Practical VTI approximations: a systematic anatomy   总被引：3，自引：0，他引：3  

Paul J. Fowler   《Journal of Applied Geophysics》2003,54(3-4):347

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a₁₃ with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).  相似文献   

Seismic imaging of mid-Pleistocene tunnel-valleys in the North Sea Basin—high resolution from low frequencies     

Daniel Praeg   《Journal of Applied Geophysics》2003,53(4):273-298

Seismic reflection methods provide continuous access both to stratigraphy (vertical) and to subsurface morphology (horizontal), for which the scales of interest may differ by orders of magnitude. Seismic surveys of Quaternary successions have generally sought to optimise vertical resolution, through the use of higher source frequency content. Here, I show that low-frequency bandwidth is not necessarily a limiting factor for the seismic resolution of glacigenic morpho-sedimentary features. Observations are presented from a buried network of large mid-Pleistocene (Elsterian) tunnel-valleys in the southern North Sea Basin, across a 100×130 km study area with water depths less than 30 m. Low-frequency 2D and 3D seismic multi-channel data, acquired for deeper hydrocarbon exploration, are compared with previously available high-frequency single- and multi-channel profiles (5–15 km grid spacing). The low-frequency data contribute to a new understanding of the basal morphology and fill stratigraphy of the tunnel-valleys, in part due to higher data densities (≥1 km grid spacing), but also to improved imaging of reflectors at depth. The tunnel-valleys are seen to be overdeepened troughs, shallow (≤0.5 km) relative to their widths (≤6 km). The basal unconformity defines a series of arborescent elements, convergent to the south; erosional overlap by younger elements to the north has resulted in anastomosing patterns in places. The fill is dominated by axially downlapping clinoforms, descending to the north, onlapped and overlain by subhorizontal reflectors. Well data show that sand-dominated glaciofluvial sediments are overlain by glaciolacustrine to marine muds. Better definition of the clinoforms on low- versus high-frequency multi-channel data is suggested to reflect the coarse spatial scale of the backset glaciofluvial strata. The results support a simple interpretation of time-transgressive tunnel-valley formation by coeval glaciofluvial erosion and backfill beneath the outer tens of kilometres of the northward receding Elsterian ice sheet margin. Comparable submarginal interpretations have been proposed for drainage features (tunnel-valleys and eskers) of the last deglaciation of both northern Europe and North America using integrated geomorphologic and stratigraphic methods. Commercial 2D and 3D seismic data are widely available from exploration areas such as the North Sea and are argued to constitute an underexploited resource for Quaternary research.  相似文献   

A hybrid indirect boundary element—discrete wave number method applied to simulate the seismic response of stratified alluvial valleys     

S. A. Gil-Zepeda  J. C. Montalvo-Arrieta  R. Vai  F. J. Snchez-Sesma 《Soil Dynamics and Earthquake Engineering》2003,23(1):77-86

A hybrid indirect boundary element – discrete wavenumber method is presented and applied to model the ground motion on stratified alluvial valleys under incident plane SH waves from an elastic half-space. The method is based on the single-layer integral representation for diffracted waves. Refracted waves in the horizontally stratified region can be expressed as a linear superposition of solutions for a set of discrete wavenumbers. These solutions are obtained in terms of the Thomson–Haskell propagators formalism. Boundary conditions of continuity of displacements and tractions along the common boundary between the half-space and the stratified region lead to a system of equations for the sources strengths and the coefficients of the plane wave expansion. Although the regions share the boundary, the discretization schemes are different for both sides: for the exterior region, it is based on the numerical and analytical integration of exact Green's functions for displacements and tractions whereas for the layered part, a collocation approach is used. In order to validate this approach results are compared for well-known cases studied in the literature. A homogeneous trapezoidal valley and a parabolic stratified valley were studied and excellent agreement with previous computations was found. An example is given for a stratified inclusion model of an alluvial deposit with an irregular interface with the half-space. Results are displayed in both frequency and time domains. These results show the significant influence of lateral heterogeneity and the emergence of locally generated surface waves in the seismic response of alluvial valleys.  相似文献   

A quantitative study of the energy release in the aftershocks of the Bhuj earthquake, 2001, India, using Lg phase     

G. Jayachandran  M.M. Abdul RazakA.G.V. Prasad  E. Unnikrishnan 《Physics of the Earth and Planetary Interiors》2003,138(2):131-145

