Approximations to a generalized real ray-tracing method for heterogeneous anisotropic viscoelastic media

The real raytracing approach leads to an effective solution in the real space domain using a homogenous ray velocity vector. However, it fails to yield solutions for quasi-shear waves, which suffer triplication of the wavefronts. To address this challenging problem, a generalized real ray-tracing method and its new approximations are presented to solve the complex ray equation. The numerical results show that the generalized ray-tracing method is superior to the real ray-tracing method in the presence of triplications of the quasi-shear waves in the computation of ray velocity, ray attenuation, and ray quality factors, as well as the reflection and transmission coefficients in viscoelastic anisotropic media. Based on the assumptions of the real slowness direction and real polarization vectors, two new approximations of the generalized real ray-tracing method are developed for directly computing the homogeneous complex ray velocity vectors of three wave modes (qP, qS1, and qS2). These approximations significantly improve the computational efficiency by avoiding the iterative process required by the generalized real ray-tracing method that is inherited from the real ray-tracing method. The computational accuracies are verified through transversely isotropic models and orthorhombic models with different strengths of attenuation and anisotropy. The incorporation of the new approximation into the shortest-path method turned out to be an efficient and accurate method for seismic ray tracing in heterogeneous viscoelastic and transversely isotropic media with a vertical axis of symmetry, even in the presence of strong attenuation and anisotropy.

Multi-array analysis of volcano-seismic signals at Fogo and Brava, Cape Verde

Seismic arrays provide tools for the localization of events without clear phases or events outside of the network, where the station coverage prohibits classical localization techniques. Beamforming allows the determination of the direction (backazimuth) and the horizontal (apparent) velocity of an incoming wavefront. Here we combine multiple arrays to retrieve event epicenters from the area of intersecting beams without the need to specify a velocity model. The analysis is performed in the time-domain, which allows to select a relatively narrow time window around the phase of interest while preserving frequency bandwidth. This technique is applied to earthquakes and hybrid events in the region of Fogo and Brava, two islands of the southern chain of the Cape Verde archipelago. The results show that the earthquakes mainly originate near Brava whereas the hybrid events are located on Fogo. By multiple-event beam-stacking we are able to further constrain the locations of the hybrid events in the north-western part of the collapse scar of Fogo. In previous studies, these events were attributed to shallow hydrothermal processes. However, we obtain relatively high apparent velocities at the arrays, pointing to either deeper sources or to complex ray paths. For a better understanding of possible errors of the multi-array analysis, we also compare slowness values obtained from the array analysis with those derived from earthquake locations from classical (local network) localizations. In general, the results agree well, however, the arrays also show some aberrations that can be quantified for certain event locations.

On the use of complex rays to analyse the sonic boom of the Carancas meteorite at I08BO station located into shadow zone

<p><span>The International Monitoring System (IMS) network of the Comprehensive nuclear-Test-Ban Treaty (CTBT) detects powerful natural and artificial infrasonic sources. One of these sources are meteorites which produce multi-arrival pressure signatures similar to explosion </span><span>onces</span><span>. Long range sonic boom modeling allows to distinguish these sources from one another. Our documented case is the Carancas meteorite </span><span>that</span><span> impacted the ground in Peru on September 15th, 2007, near </span><span>the IMS </span><span>infrasound station I08BO. Since this station is located within the shadow zone, classical ray tracing cannot be used to capture the characteristics of the recorded arrivals. </span><span>Analytic continuation into complex plane of emission parameters of the ray tracing method allows to analyse the propagation in shadow zone for full</span><span>y</span><span> three dimensional problems. Contribution of complex ray ordinary differential equations integration and optimisation algorithm allows to compute complex eigenrays. Simulated infrasound wave arrival times, azimuth</span><span>s</span><span> and apparent velocities at the station are compared with Carancas records.</span></p>

Effective and efficient approaches for calculating seismic ray velocity and attenuation in viscoelastic anisotropic media

In viscoelastic anisotropic media, the elastic moduli, slowness vector, phase, and ray velocity are all complex-valued quantities in the frequency domain. Solving the complex eikonal equation becomes computationally complex and time-consuming. We have developed two approximate methods to effectively calculate the ray velocity vector, attenuation, and quality factor in viscoelastic transversely isotropic media with a vertical symmetry axis (VTI) and in orthorhombic (ORT) anisotropy. The first method is based on the perturbation theory (PER) under the assumption of a homogeneous complex ray vector, which is obtained by applying the elastic background and viscoelastic perturbations to the real and imaginary components of the modulus tensor, respectively. The perturbations of the slowness vectors of the three wave modes (qP, qSV, and qSH) are determined through the vanishing Hamiltonian function. The second method is derived by applying a real slowness direction (RSD) to the inhomogeneous complex slowness vector and then approximately calculating the complex ray velocity vector with the condition of the homogeneous complex vector. The numerical results verify that the two approaches can produce accurate ray velocity vector, attenuation, and quality factors of the qP-wave in viscoelastic VTI and ORT media. The RSD method can yield high accuracies of ray velocity for the qSV- and qSH-wave in viscoelastic VTI models even at triplication of the qSV wavefronts, as well as qS1 and qS2 in a weak ORT medium ([Formula: see text] > 20), except for near the cusp of the qS1 wavefronts (errors approximately 6%) where the PER has more than 10% error.

URBAN PLANNING TRANSFORMATION OF FUNCTIONAL PLANNING STRUCTURE OF SUBURBAN ZONES AND BELTS OF MEGAPOLIS. FOREIGN EXPERIENCE

The article considers the features of the functional planning structure transformation of North American megalopolises in the context of the construction of inland railways. The subject of inquiry is the territories of the sett lement system formation in North America from the beginning of colonial invasions, where the interests of Great Britain, France and Spain intersected to the current stage of megacities. There is investigated the infl uence of railway transport on the development of megacities in North America. The subject of research is the Canadian Pacifi c Railroad and the US Transcontinental Railroad, which contributed to the countries urbanization and industrialization. The prerequisites for the transformation of suburban areas were the intensity of labor, cultural, household and industrial links between the center and the periphery in the meridional and latitudinal directions, formation of new kind of scientifi c and industrial complexes, multi-nodes, its infl uence on the functional planning structure of suburban areas and outskirts of megacities. The article introduces the concept of “multi-node”. Multi-nodes are multifunctional urban development complexes with transport infrastructure and engineering facilities which form a complex of terminals for goods transshipment and passengers transferring from one kind of transport to another, as well as public spaces integrated into the urban environment, scientifi c and innovative enterprises with full autonomy and communication that provides the megalopolis with energy resources. Multi-node complexes are located closely to each other and form an integral group, most often around the near-airport territories. This group may not have clear planning boundaries in the form of streets, driveways, fences, and so on. The purpose of the research is to study the sequence of the functional and planning structure formation of the city in dynamics. At the initial stage, from the linear structure of the city along the railway to a more complex ray system, and in the future - the formation of the ring type planning structures, that provide switching of traffi c fl ows on all azimuths directions. It is planning to be constructed a theoretical model of interaction between subcentres and multi-nodes in the suburban zones of intracontinental megacities.

Seismic complex ray tracing in 2D/3D viscoelastic anisotropic media by a modified shortest-path method

In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical examples verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.