Reference transversely isotropic medium approximating a given generally anisotropic medium

For a given stiffness tensor (tensor of elastic moduli) of a generally anisotropic medium, we can estimate the extent to which the medium is transversely isotropic, and determine the direction of its reference symmetry axis. In this paper, we rotate the given stiffness tensor about this reference symmetry axis, and determine the reference transversely isotropic (uniaxial) stiffness tensor as the average of the rotated stiffness tensor over all angles of rotation. The obtained reference transversely isotropic (uniaxial) stiffness tensor represents an analytically differentiable approximation of the given generally anisotropic stiffness tensor. The proposed analytic method is compared with a previous numerical method in two numerical examples.     

Frequency-domain ray series for viscoelastic waves with a non-symmetric stiffness matrix

In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In order to indicate which phenomena could be observed in the wave field if the stiffness matrix were non–symmetric, we propose the frequency–domain ray series for viscoelastic waves with a non–symmetric stiffness tensor in this paper.     

Development versus conservation: evaluation of landscape structure changes in Dem?novská Valley,Slovakia

This paper presents the changes of landscape structure in the Dem?novská Valley which ranks among the most valuable protected areas of Slovakia. The area was selected on the basis of changes associated with the rapidly growing tourism industry and the rise of an important destination in the center of Low Tatras National Park, Slovakia. To document any changes, we visually interpreted data from aerial and satellite images in three periods(1949, 2007 and 2013) and for predicting future changes we used land use planning documentation. Interpreted data were analyzed using overlay analysis and landscape metrics. Results showed extensive changes in the landscape structure mainly connected with the development of tourism infrastructure. We also identified long-term changes whose causes stem from the transformation of society and forest management in the past. The dynamics and extent of these changes may increase in the future. We propose to stop future development of ski slopes and expansion of related infrastructure, to focus on sustainability and environmentally friendly operation of the existing ski resort and to invest a substantial portion of profits to support projects aimed to preserve surrounding lands and wildlife.     

Sensitivity of seismic waves to structure

We study how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. In-finitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation. For each incident wave, each Gabor function generates at most 5 scattered waves, propagating in specific directions and having specific polarisations. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles. In this paper, we concentrate on the Gaussian packets caused by narrow-band scattering. For a particular source, each Gaussian packet scattered by a Gabor function at a given spatial location is sensitive to just a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band.     

Transformation of spatial and perturbation derivatives of travel time at a curved interface between two arbitrary media

We consider the partial derivatives of travel time with respect to both spatial coordinates and perturbation parameters. These derivatives are very important in studying wave propagation and have already found various applications in smooth media without interfaces. In order to extend the applications to media composed of layers and blocks, we derive the explicit equations for transforming these travel–time derivatives of arbitrary orders at a general smooth curved interface between two arbitrary media. The equations are applicable to both real–valued and complex–valued travel time. The equations are expressed in terms of a general Hamiltonian function and are applicable to the transformation of travel–time derivatives in both isotropic and anisotropic media. The interface is specified by an implicit equation. No local coordinates are needed for the transformation.     

Transformation relations for second-order derivatives of travel time in anisotropic media

In the computation of paraxial travel times and Gaussian beams, the basic role is played by the second-order derivatives of the travel-time field at the reference ray. These derivatives can be determined by dynamic ray tracing (DRT) along the ray. Two basic DRT systems have been broadly used in applications: the DRT system in Cartesian coordinates and the DRT system in ray-centred coordinates. In this paper, the transformation relations between the second-order derivatives of the travel-time field in Cartesian and ray-centred coordinates are derived. These transformation relations can be used both in isotropic and anisotropic media, including computations of complex-valued travel times necessary for the evaluation of Gaussian beams.     

The Amazon River headstream area in the Cordillera Chila,Peru: hydrographic,hydrological and glaciological conditions

Abstract

The source of the world's largest river has fascinated scientists and adventurers for a long time. Extensive studies have been undertaken in the unexplored Llogueta River valley, Cordillera Chila, to identify the main stream of the Amazon River. Analysis of the Lloqueta River network and measurements of its hydrographic and hydrometric characteristics are presented in this study. On the basis of the acquired data, the northern hillside of the Cordillera Chila massif, concretely the basins of four mountainous courses—the Carhuasanta, Apacheta, Ccaccansa and Sillanque rivers—should be regarded as the headwaters territory of the Amazon River. Factors influencing the river system—glaciers and soils—were examined for each catchment. Glacier retreat in the last 50 years has left perennial snowfields only in the highest part of the study area, resulting in modification of the headwater runoff regimes. Preliminary results are afforded by the continual automatic water-level monitoring of the Lloqueta River since June 2008. Our investigations have determined that all types of soil in the area could be classified into two main categories: hydromorphic soils or poorly developed cryic soils.

Citation Janský, B., Engel, Z., Kocum, J., ?efrna, L. & ?esák, J. (2011) The Amazon River headstream area in the Cordillera Chila, Peru: hydrographical, hydrological and glaciological conditions. Hydrol. Sci. J. 56(1), 138–151.     

Phase shift of the Green tensor due to caustics in anisotropic media

Equations are presented to determine the phase shift of the amplitude of the elastic Green tensor due to both simple (line) and point caustics in anisotropic media. The phase-shift rules for the Green tensor are expressed in terms of the paraxial-ray matrices calculated by dynamic ray tracing. The phase-shift rules are derived both for 2×2 paraxial-ray matrices in ray-centred coordinates and for 3×3 paraxial-ray matrices in general coordinates. The reciprocity of the phase shift of the Green tensor is demonstrated. Then a simple example is given to illustrate the positive and negative phase shifts in anisotropic media, and also to illustrate the reciprocity of the phase shift of the Green tensor.     

Determination of the reference symmetry axis of a generally anisotropic medium which is approximately transversely isotropic

For a given stiffness tensor (tensor of elastic moduli) of a generally anisotropic medium, we estimate to what extent the medium is transversely isotropic (uniaxial) and determine the direction of its reference symmetry axis expressed in terms of the unit reference symmetry vector. If the medium is exactly transversely isotropic (exactly uniaxial), we obtain the direction of its symmetry axis. We can also calculate the first–order and second–order spatial derivatives of the reference symmetry vector which may be useful in tracing the reference rays for the coupling ray theory. The proposed method is tested using various transversely isotropic (uniaxial) and approximately transversely isotropic (approximately uniaxial) media.     

Grid travel-time tracing: Second-order method for the first arrivals in smooth media

A new computational scheme for calculating the first-arrival travel times on a rectangular grid of points is proposed. The new proposed method is of second-order accuracy. This means that the error of the calculated travel time is proportional to the second power of the grid spacing. The method should be sufficiently accurate for all applications in smooth seismic models. On the other hand, the method is not, in its present form, proposed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. Equations are also presented for the appropriate evaluation of the errors of calculated travel times to check their accuracy, and the proposed method is compared with other numerical methods. The method is developed, described and demonstrated in 2-D, but may also be extended to 3-D models and to general models with structural interfaces.