1,834,235 research outputs found
Representations for the Marchenko Method for imperfectly sampled data
No full textThe Marchenko method is based on two integral representations for focusing functions and Green’s functions. In practice the integrals are replaced by finite summations. This works well for regularly sampled data, but the quality of the results degrades in case of imperfect sampling. We reformulate the integral representations into summation representations which properly account for imperfectly sampled data and we illustrate these representations with numerical examples. We indicate how these representations may be used to modify the Marchenko method to account for imperfect sampling.Accepted Author ManuscriptImPhys/Acoustical Wavefield ImagingApplied Geophysics and Petrophysic
Fast nonrecursive 1D inversion by filtering acoustic-reflection data
No full textWe derive a fast acoustic inversion method for a piecewise homogeneous horizontally layered medium. The method obtains medium parameters from the reflection response. The method can be implemented to obtain the parameters on either side of a reflector at an arbitrary depth. Three processing steps lead to the inversion result. First, we solve a modified Marchenko type equation to obtain a focusing wavefield. We then apply wavefield continuation across a reflecting boundary to the focusing wavefield and retrieve the reflection coefficient of a reflector as a function of horizontal slowness. Finally, we use the reflection coefficient to obtain the velocities and the ratio of the densities above and below the reflector. Because the two-way traveltime difference of the primary reflection and the one above it becomes known during the process, the thickness of the layer above the reflector is also found. The method can be applied multiple times in different zones, or recursively in a target zone without having to solve more Marchenko type equations. The numerical example illustrates that the method works well on modeled data without the need for a priori model information.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and PetrophysicsImPhys/Acoustical Wavefield Imagin
Multiple elimination and transmission compensation in primary reflections in data domain
No full textWe retrieve transmission compensated subsurface primary reflections from the reflection response measured at the surface. This is achieved by filtering the reflection response. The application of this scheme does not require model information. In this process, the reflection response is convolved and correlated with itself. The result after each convolution and correlation is truncated in the time domain. Free-surface and internal multiple reflections are removed and the two-way transmission effects in the primary reflections are compensated for in one step. The output of this scheme is a data set that contains only transmission compensated primary reflections. The obtained data set can be used as input to retrieve an artefact-free image of the medium. We illustrate the method with a two-dimensional example that shows how free-surface and internal multiple reflections are removed and transmission loss in primary reflections are compensated for. The method can have a wide range of applications in 3D strongly scattering media that are accessible from one side only.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic
Marchenko wavefield redatuming, imaging conditions, and the effect of model errors
No full textRecently, a novel method to redatum the wavefield in the sub-surface from a reflection response measured at the surface has gained interest for imaging primaries in the presence of strong internal multiples. A prerequisite for the algorithm is an accurate and correct estimate of the direct-wave Green's function. However, usually we use an estimate for the direct-wave Green's function computed in a background velocity medium. Here, we investigate the effect of amplitude and phase errors in that estimate. We formulate two novel imaging conditions based on double-focusing the measured reflection response inside the subsurface. These yield information on the amplitude error in the estimate for the direct-wave Green's function which we can then correct, but the phase error remains elusive.Applied Geophysics and Petrophysic
Beyond Marchenko: Obtaining virtual receivers and virtual sources in the subsurface
No full textBy solving the Marchenko equations, the Green’s function can be retrieved between a virtual receiver in the subsurface to points at the surface (no physical receiver is required at the virtual location). We extend the idea of these equations to retrieve the Green’s function between any two points in the subsurface; i.e, between a virtual source and a virtual receiver (no physical source or physical receiver is required at either of these locations). This Green’s function is called the virtual Green’s function and includes all the primaries, internal and free-surface multiples. Similar to the Marchenko Green’s function, we require the reflection response at the surface (single-sided illumination) and an estimate of the first arrival travel time from the virtual location to the surface.Applied Geophysics and Petrophysic
New method for discriminating 4D time shifts in the overburden and reservoirr
No full textUnderstanding seismic changes in the subsurface is important for reservoir management and health, safety and environmental (HSE) issues. Typically the changes are interpreted based on the time shifts in seismic time-lapse (4D) data, where sources are at the surface and receivers are either at the surface or in a borehole. With these types of acquisition geometry, it is more straightforward to detect and interpret changes in the overburden, close to the source and receivers, than changes in the deeper part close to the reservoir, because the time shift is accumulative along its ray path from source to receiver. We propose a new method for reconstructing the reflection responses of the overburden and the reservoir, separately, for 4D time shift analysis. This method virtually moves sources and receivers to a horizontal borehole level, which enables a more direct interpretation of the time shifts to the changes close to the borehole, instead of to the surface. A realistic field model is used to demonstrate the method, and we observe a clear discrimination of the different time shifts in the overburden and reservoir, which is not obvious in the original datasets.Applied Geophysics and Petrophysic
