Velocity analysis after migration

The double‐square‐root (DSR) equation used in pre‐stack migration is formulated in terms of velocity‐dependent and velocity‐independent terms. The velocity‐dependent term is shown to be the hyperbolic normal moveout (NMO) correction, whereas the velocity‐independent term is related to the recording geometry only. This separation of the velocity‐dependent term offers a means of applying vertical corrections to an initial migration velocity field. Using this concept, procedures are described both for velocity determination and for achieving improved structural imaging.
This decoupling is accurate both for constant‐velocity media and for media whose velocity varies as a function of depth. In media whose velocity varies as a function of both space and depth, a procedure is described for building velocity models through common‐image gather (CIG) stacking following prestack depth migration (PSDM) and time conversion (TC). This so‐called PSDM‐TC stack procedure provides a means of (a) incorporating both vertical and lateral velocity updates into an initial velocity model, (b) obtaining improved structural imaging by using a non‐optimal velocity model for the prestack depth migration, and (c) updating velocity by flattening CIGs and maximizing stack energy. The procedure can be applied to both P‐P wave and P‐SV wave migration.     

Studies of Water Velocity in the Capillary Fringe: The Point Velocity Probe

The point velocity probe (PVP) is a device that can measure groundwater velocity at the centimeter scale, and unlike devices that measure velocity within well screens, the PVP operates while in direct contact with the porous medium. Because of this feature, it was postulated that the PVP could be effective in measuring velocity within the capillary fringe. This hypothesis was tested using a laboratory flow-through cell filled with a medium-fine sand from Canadian Forces Base Borden. The cell was constructed to simulate conditions such that the PVP was positioned from 2.5 cm below the water table to 79 cm above the water table. As the water table was lowered, the PVP gave highly consistent values of velocity over the range equivalent to 2.5 cm below the water table to 44 cm above the water table, the approximate extent of the capillary fringe. The average measured velocity was 11.3 cm/d ± 11.6%, somewhat higher than that calculated based on the measured discharge through the cell (7.5 cm/d ± 5.5%). With a further decline in the water table there was a progressive decrease in the measured velocity values, consistent with the declining hydraulic conductivity as the sand material drained. Readings could not be made beyond about 57 cm, where the water content was approximately 75% of saturation. These experiments showed that the PVP is capable of measuring groundwater velocity within the saturated zone above the water table and possibly into the unsaturated zone. Currently, this is the only instrument available with this capability.     

Prediction of the Shear Wave Velocity from Compressional Wave Velocity for Gachsaran Formation

Shear and compressional wave velocities, coupled with other petrophysical data, are very important for hydrocarbon reservoir characterization. In situ shear wave velocity (Vs) is measured by some sonic logging tools. Shear velocity coupled with compressional velocity is vitally important in determining geomechanical parameters, identifying the lithology, mud weight design, hydraulic fracturing, geophysical studies such as VSP, etc. In this paper, a correlation between compressional and shear wave velocity is obtained for Gachsaran formation in Maroon oil field. Real data were used to examine the accuracy of the prediction equation. Moreover, the genetic algorithm was used to obtain the optimal value for constants of the suggested equation. Furthermore, artificial neural network was used to inspect the reliability of this method. These investigations verify the notion that the suggested equation could be considered as an efficient, fast, and cost-effective method for predicting Vs from Vp.     