The devastating earthquake on 26 January 2001 at Bhuj, India, resulted in large-scale death and destruction of properties of several million US dollars. The moment magnitude of the earthquake was 7.7 and its maximum focal intensity exceeded X in MM scale. The rate of aftershocks of this earthquake, recorded at Gauribidanur seismic array station (GBA), shows a monotonic decay with time superposed with oscillations. For the Indian continent the Lg phase is a prominent arrival at regional distances. The estimate of Lg amplitude is obtained by optimally fitting the Lg wave train to a exponential decay curve. The logarithm of these amplitudes and logarithm of root mean square (rms) value of actual amplitudes of the Lg are calibrated with USGS m_b to create a local m_bLg magnitude scale. The energy released from these aftershocks is calculated from the rms value of Lg phase. The plot of cumulative energy release with time follows the power law of the form t^p, superposed with oscillations. The exponent of the power law, p, is estimated both by a time-window scanning method and by an interpolation method. The value of p is 0.434 for time-window scanning method and 0.432 for the interpolation method. The predominant periods found in the oscillatory part of the cumulative energy, obtained by differencing the observed from the power law fit, are 10.6, 7.9, 5.4, 4.6 and 3.5 h for time-window scanning method. The corresponding periods for interpolation method are 13.4, 11.5, 7.4, 4.2, 3.5, 2.6 and 2.4 h.  相似文献   

Seismic wave velocity and anisotropy of serpentinized peridotite in the Oman ophiolite     

Benoît Dewandel  Franoise Boudier  Hartmut Kern  Waris Warsi  David Mainprice 《Tectonophysics》2003,370(1-4):77-94

Shallow seismic measurements in harzburgite from the Oman ophiolite performed in a zone where the maximum horizontal anisotropy is expected (vertical foliation and horizontal lineation) point to a dominant dependence of seismic properties on fracturing.

Optical microscopy studies show that microcracks are guided by the serpentine (lizardite) penetrative network oriented subparallel to the harzburgite foliation and subperpendicular to the mineral lineation, and that serpentine (lizardite) vein filling has a maximum concentration of (001) planes parallel to the veins walls. The calculated elastic properties of the oriented alteration veins filled with serpentine in an anisotropic matrix formed by oriented crystals of olivine and orthopyroxene are compared with seismic velocities measured on hand specimens.

Laboratory ultrasonic data indicate that open microcracks are closed at 100 MPa pressure, e.g. (J. Geophys. Res. 65, (1960) 1083) and (Proc. ODP Sci. Results Leg 118, (1990) 227). Above this pressure, laboratory measurements and modeling show that P-compressional and S-shear wave velocities are mainly controlled by the mineral preferred orientation. Veins sealed with serpentine are effective in slightly lowering P and S velocities and increasing anisotropy. The penetrative lizardite network does not affect directly the geometry of seismic anisotropy, but contributes indirectly in the fact that this network controls the microcrack orientations.

Comparison between seismic measurements of peridotite and gabbro in the same conditions suggest that P- and S-waves anisotropies are a possible discriminating factor between the two lithologies in the suboceanic lithosphere.  相似文献   

Architecture of fault zones determined from outcrop, cores, 3-D seismic tomography and geostatistical modeling: example from the Albalá Granitic Pluton, SW Iberian Variscan Massif     

J. Escuder Viruete  R. Carbonell  D. Martí  M. J. Jurado  A. Prez-Estaún 《Tectonophysics》2003,361(1-2):97-120

The 3-D seismic tomographic data are used together with field, core and well log structural information to determine the detailed 3-D architecture of fault zones in a granitic massif of volume 500×575×168 m at Mina Ratones area in the Albalá Granitic Pluton. To facilitate the integration of the different data, geostatistical simulation algorithms are applied to interpolate the relatively sparse structural (hard) control data conditioned to abundant but indirect 3-D (soft) seismic tomographic data. To effectively integrate geologic and tomographic data, 3-D migration of the velocity model from the time domain into the depth domain was essential. The resulting 3-D model constitutes an image of the fault zone architecture within the granitic massif that honours hard and soft data and provides an evaluation of the spatial variability of structural heterogeneities based on the computation of 3-D experimental variograms of Fracture Index (fault intensity) data. This probabilistic quantitative 3-D model of spatially heterogeneous fault zones is suitable for subsequent fluid flow simulations. The modeled image of the 3-D fault distribution is consistent with the fault architecture in the Mina Ratones area, which basically consists of two families of subvertical structures with NNE–SSW and ENE–WSW trends that displaces the surfaces of low-angle faults (North Fault) and follows their seismically detected staircase geometry. These brittle structures cut two subvertical dykes (27 and 27′ Dykes) with a NNE–SSW to N–S trend. The faults present high FI (FI>12) adjacent bands of irregular geometry in detail that intersect in space delimiting rhombohedral blocks of relatively less fractured granite (FI<6). Both structural domains likely correspond with the protolith and the damaged zone/fault core in the widely accepted model for fault zone architecture. Therefore, the construction of 3-D grids of the FI in granitic areas affected by brittle tectonics permits the quantitative structural characterization of the rock massif.  相似文献   

