1 

Characterization of a heterogeneous landfill using seismic and electrical resistivity data
Understanding the processes occurring inside a landfill is important for improving the treatment of landfills. Irrigation and recirculation of leachate are widely used in landfill treatments. Increasing the efficiency of such treatments requires a detailed understanding of the flow inside the landfill. The flow depends largely on the heterogeneous distribution of density. It is, therefore, of great practical interest to determine the density distribution affecting the flow paths inside a landfill. Studies in the past have characterized landfill sites but have not led to highresolution, detailed quantitative results. We performed an Swave reflection survey, multichannel analysis of surface waves (MASW), and electrical resistivity survey to investigate the possibility of delineating the heterogeneity distribution in the body of a landfill. We found that the highresolution Swave reflection method offers the desired resolution. However, in the case of a very heterogeneous landfill and a high noise level, the processing of highresolution, shallow reflection data required special care. In comparison, MASW gave the general trend of the changes inside the landfill, whereas the electrical resistivity (ER) survey provides useful clues for interpretation of seismic reflection data. We found that it is possible to localize finescale heterogeneities in the landfill using the Swave reflection method using a highfrequency vibratory source. Using empirical relations specific to landfill sites, we then estimated the density distribution inside the landfill, along with the associated uncertainty considering different methods. The final interpretation was guided by supplementary information provided by MASW and ER tomography.

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2 

Sensitivity of the nearsurface vertical electric field land ControlledSource Electromagnetic monitoring
We investigate potential benefits of measuring the vertical electric field component in addition to the routinely measured horizontal electric field components in onshore timelapse controlledsource electromagnetics. Synthetic electromagnetic data based on a model of the Schoonebeek onshore oil field are used. We confirm that the vertical electric field component is more sensitive to small changes in the reservoir than the horizontal components, yet its amplitudes are small. Accordingly, optimal sourcereceiver geometry and precise knowledge of the verticality of the receiver dipole will be required for successful utilization of the vertical electric field.

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3 

Experimental verification of stressinduced anisotropy

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4 

Biangular decomposition of seismic data

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5 

A theoretical and experimental approach to the geophoneground coupling problem based on acoustic reciprocity

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6 

A microelectromechanical system digital 3C array seismic cone penetrometer
A digital 3C array seismic cone penetrometer has been developed for multidisciplinary geophysical and geotechnical applications. Seven digital triaxial microelectromechanical system accelerometers are installed at 0.25m intervals to make a 1.5mlong downhole seismic array. The accelerometers have a flat response up to 2 kHz. The seismic array is attached to a class 1 digital seismic cone, which measures cone tip resistance, sleeve friction, porepressure, and inclination. The downhole 3C array can be used together with impulsive seismic sources and/or highfrequency vibrators that are suitable for highresolution shallow applications. Results from two field experiments showed that a good data quality, including a constant source function within an array, and a dense depthsampling allowed robust estimation of seismic velocity profiles in the shallow subsoil. Using horizontal and vertical seismic sources, downhole 9C seismic array data can be easily acquired. The quality of the shearwave data is much superior when the surface seismic source is a controlled, highfrequency vibrator in stead of a traditional sledge hammer. A remarkable correlation in depth, in a fine scale, between lowstrain seismic shear wave velocity and highstrain cone tip resistance could be observed. The array measurements of the fullelastic wavefield and the broad spectral bandwidth are useful in investigating frequencydependent seismic wave propagation in the porous nearsurface soil layers, which is informative of the in situ fluidflow properties. Stable estimates of dispersive seismic velocity and attenuation can be obtained.

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7 

A new empirical complex electrical resistivity model
Macroscopic measurements of electrical resistivity require frequencydependent effective models that honor the microscopic effects observable in macroscopic measurements. Effective models based on microscopic physics exist alongside with empirical models. We adopted an empirical model approach to modify an existing physical model. This provided a description of electrical resistivity as a function of not only frequency, but also water saturation. We performed twoelectrode laboratory measurements of the complex resistivity on a number of fine and mediumgrained unconsolidated sand packs saturated with water of three different salinities. For frequencies between 0.1 and 1 MHz, the data were fitted with the new model and compared to fits with Archie’s law. Our model described the relaxation times and DC resistivity values as negative exponential functions with increasing water saturation. All data could be accurately described as a function of frequency and water saturation with nine parameters.

