Analysis of the resolution function in seismic prestack depth imaging

We consider the problem of estimating subsurface quantities such as velocity or reflectivity from seismic measurements. Because of a limited aperture and band-limited signals, the output from a seismic prestack reconstruction method is a distorted or blurred image. This distortion can be computed using the concept of resolution function, which is a quantity readily accessible in the Fourier space of the model. The key parameter is the scattering wavenumber, which at a particular image point is defined by the incident and scattered ray directions in a given background model. Any location in any background model can be considered. In general, the resolution function will depend on the following four quantities: the background velocity model, the frequency bandwidth, the wavefield type and the acquisition geometry.
We first establish the resolution function for a general scattering model assuming local reaction. We then adapt this result for two well-known scattering models: Born and Kirchhoff. For each of these approximations the corresponding resolution function is derived and discussed. Finally, by employing a simple synthetic data example we demonstrate the ability of the resolution function to predict the image distortions.     

Salt diapirs without well defined boundaries – a feasibility study of semi‐automatic detection

Prestack depth imaging of seismic data in complex areas such as salt structures requires extensive velocity model updating. In many cases, salt boundaries can be difficult to identify due to lack of seismic reflectivity. Traditional amplitude based segmentation methods do not properly tackle this problem, resulting in extensive manual editing. This paper presents a selection of seismic attributes that can reveal texture differences between the salt diapirs and the surrounding geology as opposed to amplitude‐sensitive attributes that are used in case of well defined boundaries. The approach consists of first extracting selected texture attributes, then using these attributes to train a classifier to estimate the probability that each pixel in the data set belongs to one of the following classes: near‐horizontal layering, highly‐dipping areas and the inside of the salt that appears more like a low amplitude area with small variations in texture. To find the border between the inside of the salt and the highly‐dipping surroundings, the posterior probability of the class salt is input to a graph‐cut algorithm that produces a smooth, continuous border. An in‐line seismic section and a timeslice from a 3D North Sea data set were employed to test the proposed approach. Comparisons between the automatically segmented salt contours and the corresponding contours as provided by an experienced interpreter showed a high degree of similarity.     

A sample of controlled experiments in diff radion tomography1

Various applications of a new geophysical reconstruction method, generalized acoustical diffraction tomography (GADT), which is based on transmission data as input are considered. Conventional diffraction tomography methods normally require linearization with respect to a uniform reference medium and regular sampling along a straight line. Thus, these methods will not work well when the background is strongly non-uniform and/or the acquisition geometry is arbitrary. However, GADT can, in principle, handle both irregularly spaced data, curved acquisition lines, and non-uniform background models. A number of controlled model tank and field experiments, where the model and the test object(s) are known a priori, have been carried out. After acquiring the tomographic data in each experiment, these are used to compute a reconstruction of the model, which can then be compared with the actual, known model. The method's ability to yield high-quality images of the different targets is demonstrated.     

Attenuation of marine seismic interference noise employing a customized U-Net

Marine seismic interference noise occurs when energy from nearby marine seismic source vessels is recorded during a seismic survey. Such noise tends to be well preserved over large distances and causes coherent artefacts in the recorded data. Over the years, the industry has developed various denoising techniques for seismic interference removal, but although well performing, they are still time-consuming in use. Machine-learning-based processing represents an alternative approach, which may significantly improve the computational efficiency. In the case of conventional images, autoencoders are frequently employed for denoising purposes. However, due to the special characteristics of seismic data as well as the noise, autoencoders failed in the case of marine seismic interference noise. We, therefore, propose the use of a customized U-Net design with element-wise summation as part of the skip-connection blocks to handle the vanishing gradient problem and to ensure information fusion between high- and low-level features. To secure a realistic study, only seismic field data were employed, including 25,000 training examples. The customized U-Net was found to perform well, leaving only minor residuals, except for the case when seismic interference noise comes from the side. We further demonstrate that such noise can be treated by slightly increasing the depth of our network. Although our customized U-Net does not outperform a standard commercial algorithm in quality, it can (after proper training) read and process one single shot gather in approximately 0.02 s. This is significantly faster than any existing industry denoising algorithm. In addition, the proposed network processes shot gathers in a sequential order, which is an advantage compared with industry algorithms that typically require a multi-shot input to break the coherency of the noise.     

