Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Table Of Integrals Series And Products

Special Functions and Their Applications. By N. N. Lebedev, translated by R. A. Silverman. Pp. xii, 308. 96s. 1965. (Prentice-Hall)

The series solution of wave functions for 2D scattering and diffraction of plane SH (shear horizontal) waves induced by a U‐shaped canyon is proposed herein to account for the topographic effect of such a canyon. The wave function expansion method has been frequently employed to study the topographic effect because it can reveal the physics of the wave scattering and can test the accuracy of other methods. Through a new domain decomposition strategy, the half‐space having a U‐shaped canyon is divided into three subregions. Hence, we defined three cylindrical coordinate systems. In each coordinate system, the wave field satisfying the Helmholtz equation was represented by means of the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then three wave fields are all represented in the same coordinate system using the Graf addition theorem. The unknown coefficients are solved by satisfying the continuity conditions of the auxiliary boundary and the traction‐free boundary conditions on the bottom of the canyon. To show the effects of symmetrical and nonsymmetrical U‐shaped canyons on the surface ground motion, a parametric analysis is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of wave propagating and scattering. It is found that a zone of amplification can obviously take place at the bottom of a U‐shaped canyon with nearly vertical walls.

Effects of Topographic Amplification Induced by a U‐Shaped Canyon on Seismic Waves

SUMMARY A novel analytical approach to the SH-waves scattering problem of a single deep symmetrical V-shaped canyon is presented. The adopted strategy of domain decomposition prevents the auxiliary boundary from being pierced by the lowest part of the canyon, and inherently encompasses the singular behaviour of the stress field around the bottom of the canyon. Appropriate wavefunctions and Graf’s addition formulas are well utilized. The introduction of the method of images fulfills the stress-free condition at the ground level. In the deep V-shaped cases, comparisons with previously published data show good agreement. In the degenerate cases where the width of the canyon approaches zero, the presented results coincide with those obtained from the exact series solution of a single zero-thickness vertical edge crack. Both frequency- and time-domain results are given. Effects of the parameters on steady-state surface motions are illustrated and discussed. Transient changes in surface and subsurface displacement fields are included. The proposed series solution not only provides reliable results sufficiently under high-frequency excitations, but also fills the gap in the preceding cases of shallow canyons.

An analytical approach for the scattering of SH waves by a symmetrical V-shaped canyon: deep case

/pdf/an-analytical-approach-for-the-scattering-of-sh-waves-by-a-1ograf5gkk.pdf

An analytical approach for the scattering of SH waves by a symmetrical V-shaped canyon: deep case: An analytical approach to SH-waves scattering

SUMMARY

The scattering problem of plane SH waves by convex circular-arc topography is investigated. The series solution corresponding to this problem is derived via the wavefunction expansion method, combining with the region-matching technique. For the semi-circular case, the proposed formulation can be reduced to a simpler form than that given in the literature and consequently is easier to calculate. Both the steady-state and transient responses for some parameters are evaluated and discussed. Besides, based on the theory of geometric optics, for a concave mirror the focusing of light will take place, implying that analogous phenomenon may arise in the case of present topography. Such a focusing phenomenon will cause localized concentration of high amplitude of wave motion, which may have a great influence on underground structures. Therefore, the focusing effect by convex circular-arc surface is further examined in both the frequency and time domains. Numerical results show that the geometry under consideration is indeed capable of focusing wave energy, which is a significant contributor to the amplification behaviour.

Scattering and focusing of SH waves by a convex circular‐arc topography

The judicious region-matching technique is adopted to derive a series solution for shear horizontal waves scattering from a truncated semicircular canyon on the ground surface. A circular-arc auxiliary boundary is introduced to divide the analyzed region into two subregions. The antiplane motion of each subregion is represented in terms of an infinite series of cylindrical wavefunctions with unknown coefficients. By employing the Graf’s addition formula, boundary conditions on the curved canyon surface and continuity conditions on the auxiliary boundary, the unknown coefficients can be determined. Two modifications of the present theoretical derivation are done for the semicircular canyon and free surface cases. The plotted results reveal how the surface displacement amplitudes are influenced by varying the truncation depth.

Scattering of SH Waves by Truncated Semicircular Canyon

/pdf/scattering-of-sh-waves-by-a-circular-sectorial-canyon-3rof1d0df6.pdf

Deng-How Tsaur

Papers

An analytical approach for the scattering of SH waves by a symmetrical V-shaped canyon: deep case

An analytical approach for the scattering of SH waves by a symmetrical V-shaped canyon: deep case: An analytical approach to SH-waves scattering

Scattering and focusing of SH waves by a convex circular‐arc topography

Scattering of SH Waves by Truncated Semicircular Canyon

Scattering of SH waves by a circular sectorial canyon