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8 

Increasing the sensitivity of controlledsource electromagnetics with synthetic aperture
Controlledsource electromagnetics (CSEM) has been used as a derisking tool in the hydrocarbon exploration industry. We apply the concept of synthetic aperture to the lowfrequency electromagnetic field in CSEM. Synthetic aperture sources have been used in radar imaging for many years. Using the synthetic aperture concept, big synthetic sources can be constructed by adding the response to small sources (building blocks) in different ways, and consequently, big sources with different radiation patterns can be created. We show that the detectability of hydrocarbons is significantly enhanced by applying synthetic aperture to CSEM data. More challenging targets such as deep reservoirs (4km belowsea floor) can be detected. The synthetic aperture technique also increases the sensitivity of the field to subsurface targets in the towing streamer acquisition.We also show that a pseudovertical source (orthogonally distributed dipole pairs) can be constructed synthetically, and that the detection capability of this pseudovertical source is increased by applying field steering. The synthetic aperture concept opens a new line of research in CSEM, with the freedom to design suitable synthetic aperture sources for a given purpose.

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9 

Quasianalytical method for frequencytotime conversion in CSEM applications
Frequencytotime transformations are of interest to controlledsource electromagnetic methods when timedomain data are inverted for a subsurface resistivity model by numerical frequencydomain modeling at a selected, small number of frequencies whereas the data misfit is determined in the time domain. We propose an efficient, Pronytype method using frequencydomain diffusivefield basis functions for which the timedomain equivalents are known. Diffusive fields are characterized by an exponential part whose argument is proportional to the square root of frequency and a part that is polynomial in integer powers of the square root of frequency. Data at a limited number of frequencies suffice for the transformation back to the time. In the exponential part, several diffusiontime values must be chosen. Once a suitable range of diffusiontime values are found, the method is quite robust in the number of values used. The highest power in the polynomial part can be determined from the source and receiver type. When the frequencydomain data are accurately approximated by the basis functions, the timedomain result is also accurate. This method is accurate over a wider time range than other methods and has the correct latetime asymptotic behavior. The method works well for data computed for layered and 3D subsurface models.

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10 

Focusing the wavefield inside an unknown 1D medium: Beyond seismic interferometry
With seismic interferometry one can retrieve the response to a virtual source inside an unknown medium, if there is a receiver at the position of the virtual source. Using inverse scattering theory, we demonstrate that, for a 1D medium, the requirement of having an actual receiver inside the medium can be circumvented, going beyond seismic interferometry. In this case, the wavefield can be focused inside an unknown medium with independent variations in velocity and density using reflection data only.

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11 

Blended acquisition with dispersed source arrays
Blended source arrays are historically configured with equal source units, such as broadband vibrators (land) and broadband airgun arrays (marine). I refer to this concept as homogeneous blending. I have proposed to extend the blending concept to inhomogeneous blending, meaning that a blended source array consists of different source units. More specifically, I proposed to replace in blended acquisition the traditional broadband sources by narrowband versions — imagine coded single air guns with different volumes or coded single narrowband vibrators with different central frequencies — together representing a dispersed source array (DSA). Similar to what we see in today's audio systems, the DSA concept allows the design of dedicated narrowband source elements that do not suffer from the low versus high frequency compromise. In addition, the DSA concept opens the possibility to use source depths and spatial sampling intervals that are optimum for the low, mid, and highfrequency sources (multiscale shooting grids). DSAs are considered to be an important step in robotizing the seismic acquisition process.