From closed-boundary to single-sided homogeneous Green's function representations
No full textThe homogeneous Green’s function (i.e., the Green’s function and its time-reversed counterpart) plays an important role in optical, acoustic and seismic holography, in inverse scattering methods, in the field of time-reversal acoustics, in reversetime migration and in seismic interferometry. Starting with the classical closed-boundary representation of the homogeneous Green’s function, we modify the configuration to two parallel boundaries. We discuss step-by-step a process that eliminates the integral along the lower boundary. This leads to a single-sided representation of the homogeneous Green’s function. Apart from imaging, we foresee interesting applications in inverse scattering, time-reversal acoustics, seismic interferometry, passive source imaging, etc.Applied Geophysics and Petrophysic
Deconvolution and correlation-based interferometric redatuming by wavefield inversion
No full textSeismic interferometry is a method to retrieve Green’s functions for sources (or receivers) where there are only receivers (or sources, respectively). This can be done by correlationor deconvolution-based methods. In this work we present anew approach to reposition the seismic array from the earth’s surface to an arbitrary datum at depth using the one-way reciprocity theorems of convolution and correlation type. The redatuming process is done in three steps: (a) retrieving the downward Green’s function for sources at the earth’s surfaceand receivers at the datum, (b) retrieving the corresponding upward Green’s function, and (c) retrieving the reflected upward wavefield for sources and receivers at the datum. Input for steps (a) and (b) are the surface data and wavefields simulated in a velocity model of the datum overburden. Step (c)uses the responses of steps (a) and (b) as input data in the convolution-based interferometric equation. The method accounts for inhomogeneities in the overburden medium, thus reducing anticausal events and artefacts as compared to a purely correlation-based procedure.ImPhys/Acoustical Wavefield ImagingApplied Geophysics and Petrophysic
Electromagnetic Marchenko imaging in 1D for dissipative media
No full textWe present a one-dimensional lossless scheme to compute an image of a dissipative medium from two single-sided reflection responses. One reflection response is measured at or above the top reflector of a dissipative medium and the other reflection response is computed as if measured at or above the top reflector of a medium with negative dissipation which we call the effectual medium. These two reflection responses together can be used to construct the approximate reflection data of the corresponding lossless medium by multiplying and taking the square root in time domain. The corresponding lossless medium has the same reflectors as the dissipative medium. Then the constructed reflection data can be used to compute the focusing wavefield which focuses at the chosen location in subsurface of the dissipative medium. From the focusing function and constructed reflection response the Green’s function for a virtual receiver can be obtained. Because the up- and downgoing parts of the Green’s function are retrieved separately, these are used to compute the image. We show with an example that the method works well for a sample in a synthesized waveguide that could be used for measurements in a laboratory.Applied Geophysics and Petrophysic
Optimum seismic acquisition geometry design with the help of artificial intelligence
No full textAcquisition geometry design aims at finding the most affordable acquisition geometry that satisfies the objectives of the seismic survey. The parameters of an acquisition geometry can be specified in terms of the number of sources and detectors, their location, the blending parameters and the DSA (dispersed source array) parameters. In our acquisition geometry design, we include the effects of the (expected) subsurface, i.e., we assume the subsurface to be known. Consequently, the ideal data set – carpet shooting and carpet detection – can be modeled. A practical data set can be considered to be a subset of this ideal one. Acquisition design comes down to determining the optimum subset. Following compressive sensing, this subset is sparse and irregular. As a quality measure, we apply decompression (deblending and interpolation) to the subset, which leads to an estimate of the ideal data set, and then compare this estimate with the known ideal data set. The difference is the residue that should satisfy a predefined quality criterion. This procedure is the inner loop of a genetic algorithm. A CNN (convolutional neural network) is trained to improve the efficiency of the genetic algorithm by enhancing the effectiveness of each next generation. Furthermore, the solution space is limited to reduce the amount of computations needed. Finally, in this application it is acceptable to end up in a local minimum. The latter corresponds to an acquisition geometry that fully satisfies the quality and economic criteria (although some acquisition geometry may exist that provides even better results). Our design method leads to results that are better than those obtained with randomized acquisition geometries.Accepted Author ManuscriptApplied Geophysics and Petrophysic
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