1 

Experimental verification of stressinduced anisotropy

[PDF]

2 

Biangular decomposition of seismic data

[PDF]

3 

Hydraulic fracture characterization with dispersion measurements of seismic waves

[PDF]

4 

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

[PDF]

5 

A new method to convert unleveled marine seismic data to leveled splitspread data

[PDF]

6 

The reflectivity operator for curved interfaces

[PDF]

7 

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.

[PDF]
[Abstract]

8 

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.

[PDF]
[Abstract]

9 

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.

[PDF]
[Abstract]

10 

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.

[PDF]
[Abstract]

11 

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.

[PDF]
[Abstract]

12 

Introduction to the supplement on seismic interferometry

[PDF]

13 

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.

[PDF]
[Abstract]

14 

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.

[PDF]
[Abstract]

15 

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.

[PDF]
[Abstract]

16 

Green's function representations for seismic interferometry
The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of timereversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The RayleighBetti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

[PDF]
[Abstract]

17 

Seismic processing in the inverse data space
Until now, seismic processing has been carried out by applying inverse filters in the forward data space. Because the acquired data of a seismic survey is always discrete, seismic measurements in the forward data space can be arranged conveniently in a data matrix (P). Each column in the data matrix represents one shot record. If we represent seismic data in the temporal frequency domain, then each matrix element consists of a complexvalued number. Considering the dominant role of multiple scattering in seismic data, it is proposed to replace data matrix P by its inverse P–1 before starting seismic processing. Making use of the feedback model for seismic data, multiple scattered energy is mapped onto the zero time axis of the inverse data space. The practical consequence of this remarkable property may be significant: multiple elimination in the inverse data space simplifies to removing data at zero time only. Moving to the inverse data space may cause a fundamental change in the way we preprocess and image seismic data.

[PDF]
[Abstract]

18 

Discrimination between phase and amplitude attributes in timelapse seismic streamer data
Timelapse seismic experiments aim to obtain information about productionrelated effects in hydrocarbon reservoirs to increase the recovery percentage. However, nonrepeatability problems such as acquisition differences, overburden effects, and noise are often significantly stronger than the imprint of production changes in timelapse seismic data sets. Consequently, it is very difficult to appraise the changes in petrophysical reservoir parameters over time. We introduce a 4D monitoring approach based on the spectral ratio method. This method produces two timelapse attributes: the relative change in reflection coefficient and the traveltime shift at reflecting interfaces. These attributes can be used for appraising productionrelated changes in the subsurface. The approach corrects for timeinvariant nonrepeatability effects in the overburden and sourcereceiver coupling problems in timelapse surveys. The validity of the method is limited to structurally simple overburden and reservoirs with weak lateral variations. First, we validate the methodology using a synthetic timelapse seismic experiment. Next, we apply the method to a real timelapse data set from the Troll West gas province in the North Sea. In the real example, we could not detect movement in the fluid contact of 5–15 m. The expected change in amplitude is less than 10%, which is probably below the background noise level for this data set.

[PDF]
[Abstract]

19 

A new elastic model for ground coupling of geophones with spikes
Ground coupling are terms that describe the transfer from seismic ground motion to the motion of a geophone. In previous models, ground coupling was mainly considered as a disk lying on top of a halfspace, not considering the fact that in current practice geophones are spiked and are buried for optimal response. In this paper we introduce a new model that captures the spike added to the geophone and models the effect of geophone burial. The geophone is modeled as a rigid, movable cylinder embedded in a halfspace near or at the surface. The coupling problem is then tackled by a scattering approach using the elastic form of reciprocity; we consider the vertical component only. The main feature in the coupling function is a resonance whose location and shape depend on the different parameters of the geophone and the soil. In accordance with previous models, adding mass reduces the frequency of resonance. However, we show that pure mass loading assumption is too restrictive for standard geophones. Our new model shows that increasing the spike radius and length decreases the frequency of resonance and the resonance is more peaked. Furthermore, burying the geophone decreases the frequency of resonance, but when one takes into account that the soil at depth is more compact, then the behavior is as observed in practice — namely, an increase in frequency of resonance. As for the properties of the soil, the shearwave velocity has the largest effect; when increased, it shifts the frequency of resonance to the highfrequency end as desired.

[PDF]
[Abstract]

20 

3D surfacerelated multiple prediction: A sparse inversion approach
The theory of iterative surfacerelated multiple elimination holds for 2D as well as 3D wavefields. The 3D prediction of surface multiples, however, requires a dense and extended distribution of sources and receivers at the surface. Since current 3D marine acquisition geometries are very sparsely sampled in the crossline direction, the direct Fresnel summation of the multiple contributions, calculated for those surface positions at which a source and a receiver are present, cannot be applied without introducing severe aliasing effects. In this newly proposed method, the regular Fresnel summation is applied to the contributions in the densely sampled inline direction, but the crossline Fresnel summation is replaced with a sparse parametric inversion. With this procedure, 3D multiples can be predicted using the available input data. The proposed method is demonstrated on a 3D synthetic data set as well as on a 3D marine data set from offshore Norway.

[PDF]
[Abstract]