One-dimensional Shear Velocity Structure of Northern Africa from Rayleigh Wave Group Velocity Dispersion

—?Rayleigh wave group velocity dispersion measurements from 10?s to 160?s periods have been made for paths traversing Northern Africa. Data were accumulated from the IRIS DMC, GEOSCOPE, and MEDNET seismic networks covering the years 1991–1997. The group velocity measurements are made including the effects of debiasing for instantaneous period and a single-iteration, mode-isolation (phase match) filter. The curves are grouped by tectonic province and compared to tomographic model-based curves in an effort to test and validate the tomographic models. Within each tectonic category (rift, orogenic zone, or craton) group velocity curves from various provinces are similar. Between tectonic categories, however, there are marked differences. The rift related paths exhibit the lowest group velocities observed, and cratonic paths the fastest. One-dimensional shear velocity inversions are performed, and while highly nonunique, the ranges of models show significant differences in upper mantle velocities between the tectonic provinces.¶This work is part of a larger project to determine group velocity maps for North Africa and the Middle East. The work presented here provides important tools for the validation of tomographic group velocity models. This is accomplished by comparing group velocity curves calculated from the tomographic models with carefully selected high-quality group velocity measurements. The final group velocity models will be used in M _s measurements, which will contribute to the m _b :M _s discriminant important to the Comprehensive Nuclear-Test-Ban Treaty (CTBT). The improved shear wave velocity models provided by this study also contribute to the detection, location, and identification of seismic sources.     

大理岩的波速各向异性测量

利用 GC- 1 0 0型工程多波参数分析仪 ,对山东莱州大理岩进行了波速各向异性的实验室观测。实验采用两组岩样 ,一组为带有先天的优势定向排列裂缝的岩样 ,另一组为带有优势层理走向的完整岩石。在未加载的状态下 ,发现两组岩样都有明显的波速方位各向异性。对于带有先天的优势定向排列裂缝的岩样 ,甚至可以在无加载状态下观测到剪切波的分裂现象     

Uncertainty in Shear-Wave Velocity Profiles

Journal of Seismology - This paper considers the uncertainty in the shear wave velocity (Vs) of soil and rock profiles for use in earthquake site response calculations. This uncertainty is an...     

横波速度预测方法

准确的横波测井速度是叠前地震反演和叠前地震属性分析的必要参数,然而实际生产中往往缺乏横波速度信息.采用经验公式往往精度有限,本文采用Biot-Gassmann低频速度模型,以及Pride公式建立起基质弹性模量与骨架弹性模量关系,证明了纵波速度大小随固结系数的增大而减小,因而可以通过迭代方式计算出合适的固结系数,进而得到横波速度大小.通过两个实例说明该方法能得到很高的预测精度.     

Velocity analysis using AB semblance

I derive and analyse an explicit formula for a generalized semblance attribute, which is suitable for the velocity analysis of prestack seismic gathers with distinct amplitude trends. While the conventional semblance can be interpreted as a squared correlation with a constant, the AB semblance is defined as a correlation with a trend. This measure is particularly attractive for analysing class II AVO anomalies and converted waves. Analytical derivations and numerical experiments show that the resolution of the AB semblance is approximately twice as low as that of the conventional semblance. However, this does not prevent it from being an effective attribute. I use synthetic and field data examples to demonstrate the improvements in velocity analysis from AB semblance.     

Velocity analysis based on data correlation

Several methods exist to automatically obtain a velocity model from seismic data via optimization. Migration velocity analysis relies on an imaging condition and seeks the velocity model that optimally focuses the migrated image. This approach has been proven to be very successful. However, most migration methods use simplified physics to make them computationally feasible and herein lies the restriction of migration velocity analysis. Waveform inversion methods use the full wave equation to model the observed data and more complicated physics can be incorporated. Unfortunately, due to the band‐limited nature of the data, the resulting inverse problem is highly nonlinear. Simply fitting the data in a least‐squares sense by using a gradient‐based optimization method is sometimes problematic. In this paper, we propose a novel method that measures the amount of focusing in the data domain rather than the image domain. As a first test of the method, we include some examples for 1D velocity models and the convolutional model.     

