Polarization and amplitude attributes of reflected plane and spherical waves

The characteristics of a reflected spherical wave at a free surface are investigated by numerical methods; in particular, the polarization angles and amplitude coefficients of a reflected spherical wave are studied. The classical case of the reflection of a plane P wave from a free surface is revisited in order to establish our terminology, and the classical results are recast in a way which is more suited for the study undertaken. The polarization angle of a plane P wave, for a given angle of incidence, is shown to be 90° minus twice the angle of reflection of the reflected S wave. For a Poisson's ratio less than 1/3, there is a non-normal incident angle for which both amplification coefficients are 2 precisely; for this incident angle the direction of the particle motion at the free surface is also the direction of the incident wave. For a wave emanating from a spherical source, the polarization angle, for all angles of incidence, is always less than, or equal to, the polarization angle of a plane P wave. The vector amplification coefficient of a spherical wave, for all angles of incidence, is always greater than the vector amplification coefficient of a plane P wave. As expected, the results for a spherical wave approach the results for a plane P wave in the far field. Furthermore, there was a good agreement between the theoretical modelling and the numerical modelling using the dynamic finite element method (DFEM).     

Symmetries in the reflection and transmission of elastic waves

Summary. The symmetry relations between the reflection and transmission coefficients for plane elastic waves incident upon an arbitrary horizontally stratified medium are derived by a novel approach. Previous results, particularly for a single interface, are obtained as special cases of this treatment.
In addition, for perfectly elastic media, projection operators for travelling and evanescent waves are introduced and used to derive a number of new relationships between the reflection and transmission coefficients.     

Vario-scale data structures supporting smooth zoom and progressive transfer of 2D and 3D data

This paper introduces the concept of the smooth topological Generalized Area Partitioning (tGAP) structure represented by a space-scale partition, which we term the space-scale cube. We take the view of ‘map generalization as extrusion of data into an additional dimension’. For 2D objects the resulting vario-scale representation is a 3D structure, while for 3D objects the result is a 4D structure.

This paper provides insights in: (1) creating valid data for the cube and proof that this is always possible for the implemented 2D tGAP generalization operators (line simplification, merge and split/collapse), (2) obtaining a valid 2D polygonal map representation at arbitrary scale from the cube, (3) using the vario-scale structure to provide smooth zoom and progressive transfer between server and client, (4) exploring which other possibilities the cube brings for obtaining maps having non-homogenous scales over their domain (which we term mixed-scale maps), and (5) using the same principles also for higher dimensional data; illustrated with 3D input data represented in a 4D hypercube.

The proposed new structure has very significant advantages over existing multi-scale/multi-representation solutions (in addition to being truly vario-scale): (1) due to tight integration of space and scale, there is guaranteed consistency between scales, (2) it is relatively easy to implement smooth zoom, and (3) compact, object-oriented encoding is provided for a complete scale range.     

Fault‐controlled fluid flow inferred from hydrothermal vents imaged in 3D seismic reflection data,offshore NW Australia

Fluid migration pathways in the subsurface are heavily influenced by pre‐existing faults. Although studies of active fluid‐escape structures can provide insights into the relationships between faults and fluid flow, they cannot fully constrain the geometry of and controls on the contemporaneous subsurface fluid flow pathways. We use 3D seismic reflection data from offshore NW Australia to map 121 ancient hydrothermal vents, likely related to magmatic activity, and a normal fault array considered to form fluid pathways. The buried vents consist of craters up to 264 m deep, which host a mound of disaggregated sedimentary material up to 518 m thick. There is a correlation between vent alignment and underlying fault traces. Seismic‐stratigraphic observations and fault kinematic analyses reveal that the vents were emplaced on an intra‐Tithonian seabed in response to the explosive release of fluids hosted within the fault array. We speculate that during the Late Jurassic the convex‐upwards morphology of the upper tip‐lines of individual faults acted to channelize ascending fluids and control where fluid expulsion and vent formation occurred. This contribution highlights the usefulness of 3D seismic reflection data to constraining normal fault‐controlled subsurface fluid flow.     