Geoid determination using adapted reference field, seismic Moho depths and variable density contrast   总被引：4，自引：0，他引：4  

H. A. Abd-Elmotaal  N. Kühtreiber 《Journal of Geodesy》2003,77(1-2):77-85

 The traditional remove-restore technique for geoid computation suffers from two main drawbacks. The first is the assumption of an isostatic hypothesis to compute the compensation masses. The second is the double consideration of the effect of the topographic–isostatic masses within the data window through removing the reference field and the terrain reduction process. To overcome the first disadvantage, the seismic Moho depths, representing, more or less, the actual compensating masses, have been used with variable density anomalies computed by employing the topographic–isostatic mass balance principle. In order to avoid the double consideration of the effect of the topographic–isostatic masses within the data window, the effect of these masses for the used fixed data window, in terms of potential coefficients, has been subtracted from the reference field, yielding an adapted reference field. This adapted reference field has been used for the remove–restore technique. The necessary harmonic analysis of the topographic–isostatic potential using seismic Moho depths with variable density anomalies is given. A wide comparison among geoids computed by the adapted reference field with both the Airy–Heiskanen isostatic model and seismic Moho depths with variable density anomaly and a geoid computed by the traditional remove–restore technique is made. The results show that using seismic Moho depths with variable density anomaly along with the adapted reference field gives the best relative geoid accuracy compared to the GPS/levelling geoid. Received: 3 October 2001 / Accepted: 20 September 2002 Correspondence to: H.A. Abd-Elmotaal  相似文献   

震级加权四指标Blade算法及在地震带识别中的应用     

秦承志  裴韬  周成虎  李全林  韩志军  汪闽  蔡强 《地震》2003,23(2):59-69

Blade算法的产生是根据地震点的分布寻找地震断层，其优势在于能从较稀疏的点分布中找出线型条带模式，但不足的是完全不考虑地震的震级屑性。针对Blade算法的几个不足之处逐步改进，提出了震级加权四指标Blade算法。算法主要的改进体现在：①引入以震级为变量的权重函数，体现了高震级地震的控制作用，通过模拟与实例比较了三种权重函数的效果；②改进原方法中所挑出的Blade中心必须有地震点，引入四指标评价体系代替原方法的二指标评价体系，同时还根据指标值将挑选出的线型条带修正到更淮确的位置。将原算法与改进算法应用于华北地区4级以上的地震数据集以按寻地震带，结果表明，震级加权四指标Blade算法较Blade算法有显改进，取得了较好的应用效果。  相似文献   

利用地震层析成像数据计算地幔对流新模型的探讨   总被引：5，自引：3，他引：5       下载免费PDF全文

傅容珊  黄建华  董树谦  张群山  常筱华 《地球物理学报》2003,46(6):772-778

假设地幔地震层析成像数据对应的地幔横向不均匀结构是地幔热对流的结果. 将地震层析成像数据转化为地幔温度(或密度)不均匀分布，考虑热流体动力学的三个基本方程，顾及热输运方程中的非线性项，直接将地震层析成像转化的地幔温度不均匀分布作为内部荷载引入基本方程, 反演计算地幔对流. 本文在利用地震层析成像数据计算地幔对流模型的新理论和方法的基础上，用SH12WM13地震层析成像模型数据，计算了全球地幔对流格局. 结果表明，对流格局不仅依赖地震层析成像数据，而且在很大程度上受地幔动力学框架、热动力参数和边界条件的所确定的系统响应函数的影响. 显示了地幔中复杂的对流格局，特别是区域性层状对流以及多层对流环可能在地幔中存在的现象.  相似文献   

忻州市房屋建筑地震损失与人员伤亡预测     

兰青龙  郭星全 《高原地震》1997,(1)

在对忻州市现有房屋建筑进行调查研究的基础上，对房屋建筑按结构进行了分类，并对各类房屋进行了抗震分析，进而建立了相应的易损性矩阵，最终结果得到以小区为单元遭遇不同强度地震作用的地震损失和人员伤亡，以及50年地震期望损失。  相似文献