Low‐frequency wave propagation in periodically layered media

In this paper, we consider wave propagation in a layered medium. Using the Baker‐Campbell‐Hausdorff series, we expand the logarithm of a propagator matrix in series of frequency. The series coefficients allow us to extend the effective Backus medium for low frequencies. The proposed technique is applied to vertical propagation in a periodically layered and binary medium as well as for a gradient medium. The velocity dispersion equations are derived for these media. We also consider the layered medium with monoclinic anisotropy. We illustrate the accuracy of the proposed method on synthetic and well‐log data.     

Effect of anelastic patchy saturated sand layers on the reflection and transmission responses of a periodically layered medium

Based on analytic relations, we compute the reflection and transmission responses of a periodically layered medium with a stack of elastic shales and partially saturated sands. The sand layers are considered anelastic (using patchy saturation theory) or elastic (with effective velocity). Using the patchy saturation theory, we introduce a velocity dispersion due to mesoscale attenuation in the sand layer. This intrinsic anelasticity is creating frequency dependence, which is added to the one coming from the layering (macroscale). We choose several configurations of the periodically layered medium to enhance more or less the effect of anelasticity. The worst case to see the effect of intrinsic anelasticity is obtained with low dispersion in the sand layer, strong contrast between shales and sands, and a low value of the net‐to‐gross ratio (sand proportion divided by the sand + shale proportion), whereas the best case is constituted by high dispersion, weak contrast, and high net‐to‐gross ratio. We then compare the results to show which dispersion effect is dominating in reflection and transmission responses. In frequency domain, the influence of the intrinsic anelasticity is not negligible compared with the layering effect. Even if the main resonance patterns are the same, the resonance peaks for anelastic cases are shifted towards high frequencies and have a slightly lower amplitude than for elastic cases. These observations are more emphasized when we combine all effects and when the net‐to‐gross ratio increases, whereas the differences between anelastic and elastic results are less affected by the level of intrinsic dispersion and by the contrast between the layers. In the time domain, the amplitude of the responses is significantly lower when we consider intrinsic anelastic layers. Even if the phase response has the same features for elastic and anelastic cases, the anelastic model responses are clearly more attenuated than the elastic ones. We conclude that the frequency dependence due to the layering is not always dominating the responses. The frequency dependence coming from intrinsic visco‐elastic phenomena affects the amplitude of the responses in the frequency and time domains. Considering intrinsic attenuation and velocity dispersion of some layers should be analyzed while looking at seismic and log data in thin layered reservoirs.     

欧亚北部跨大陆交通经济带发展工程（英文）

跨西伯利亚大铁路的主要作用在于实现欧亚两洲西部和东部的交流。沿西伯利亚大铁路及其分支的交通经济带的形成意义重大。本文揭示了西伯利亚大铁路及其分支以及"一体化的欧亚基础设施系统"这一宏伟工程长远发展的主要特征,描述了西伯利亚大铁路和中国新丝绸之路影响区域的比较特征,提出了欧亚跨大陆板块交通经济带发展中面临的环境问题。研究认为,尽管在欧亚交通领域西伯利亚大铁路会面临一些竞争,但通过促进沿交通走廊区域的可持续发展,新丝绸之路建设将会为参与的国家带来显著的社会经济效益和环境效益,也必然会促进欧亚更密切的区域经济一体化和区域安全。     

Pure P- and S-wave equations in transversely isotropic media

Pure-mode wave propagation is important for applications ranging from imaging to avoiding parameter tradeoff in waveform inversion. Although seismic anisotropy is an elastic phenomenon, pseudo-acoustic approximations are routinely used to avoid the high computational cost and difficulty in decoupling wave modes to obtain interpretable seismic images. However, such approximations may result in inaccuracies in characterizing anisotropic wave propagation. We propose new pure-mode equations for P- and S-waves resulting in an artefact-free solution in transversely isotropic medium with a vertical symmetry axis. Our approximations are more accurate than other known approximations as they are not based on weak anisotropy assumptions. Therefore, the S-wave approximation can reproduce the group velocity triplications in strongly anisotropic media. The proposed approximations can be used for accurate modelling and imaging of pure P- and S-waves in transversely isotropic media.     