Synoptic interpretation of seismic reflection and refraction data

Summary. The structure of the upper lithosphere beneath southern Germany, northern Switzerland and west-central Utah (U.S.A.) has been investigated in detail by various geophysical methods. A synoptic interpretation of travel time and amplitude data obtained in seismic refraction and wide-angle reflection surveys, combined with near-normal incidence reflection observations, now permits the elucidation of the fine structure in a more quantitative and unified manner. With this scheme it is possible to unambiguously identify low-velocity zones and to deduce velocity gradients if reliable amplitude information is included in the inversion process.     

Seismic body waves in anisotropic media: reflection and refraction at a plane interface

Summary. A formulation is derived for calculating the energy division among waves generated by plane waves incident on a boundary between generally anisotropic media. A comprehensive account is presented for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine half-space, where the interface is parallel to a plane of elastic symmetry. For comparison, a less anisotropic medium having transverse isotropy with a horizontal axis of symmetry is also considered. The particle motion polarizations of waves in anisotropic medium differ greatly from the polarizations in isotropic media, and are an important diagnostic of the presence of anisotropy. Incident P and SV waves generate quasi- SH waves, and incident SH waves generate quasi- P and quasi- SV waves, often of considerable relative magnitude. The direction of energy transport diverges from the propagation direction.     

Mid-Palaeocene palaeogeography of the eastern North Sea basin: integrating geological evidence and 3D geodynamic modelling

The Mid‐Palaeocene palaeogeography of Denmark and the surrounding areas have been reconstructed on the basis of published geological data integrated with 3D geodynamic modelling. The use of numerical modelling enables quantitative testing of scenarios based on geological input alone and thus helps constrain likely palaeo‐water depths in areas where the geological data are inconclusive or incomplete. The interpretation of large‐scale erosional valleys and small‐scale circular depressions at the Mid‐Palaeocene Top Chalk surface in the Norwegian–Danish basin as either submarine or subaerial features is enigmatic and has strong implications for palaeogeographical reconstructions of the eastern North Sea basin. A 3D thermo‐mechanical model is employed in order to constrain the likely palaeo‐water depths of the eastern North Sea basin during the Palaeocene. The model treats the lithosphere as an elasto‐visco‐plastic continuum and models the lithospheric response to the regional stress field and thermal structure. The model includes the effects of sea‐level change, sedimentation and erosion, from the Mid Cretaceous to the present. Modelling results reproduce to first order geological data such as present sediment isopachs and palaeo‐water depths. It is concluded that the Mid Palaeocene water depths in the Norwegian–Danish basin were about 250 m. The erosional valleys and circular depressions at the top of the Upper Cretaceous‐Danian Chalk Group are thus interpreted to have formed in relatively deep water rather than due to subaerial exposure. Likely interpretations of the structures are therefore submarine valleys and pockmarks.     

3D numerical modelling of graben interaction and linkage: a case study of the Canyonlands grabens,Utah

Graben systems in extensional settings tend to be segmented with evidence of segment interaction. To gain a better understanding of the evolution of structures formed during graben growth and interaction, we here study the Grabens area of Canyonlands National Park, Utah, where a wide range of such structures is well exposed. With the aid of 3D numerical models, we attempt to reproduce structures observed in that region and to understand controls on the structural style of graben interaction by varying the spacing between pre‐existing structures. The sensitivity of the system to the thickness of the salt layer is also tested. Four distinct types of structures are observed when the spacing between inherited weak zones is varied: (1) grabens connecting in a relay zone divided by a narrow central horst; (2) graben segments interacting via a secondary stepover graben; (3) grabens propagating alongside each other with limited segment interaction; and (4) an abandoned graben segment in a system of multiple competing grabens. The presence of a basal salt layer (Paradox Member) promotes efficient graben propagation. A comparison between the observed structures and the numerical model results indicates that the detachment salt layer is relatively thin in the study area.