Study on Shear Wave Velocity Structure and Velocity Ratio Beneath Ordos Block and Its Eastern and Southern Margins

Using pure S wave fitting method, we studied the shear wave velocity structures under the Ordos block and its eastern and southern marginal areas. The results show that the velocity structure beneath Yulin station in the interior of Ordos block is relatively stable, where no apparent change between high and low velocity layers exists and the shear wave velocity increases steadily with the depth. There is a 12km thick layer at the depth of 25km under this station, with an S wave velocity (Vs=3.90km/s) lower than that at the same depth in its eastern and southern areas (Vs≥4.00km/s). The crust under the eastern margin of Ordos block is thicker than that of the Yulin station, and the velocity structures alternate between the high and low velocity layers, with more low velocity layers. It has the same characteristic as having a 10km-thick low velocity layer (Vs=3.80km/s) in the lower crust but buried at a depth of aout 35km. Moreover, we studied the Vp/Vs ratio under each station in combination with the result of P wave velocity inversion. The results show that, the average velocity ratio of the Yulin station at the interior of Ordos block is only 1.68, with a very low ratio (about 1.60) in the upper crust and a stable ratio of about 1.73 in the mid and lower crust, which indicates the media under this station is homogenous and stable, being in a state of rigidity. But at the stations in the eastern and southern margins of the Ordos block, several layers of high velocity ratio (about 1.80) have been found, in which the average velocity ratio under Kelan and Lishi stations at the eastern margin is systemically higher than that of the general elastical body waves (1.732). This reflects that the crust under the marginal areas is more active relatively, and other materials may exist in these layers. Finally, we discussed the relationship among earthquakes, velocity structures beneath stations and faults.     

鄂尔多斯块体及其东南缘剪切波速度结构与波速比研究

利用深源远震的纯S波波形拟合方法研究了鄂尔多斯块体及其东、南缘的剪切波速度结构。结果显示，鄂尔多斯块体内部榆林台站下方速度结构相当稳定，没有很明显的高低速层变化，随着深度的增加，剪切波速度稳步升高；在该台下方25km深处有一个厚度达12km的层位(ys=3．90km／s)，该层的波速度相对其东部同等深度处的波速度偏低(以≥4．00km／s)。鄂尔多斯地块东部边缘的地壳厚度都比榆林厚，而且呈现高、低速层相间结构，低速层明显增多，与块体内部比较一致的特征为下地壳是一个厚达10km的速度较低的下地壳(yS=3．8km／s)，但埋深在35km左右。另外反演得到了各个台站的P波速度结构，并对相应的波速比(Vp/Vs)进行了研究，发现位于鄂尔多斯块体内部的榆林台波速比平均值仅为1．68，上地壳波速比处在非常低的状态(1．60左右)，中下地壳一直到上地幔的波速比稳定在1．73左右，反映介质均匀稳定，处于一种刚性状态；而鄂尔多斯块体东、南边缘的台站，都有几个波速比较高(1．80左右)的层位，其中东部边缘苛岚和离石地区的波速比平均值系统超过一般的弹性体波速比平均值1．732，反映了边缘地区地壳活动相对比较活跃，介质层中可能有其他物质的影响。     

Velocity anisotropy and symmetry of dunite fabric

Summary From the space distribution of P- and S-wave velocities, determined at a hydrostatic pressure of 1 GPa, complete sets of elastic constants were calculated for the Twin Sisters dunite. It was found that orthorhombic symmetry is a reasonable approximation for the dunite sample; with one exception the deviations of the individual constants, determined from different waves, do not exceed a few percent. As a seismological application a simple model of a 120 km thick lithosphere, formed by the dunite, was considered for calculating the differences in the time arrivals of SV and SH waves. The greatest time differences, about 3s, were obtained in the vertical plane containing the direction of the greatest P-wave velocity, however, for the real lithosphere we estimate effects which only cause differences of the order of 1s.     

