japan during site excavation. The aim of the experiment was to detect old stone walls under the castle, and to compare the effectiveness of 50- and 100-MHz antennae in locating and identifying archaeological features. Both common-offset and common-midpoint (CMP) data of 50- and 100-MHz were collected along three survey lines. We processed the data and compared the results obtained by different observation and data-processing methods. It is easy to identify reflections from underground objects on 1-m common-offset 100-MHz profiles, but it is difficult to recognize them on 50-MHz profiles of the same offset. The comparable post-stack migration result of the stacked data of 50-MHz and the migration stack section of 50-MHz CMP data with the results of 100-MHz common-offset data, however, indicate that low frequency radar images can be improved by both data acquisition and processing techniques. We also know from the processed results that the migration stack method is better than the post-stacking migration method. The GPR results are consistent to a great extent with the excavations. The GPR method can be applied to archaeological investigations, before and during excavation. Appropriate data acquisition and processing schemes are important in archaeological prospection using GPR. Copyright © 2001 John Wiley & Sons, Ltd.

Velocity inversion from common offset data

The authors consider all of three-dimensional (x,y,z) space to be a constant density acoustic medium, thus characterised by a sound speed c(x,y,z). They assume c identical to 1 for z<or=0 and c=(x,z) only for z>0. At each point (xs, 0,0) an impulsive source of acoustic waves is set off, and the resulting reflected waves are measured as a function of time t, for 0<or=t<or=Tmax at receiver location (xR, 0,0) with xR=xs+h for some fixed offset h. From this data they wish to determine the velocity c(x,z) for 0<or=z<or=Zmax=1/2(Tmax2-h2)12/. They study the Born approximation to this problem, i.e. they assume that c-1 is small enough so that the map from velocity to surface response can be adequately approximated by its linearisation at reference velocity c0 identical to 1. They show that this inverse problem is equivalent to an uncoupled system of one-dimensional, second-kind volterra integral equations, indexed by horizontal frequency. Using properties of the kernels in these equations they derive continuous dependence and uniqueness results for the inverse problem, and a constructive solution method is given. The case of multi-offset data is also considered.