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12 

Seismic interferometry: Reconstructing the earth's reflection response
In 1968, Jon Claerbout showed that the reflection response of a 1D acoustic medium can be reconstructed by autocorrelating the transmission response. Since then, several authors have derived relationships for reconstructing Green's functions at the surface, using crosscorrelations of (noise) recordings that were taken at the surface and that derived from subsurface sources.For acoustic media, we review relations between the reflection response and the transmission response in 3D inhomogeneous lossless media. These relations are derived from a oneway wavefield reciprocity theorem. We use modeling results to show how to reconstruct the reflection response in the presence of transient subsurface sources with distinct excitation times, as well as in the presence of simultaneously acting noise sources in the subsurface. We show that the quality of reconstructed reflections depends on the distribution of the subsurface sources. For a situation with enough subsurface sources — that is, for a distribution that illuminates the subsurface area of interest from nearly alldirections — the reconstructed reflection responses and the migrated depth image exhibit all the reflection events and the subsurface structures of interest, respectively. With only a few subsurface sources, that is, with insufficient illumination, the reconstructed reflection responses are noisy and can even become kinematically incorrect. At the same time, however, the depth image, which was obtained from their migration, still shows clearly all the illuminated subsurface structures at their correct positions.For the elastic case, we review a relationship between the reflection Green's functions and the transmission Green's functions derived from a twoway wavefield reciprocity theorem. Using modeling examples, we show how to reconstruct the different components of the particle velocity observed at the surface and resulting from a surface traction source. This reconstruciton is achieved using crosscorrelations of particle velocity components measured at the surface and resulting from separate P and Swave sources in the subsurface.

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13 

Spurious multiples in seismic interferometry of primaries
Seismic interferometry is a technique for estimating the Green's function that accounts for wave propagation between receivers by correlating the waves recorded at these receivers. We present a derivation of this principle based on the method of stationary phase. Although this derivation is intended to be educational, applicable to simple media only, it provides insight into the physical principle of seismic interferometry. In a homogeneous medium with one horizontal reflector and without a free surface, the correlation of the waves recorded at two receivers correctly gives both the direct wave and the singly reflected waves. When more reflectors are present, a product of the singly reflected waves occurs in the crosscorrelation that leads to spurious multiples when the waves are excited at the surface only. We give a heuristic argument that these spurious multiples disappear when sources below the reflectors are included. We also extend the derivation to a smoothly varying heterogeneous background medium.

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14 

Imaging of multiple reflections
Current multipleremoval algorithms in seismic processing use either differential moveout or predictability. If the differential moveout between primaries and multiples is small, prediction is the only option available. In the last decade, multidimensional predictionerror filtering by weighted convolution, such as surfacerelated multiple elimination (SRME), have proved to be very successful in practice. So far, multiples have been considered as noise and have been discarded after the removal process. In this paper, we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability. In the near future, one may expect that the socalled weightedcrosscorrelation (WCC) concept may offer an attractive alternative in approaching the multiple problem. WCC creates an option to avoid the adaptive subtraction process as applied in predictionerror algorithms. Moreover, it allows the transformation of multiples into primaries. The latter means that seismic imaging with primaries and multiples (nonlinear process) can be implemented by a sequence of linear processes, including the transformation of multiples into primaries and the imaging of primaries.

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15 

Fourier reconstruction of marinestreamer data in four spatial coordinates
Many methods exist for interpolation of seismic data in one and two spatial dimensions, but few can interpolate properly in three or four spatial dimensions. Marine multistreamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled. We approach the problem of interpolation of marinestreamer data in four spatial dimensions by splitting the problem into a 1D interpolation along the densely sampled streamers and a 3D Fourier reconstruction for the remaining spatial coordinates. In Fourier reconstruction, the Fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a leastsquares inversion. The method is computationally efficient, requires no subsurface information, and can handle uniform grids with missing data as well as nonuniform grids or random sampling.The output grid of the 1D interpolation in the first step is arbitrary. When the output grid has uniform inline midpoints spacing, the 3D Fourier reconstruction in the second step is performed in the crossline midpoint, absolute offset, and azimuth coordinates. When the first step outputs to uniform absolute offset, the 3D Fourier reconstruction handles the crossline/inline midpoint and the azimuth coordinates. In both cases, the main innovation is the inclusion of the azimuthal coordinate in the Fourier reconstruction. The azimuth multiplicity must be increased for the method to be successful, which means that overlap shooting is required. We have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored. Potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3D multiple prediction and regularization to reduce samplingrelated differences in processing of timelapse data.

