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.     

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.     

Estimate of the Upper Limit on Hot Plasma Differential Emission Measure (DEM) in Non-Flaring Active Regions and Nanoflare Frequency Based on the Mg <Emphasis Type="SmallCaps">xii</Emphasis> Spectroheliograph Data from CORONAS-F/SPIRIT

Nanoflare-heating theory predicts steady hot-plasma emission in non-flaring active regions. It is hard to find this emission with conventional non-monochromatic imagers (such as the Atmospheric Imaging Assembly or the X-Ray Telescope), because their images contain a cool-temperature background. In this work, we search for hot plasma in non-flaring active regions using the Mg?xii spectroheliograph onboard the Complex Orbital Observations Near-Earth of Activity on the Sun (CORONAS)-F/SPectroheliographIc X-ray Imaging Telescope (SPIRIT). This instrument acquired monochromatic images of the solar corona in the Mg?xii 8.42 Å line, which emits only at temperatures higher than 4 MK. The Mg?xii images only contain the signal from hot plasma, without any low-temperature background. We studied the hot plasma in active regions using SPIRIT data from 18?–?28 February 2002. During this period, the Mg?xii spectroheliograph worked with a 105-second cadence almost without data gaps. Hot plasma was observed only in the flaring active regions. We did not observe any hot plasma in non-flaring active regions. The hot-plasma column emission measure in the non-flaring active region is not expected to exceed \(3 \times10^{24}\) cm^?5. The hot differential emission measure is lower than 0.01% of the DEM of the main temperature component. The absence of Mg?xii emission in the non-flaring active regions can be explained by weak and frequent nanoflares (with a delay of less than 500 seconds) or by very short and intense nanoflares that lead to non-equilibrium ionization.     

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.     

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.     

Patuxent landscape model: 1. Hydrological model development

We developed a spatially explicit, process-based model of the 2352 km² Patuxent river watershed in Maryland, and its subwatersheds to integrate data and knowledge over several spatial, temporal and complexity scales, and to serve as an aid to regional management. The model was developed using the Library of Hydro-Ecological Modules (LHEM, http://giee.uvm.edu/LHEM), which was designed to create flexible landscape model structures that can be easily modified and extended to suit the requirements of a variety of goals and case studies. The LHEM includes modules that simulate various aspects of ecosystem dynamics. In this paper we consider modules that represent the physical conditions in the environment (climatic factors, geoporphology), and hydrologic processes, both locally and spatially. Where possible the modules are formulated as Stella(R) models, spatial transport processes are presented as C++ code.     

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.