波速异常的区域特征

有关波速比异常预报地震的震例已有不少论述,然而就一个地区的波速异常区域特征则很少讨论。为进一步监视地震活动,做好地震预报工作,我们以甘肃及邻近地区近十年来发生的一些中强地震为例,研究了它们的时空特性,並同其它一些地区的研究结果进行比较,     

Velocity sensitivity in transversely isotropic media1

We consider the problem of determining and predicting how the wave speeds in particular directions for a transversely isotropic (TI) medium depend on particular combinations of the density-normalized moduli A_ij. The expressions for the q^P and q^SV velocities are known to depend on four moduli. Normally, we can only determine three independent parameters from q^P data, or two from q^SZ data, as the others have much lower sensitivity. The resolvable parameters are conveniently described by axial and off-axis parameters: for q^P rays, P_0°= A₁₁, P_90°= A₃₃ and P_45°=(A₁₁+ A₃₃)/4 + (A₁₃+2A₅₅)/2; and for q^SV rays, S_0°= S_90°=A₅₅ and S 45°= (A₁₁+ A ₃₃)/4- A₁₃/2. These parameters control the magnitude of the squared-velocities on the axes and at approximately 45°. For an arbitrary TI medium, if the medium is perturbed in a way that preserves a particular parameter, then slowness points in the associated direction and mode witl be approximately preserved in the new medium. we refer to these parameters as ‘push-pins’, i.e. if a parameter is fixed, the associated part of the slowness surface is pinned in place. Because, these five push-pins only contain four independent moduli, we can only fix at most three push-pins. Perturbing one of the other parameters inevitably perturbs the other. Numerical results illustrating the linkage between two push-pins, when three are fixed, are presented. So-called anomalous TI media occur when the roles of the q^P and q^SV waves are reversed: in some directions the faster ray has transverse polarization. That, in turn, requires anomalous velocities at the push-pins, i.e. S_0° > P_0°, S_45° > P_45° and/or S_90° > P_90° (equivalent to the usual anomalous conditions A₁₁ < A₅₅, < 0 and/or A₃₃ < A⁵⁵). In the Appendix, we confirm that anomalous sensitivities of the velocities at the five push-pins only occur in such media, although the push-pins still apply if interpreted appropriately. Truly anomalous sensitivities, in which push-pins play no role, only occur in media near the boundary between normal and anomalous.     

非线性层析反演速度建模技术

深度速度模型的构建仍然是地震成像中的巨大挑战,获得一个精确的深度速度模型和减少深度成像项目周期都是至关重要的。常规层析反演速度建模每次迭代相当于一次线性反演,且需要重新的拾取工作,导致非常耗时,效率低下。本文提出非线性层析反演速度建模技术来建立速度模型。拾取共成像点道集的RMO量,转换到叠前域,作为运动学不变量,通过层析反演迭代进行模型更新。用一个多次的线性反演来逼近一个非线性的物理过程,避免重复的拾取工作,大大提高项目的运转效率。通过实例证明该方法的有效性。      

层析成像反演速度建模方法研究

本文应用层析成像反演方法优化叠前深度偏移速度模型。阐述叠前深度偏移速度建模流程,详细介绍利用两种不同层析反演方法来优化深度域的层速度模型,对同一实际地震资料速度模型建立的应用效果表明,在资料信噪比较高的地区能提供准确解释层位信息的前提下,模型层析反演优化后的速度模型精度要比网格层析反演优化后的速度模型更高,且稳定性强。      

Velocity model updating using image gathers1

For successful prestack depth migration an accurate velocity model is needed. One method for model updating is based on image gather analysis. In an image gather all reflectors line up horizontally if the correct velocities are used for the depth migration. This is also true for dipping reflectors, as all traces of an image gather belong to the same surface coordinate. The images of the reflector in an image gather curve upwards if the velocity used for the migration is too low, or downwards if the velocity is too high. This deviation can be used for model updating. Curves which depend on depth, offset and a parameter which relates the estimated to the true model are fitted to the image. By calculating the coherence along the deviation curves, this parameter can be estimated and hence an update can be calculated. Formulae are derived for the deviation curves and the update of the velocity depth model for a multilayered model for both shot and common-offset migrated data, with and without gradients. The method is tested on synthetic data with satisfactory results.