Vladimir Troyan

On the role of reflections, refractions and diving waves in full-waveform inversion

Full-waveform inversion suffers from local minima, due to a lack of low frequencies in data. A reflector below the zone of interest may, however, help in recovering the long-wavelength components of a velocity perturbation, as demonstrated in a paper by Mora. With the Born approximation for a perturbation in a reference model consisting in two homogeneous isotropic acoustic half-spaces and the assumption of infinitely large apertures available in the data, analytic expressions can be found that describe the spatial spectrum of the recorded seismic signal as a function of the spatial spectrum of the inhomogeneity. Diving waves can be included if the deeper part of the homogeneous model is replaced by one that has a vertical velocity gradient. We study this spectrum in more detail by separately considering scattering of direct, reflected and head waves, as well as singly and multiply reflected diving waves for a gradient model. Taking the reflection coefficient of the deeper reflector into account, we obtain sensitivity estimates for each wavetype. Although the head waves have a relatively small contribution to the reconstruction of the velocity perturbation, compared to the other waves, they contain reliable long-wavelength information that can be beneficial for full-waveform inversion. If the deeper part has a constant positive velocity gradient with depth, all the energy eventually returns to the source-receiver line, given a sufficiently large acquisition aperture. This will improve the sensitivity of the scattered reflected and refracted wavefields to perturbations in the background model. The same happens for a zero velocity gradient but with a very high impedance contrast between the two half-spaces, which results in a large reflection coefficient.

Multiple migration of VSP data for velocity analysis

Summary We investigate the new method that combines the migration of VSP data and updating of the velocity model. The method is based on the comparison of subsurface images obtained by using different types of waves: the primary reflections and surface-related multiples. As a measure of similarity of the images we use the functional based on cross-correlation. Estimation of the velocity model parameters is carried out by maximization of this functional. Therefore the resulting velocity model provides the maximal similarity between images obtained by using the primary reflections and surface-related multiples. We develop an iterative procedure to maximize the functional and demonstrate the efficiency of the method using the synthetic walk-away data. The method can be used for very short VSP receiver arrays and allows us to estimate the interval velocities below receivers, which is considered to be a challenge with VSP acquisition geometry.

Velocity analysis for VSP data using multiples

Summary The quality of the subsurface images obtained using VSP data strongly depends on the velocity model used for migration. The velocity model derived from surface seismic is often not accurate enough for VSP imaging and there is a need for its improvement. We propose the method for updating of velocities using VSP data. The main idea is to use the images of the subsurface obtained using different types of waves: primary reflections and surface-related multiples. If the background velocity is correct, then these images will be similar, and they will not coincide, if the velocity model is erroneous. We develop the algorithm of velocity updating based on this criterion. The proposed method allows us to retrieve the velocity below the borehole receivers. This is complementary to first break VSP travel time tomography, which helps to retrieve velocity only above the receivers.

Scattering objects location with cross-well data

Summary Most of conventional imaging techniques are designed to locate the reflecting interfaces in the subsurface. But the scattering objects (diffractors), such as faults or salt inclusions, are also of interest for exploration. Locating these objects may be useful for seismic data interpretation, production monitoring and reservoir characterization. In this paper we propose the technique of diffractor location using the cross-well data. We use Kirchhoff migration with special weights for the diffractor imaging. We demonstrate that the diffractors, invisible with more conventional processing, have been imaged with the proposed technique.

Data‐derived optimization of sensitivity requirements for upcoming auroral imaging missions

Using an extensive database of ultraviolet images of the night-time sector of the northern auroral oval obtained from the POLAR spacecraft, and data analysis tools adopted from statistical mechanics of turbulent flows, we identify scaling relations describing substorm - time variability of the auroral intensity as a function of spatial scale and auroral intensity level. By extrapolating these relations to scales smaller than those resolved by previously flown auroral missions, we derive contrast and sensitivity constraints for a next-generation global auroral imager. The outcomes of this analysis, combined with the results reported by Uritsky et al. [2010], make it possible to optimize sensitivity and resolution requirements for future auroral imaging missions intended to observe auroral structure and dynamics across wide ranges of spatial and temporal scales.

Surface‐wave inversion for a P‐velocity profile with a constant depth gradient of the squared slowness

ABSTRACT Surface waves are often used to estimate a near‐surface shear‐velocity profile. The inverse problem is solved for the locally one‐dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P‐wave velocity profile, the P‐guided waves should be included in the inversion scheme. As an alternative to a multi‐layered model, we consider a simple smooth acoustic constant‐density velocity model, which has a negative constant vertical depth gradient of the squared P‐wave slowness and is bounded by a free surface at the top and a homogeneous half‐space at the bottom. The exact solution involves Airy functions and provides an analytical expression for the dispersion equation. If the Symbol ratio is sufficiently small, the dispersion curves can be picked from the seismic data and inverted for the continuous P‐wave velocity profile. The potential advantages of our model are its low computational cost and the fact that the result can serve as a smooth starting model for full‐waveform inversion. For the latter, a smooth initial model is often preferred over a rough one. We test the inversion approach on synthetic elastic data computed for a single‐layer P‐wave model and on field data, both with a small Symbol ratio. We find that a single‐layer model can recover either the shallow or deeper part of the profile but not both, when compared with the result of a multi‐layer inversion that we use as a reference. An extension of our analytic model to two layers above a homogeneous half‐space, each with a constant vertical gradient of the squared P‐wave slowness and connected in a continuous manner, improves the fit of the picked dispersion curves. The resulting profile resembles a smooth approximation of the multi‐layered one but contains, of course, less detail. As it turns out, our method does not degrade as gracefully as, for instance, diving‐wave tomography, and we can only hope to fit a subset of the dispersion curves. Therefore, the applicability of the method is limited to cases where the Symbol ratio is small and the profile is sufficiently simple. A further extension of the two‐layer model to more layers, each with a constant depth gradient of the squared slowness, might improve the fit of the modal structure but at an increased cost. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available.

Numerical simulation in diffraction tomography with elastic and electromagnetic sounding signals

The results of numerical simulation on restoration of parameters of local in-homogeneities are considered. Studying of restoration of elastic inhomogeneities and inhomogeneities of electrical conductivity is implemented using elastic and electromagnetic wave fields correspondingly. The direct problem for the Lame and Maxwell equations is solved by the finite difference method. Restoration of parameters is implemented by the diffraction tomography method in the time domain with the help of the first-order Born approximation. In electromagnetic case we study restoration of local inhomogeneity of electrical conductivity using the sounding by diffusion electromagnetic field.