Simultaneous core sample measurements of elastic properties and resistivity at reservoir conditions employing a modified triaxial cell – a feasibility study

Adaptations of existing triaxial cells for ultrasonic P- and S-wave measurements are well documented. This paper proposes further modification of such a cell so that also resistivity measurements can be carried out simultaneously at reservoir conditions. By employing the top cap and the pedestal of the cell as electrodes, axial resistivity measurements are now feasible. In order to minimize the polarization effect of this two-electrode arrangement, careful analyses have been carried out to optimize the choice of electrode coating and measurement frequency band. Radial resistivity measurements are also included in the system by introducing a strap-electrode system.
In a reservoir under production changes in both saturations, temperature (if steam injection) and stresses can take place. Therefore the modified triaxial system should be able to measure the integrated effects on the acoustic parameters and electric responses caused by variations in each of these parameters. The feasibility of the system to obtain such reliable information is demonstrated, employing a small selection of core samples. In the future such combined measurements on reservoir core samples can be used to link both seismic and electromagnetic observations to the actual earth model and constrain both modelling and inversion.     

Fast estimation of prestack common reflection surface parameters

We present a method for fast estimation of finite offset common reflection surface parameters. Firstly, the derivatives with respect to offset are derived from the velocity guide. Secondly, we apply structure tensors to extract the derivatives with respect to midpoint from stacked common offset sections. Finally, the mixed derivative is estimated using a one-parametric semblance search. The proposed method is compared to the global five-parametric semblance search and the pragmatic sequential two-parametric semblance search on one synthetic and one real data set. The experiments show that the proposed method is more robust against noise than the pragmatic search and have comparable robustness with the global search. The proposed method smoothes parameter estimates in a local window, and the window size is set to give the best trade-off between detail and robustness. Since the proposed method is dependent on a velocity guide, the quality of the other parameter estimates may be influenced by any inaccuracies in the guide. The main advantage of the proposed method is the computational efficiency. When compared with a gridded implementation of the semblance search, the proposed method is 10 and 400 times faster than the pragmatic and global search. Alternative search strategies significantly reduce the computational cost of the global search. However, since more than 99% of the computational cost of the proposed method comes from the semblance search to estimate the mixed derivative, it is expected that such techniques also reduce the computational cost for the proposed method.     

Improving Kirchhoff migration with repeated local plane-wave imaging? A SAR-inspired signal-processing approach in prestack depth imaging

A local plane-wave approach of generalized diffraction tomography in heterogeneous backgrounds, equivalent to Kirchhoff summation techniques when applied in seismic reflection, is re-programmed to act as repeated synthetic aperture radar (SAR) imaging for seismic prestack depth migration. Spotlight-mode SAR imaging quickly provides good images of the electromagnetic reflectivity of the ground via fast Fourier transform (FFT)-based signal processing. By calculating only the Green's functions connecting the aircraft to the centre of the illuminated patch, scattering structures around that centre are also recovered. SAR technology requires us to examine seismic imaging from the local point of view, where the quantity and quality of the available information at each image point are what are important, regardless of the survey geometry. When adapted to seismics, a local image of arbitrary size and sampling is obtained by FFT of seismic energy maps in the scattering wavenumber domain around each node of a pre-calculated grid of Green's functions. These local images can be used to generate a classic prestack depth-migrated section by collecting only their centres. However, the local images also provide valuable information around the centre, as in SAR. They can therefore help to pre-analyse prestack depth migration efficiently, and to perform velocity analysis at a very low cost. The FFT-based signal-processing approach allows local, efficient and automatic control of anti-aliasing, noise and resolution, including optimized Jacobian weights. Repeated local imaging could also be used to speed up migration, with interpolation between local images associated with a coarse grid of Green's functions, as an alternative to interpolation of Green's functions. The local images may, however, show distortions due to the local plane-wave approximation, and the velocity variations across their frame. Such effects, which are not necessarily a problem in SAR, should be controlled and corrected to further enhance seismic imaging. Applications to realistic models and to real data show that, despite the distortion effects, the local images can yield similar information to prestack depth migration, including common-image-point gathers for velocity analyses and AVO/AVA effects, at a much lower cost when a small target is considered.     

Generalized acoustic diffraction tomogra phy1

A generalized diffraction tomography algorithm is developed, which in principle can handle irregularly spaced data, curved acquisition lines and non-uniform background models. By direct comparison with medical diffraction tomography, it is shown that the generalized method involves the same two processing steps: data filtering and back-propagation. The filter handles the irregular sampling of the model space and the uneven energy coverage, while the back-propagation operator removes the wave propagation effects. Paraxial ray-tracing techniques are employed to compute both these quantities. In medical diffraction tomography, the resolution vector (i.e. the Fourier vector of the model space) is defined by the incident and scattered plane-wave directions. It is shown here that a similar relationship exists for a non-uniform background, where the resolution vector at a particular image point is defined by the incident and scattered ray directions. Consequently, the impulse response of the generalized algorithm becomes space variant. Finally, a general processing procedure for transmission mode seismic data, based on this generalized algorithm, is proposed. The potential of the method is demonstrated using synthetic cross-hole data.