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16 

Planewave depth migration
We present fast and efficient planewave migration methods for densely sampled seismic data in both the source and receiver domains. The methods are based on slant stacking over both shot and receiver positions (or offsets) for all the recorded data. If the dataacquisition geometry permits, both inline and crossline source and receiver positions can be incorporated into a multidimensional phasevelocity space, which is regular even for randomly positioned input data. By noting the maximum time dips present in the shot and receiver gathers and constantoffset sections, the number of plane waves required can be estimated, and this generally results in a reduction of the data volume used for migration. The required traveltime computations for depth imaging are independent for each particular planewave component. It thus can be used for either the source or the receiver plane waves during extrapolation in phase space, reducing considerably the computational burden. Since only vertical delay times are required, many traveltime techniques can be employed, and the problems with multipathing and first arrivals are either reduced or eliminated. Further, the planewave integrals can be pruned to concentrate the image on selected targets. In this way, the computation time can be further reduced, and the technique lends itself naturally to a velocitymodeling scheme where, for example, horizontal and then steeply dipping events are gradually introduced into the velocity analysis. The migration method also lends itself to imaging in anisotropic media because phase space is the natural domain for such an analysis.

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17 

Focal transformation, an imaging concept for signal restoration and noise removal
Interpolation of data beyond aliasing limits and removal of noise that occurs within the seismic bandwidth are still important problems in seismic processing. The focal transform is introduced as a promising tool in data interpolation and noise removal, allowing the incorporation of macroinformation about the involved wavefields. From a physical point of view, the principal action of the forward focal operator is removing the spatial phase of the signal content from the input data, and the inverse focal operator restores what the forward operator has removed. The strength of the method is that in the transformed domain, the focused signals at the focal area can be separated from the dispersed noise away from the focal area. Applications of particular interest in preprocessing are interpolation of missing offsets and reconstruction of signal beyond aliasing. The latter can be seen as the removal of aliasing noise.

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18 

A new iterative solver for the timeharmonic wave equation
The timeharmonic wave equation, also known as the Helmholtz equation, is obtained if the constantdensity acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In three dimensions, direct methods cannot be used for problems of practical sizes because the computational time and the amount of memory required become too large. Iterative methods are an alternative. These methods are often based on a conjugate gradient iterative scheme with a preconditioner that accelerates its convergence. The iterative solution of the timeharmonic wave equation has long been a notoriously difficult problem in numerical analysis. Recently, a new preconditioner based on a strongly damped wave equation has heralded a breakthrough. The solution of the linear system associated with the preconditioner is approximated by another iterative method, the multigrid method. The multigrid method fails for the original wave equation but performs well on the damped version. The performance of the new iterative solver is investigated on a number of 2D test problems. The results suggest that the number of required iterations increases linearly with frequency, even for a strongly heterogeneous model where earlier iterative schemes fail to converge. Complexity analysis shows that the new iterative solver is still slower than a timedomain solver to generate a full time series. We compare the timedomain numeric results obtained using the new iterative solver with those using the direct solver and conclude that they agree very well quantitatively. The new iterative solver can be applied straightforwardly to 3D problems.

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19 

Seismic interferometryturning noise into signal
Turning noise into useful data—every geophysicist's dream? And now it seems possible. The field of seismic interferometry has at its foundation a shift in the way we think about the parts of the signal that are currently filtered out of most analyses—complicated seismic codas (the multiply scattered parts of seismic waveforms) and background noise (whatever is recorded when no identifiable active source is emitting, and which is superimposed on all recorded data). Those parts of seismograms consist of waves that reflect and refract around exactly the same subsurface heterogeneities as waves excited by active sources. The key to the rapid emergence of this field of research is our new understanding of how to unravel that subsurface information from these relatively complexlooking waveforms. And the answer turned out to be rather simple. This article explains the operation of seismic interferometry and provides a few examples of its application.

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20 

Introduction to the supplement on seismic interferometry

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