Scanning anisotropy parameters in horizontal transversely isotropic media

The horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ? of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ?. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ?, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ? reveals that travel times are more sensitive to η than to the symmetry axis azimuth ?. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ? differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ?, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.     

Weak‐anisotropy approximation for P‐wave reflection coefficient at the boundary between two tilted transversely isotropic media

Existing and commonly used in industry nowadays, closed‐form approximations for a P‐wave reflection coefficient in transversely isotropic media are restricted to cases of a vertical and a horizontal transverse isotropy. However, field observations confirm the widespread presence of rock beds and fracture sets tilted with respect to a reflection boundary. These situations can be described by means of the transverse isotropy with an arbitrary orientation of the symmetry axis, known as tilted transversely isotropic media. In order to study the influence of the anisotropy parameters and the orientation of the symmetry axis on P‐wave reflection amplitudes, a linearised 3D P‐wave reflection coefficient at a planar weak‐contrast interface separating two weakly anisotropic tilted tranversely isotropic half‐spaces is derived. The approximation is a function of the incidence phase angle, the anisotropy parameters, and symmetry axes tilt and azimuth angles in both media above and below the interface. The expression takes the form of the well‐known amplitude‐versus‐offset “Shuey‐type” equation and confirms that the influence of the tilt and the azimuth of the symmetry axis on the P‐wave reflection coefficient even for a weakly anisotropic medium is strong and cannot be neglected. There are no assumptions made on the symmetry‐axis orientation angles in both half‐spaces above and below the interface. The proposed approximation can be used for inversion for the model parameters, including the orientation of the symmetry axes. Obtained amplitude‐versus‐offset attributes converge to well‐known approximations for vertical and horizontal transverse isotropic media derived by Rüger in corresponding limits. Comparison with numerical solution demonstrates good accuracy.     

Assessment of the design displacement values at seismic fault crossings and of their excess probability

Line structures such as pipelines that cross active faults should be designed to retain leak-tightness if the design displacement (Ddesign) occurs. Principal approaches to the Ddesign and rupture kinematics assessment are described. They are based on relationships between earthquake magnitude, rupture length and displacement, and on the detailed field data on a specific fault that crosses the pipeline route. Since the future offset at the crossing may exceed the design value, the probability of a displacement occurrence where the safety of the structure can not be ensured should be estimated. Assessment method on such event probability is described and exemplified through active fault studies carried out at several pipeline projects in Russia.     

Sulfate reduction below the sulfate-methane transition in Black Sea sediments

A sudden increase in salinity about 7000 years ago caused a shift in the deposited sediments of the Black Sea from limnic to brackish-marine. Due to the development of an anoxic deep water basin and a relatively high sulfate concentration, organic matter is mineralized primarily through sulfate reduction in modern Black Sea sediments. Earlier studies showed that sulfate-reducing bacteria are abundant within the limnic sub-surface sediment in spite of extremely low concentrations of sulfate and organic carbon. A main objective of the present study was therefore to understand the depth distribution of sulfate reduction across the different sediment units, even deep below the sulfate-methane transition. Our study combined experimental measurements of sulfate reduction using ³⁵S radiotracer with analyses of sulfur and iron geochemistry in pore water and sediment. Potential sulfate reduction rates were measured with ³⁵S in sediment samples that were amended with sulfate and organic substrates and incubated in time-series up to 48 h. Sulfate reduction could thereby be detected and quantified at depths where concentrations of sulfate were otherwise too low to enable calculation of the rates. The results demonstrate that sulfate-reducing bacteria are active several meters below the sulfate-methane transition in Black Sea sediments. The cryptic sulfate reduction below the sulfate-methane transition may be driven by sulfate produced from re-oxidation of reduced sulfur species with oxidized iron minerals buried in the deep limnic sediment.