On the accuracy of the ground force estimated in vibroseis acquisition

For a linear elastic Earth the time derivative of the ground force is considered proportional to the far-field wavelet. Under the assumption that the baseplate is stiff and the bending forces of the baseplate are negligible, the ground force is also approximated by the sum of the accelerations of the baseplate and the reaction mass weighted by the respective masses. Combining these two assumptions, the time derivative of the weighted sum is considered proportional to the far-field wavelet. This result, often referred to as the far-field wavelet assumption, although convenient and most often employed is not always valid. We explore its validity using the spectral harmonic ratios of recorded data, which are used extensively in data filtering and analysis of vibratory data. We show that the far-field wavelet assumption fails particularly for harmonic components of even order. More compact soil after repeated shots further invalidates this assumption. Non-linear modelling of the ground under the vibrator point may provide a direction towards solving this discrepancy. Finally, we describe a method for the estimation of the harmonic spectral ratios.     

THE AMPLITUDE AND PHASE RESPONSE OF A SEISMIC VIBRATOR*

The amplitude and phase response of a simple model is compared with the performance of a real vibrator working in the field. The field results show a characteristic phase response which confirms that the real drive force applied to the baseplate and its load impedance is faithfully represented by the acceleration of the reaction mass. It follows that all the parameters necessary to calculate the load impedance and the true power dissipated in the earth can be measured at the output of the vibrator. It also follows that the current method of baseplate phase compensation should be reconsidered.     

Developments in vibrator control

Hydraulic limitations, non-rigidity of the baseplate as well as variable characteristics of the ground constantly distort the downgoing energy output by vibrators. Therefore, a real time feedback control must be performed to continuously adjust the emitted force to the reference pilot signal. This ground force is represented by the weighted sum of the reaction mass and the baseplate accelerations. It was first controlled with an amplitude and phase locked loop system, poorly reactive and sensitive to noise. Later on, new vibrator electronics based on a digital model of the vibrator were introduced. This model is based on the physical equations of the vibrator and of the ground. During an 'identification' process, the model is adjusted to each particular vibrator. Completed by a Kalman adaptive filter to remove the noise, it computes ten estimated states via a linear quadratic estimator. These states are used by a linear quadratic control to compute the torque motor input and to compare the ground force estimated from the states with the pilot signal. Test results using downhole geophones demonstrate the benefit of filtered mode operation.     

Modelling and modal analysis of seismic vibrator baseplate

The vibroseis method must be extended to its limits as the search for oil and gas continues on land. To successfully improve vibroseis data quality, it is crucial to evaluate each element in the vibroseis data acquisition system and ensure that the contribution from each element is successful. Vibroseis systems depend greatly upon the ability of vibrators to generate synchronous, repeatable ground-force sweeps over a broad frequency range. This requires that the reaction mass and the baseplate of the vibrator move as rigid bodies. However, rigid-body motion is not completely true for high- frequency vibrations, especially for the vibrator baseplate. In order to accurately understand the motion of the vibrator baseplate, a finite element analysis model of the vibrator baseplate and the coupled ground has been developed. This model is useful for simulating the vibrator baseplate dynamics, evaluating the impact of the baseplate on the coupled ground and vibrator baseplate design. Model data demonstrate that the vibrator baseplate and its stilt structure are subject to six significant resonant frequencies in the range of 10–80 Hz. Due to the low rigidity of the baseplate, the baseplate stilt structure experiences severe rocking motions at lower frequencies and the baseplate pad experiences severe flexing motions at higher frequencies. Flexing motions cause partial decoupling, which gives rise to increased levels of harmonic distortion and less useable signal energy. In general, the baseplate pad suffers more bending and flexing motions at high frequencies than low frequencies, leading less efficiency in transmitting the useable energy into the ground.     

Two-dimensional development of the dynamic coupled consolidation scaled boundary finite-element method for fully saturated soils

The scaled boundary finite-element method is a powerful tool used to analyse far-field boundary soil–structure interaction problems. In this paper, the method is extended to include Biot's coupled consolidation in order to deal with fully saturated soil as a two-phase medium. The advantages of this method are explained in this paper. The detailed formulation considers the general two-dimensional (2D) analysis case, accounting for body forces and surface tractions in both bounded and unbounded media.     

ON THE DETERMINATION OF THE DOWNGOING P-WAVES RADIATED BY THE VERTICAL SEISMIC VIBRATOR*

It is well recognized that in order to realize the full potential of the Vibroseis technique, one needs to ensure accurate phase locking and a meaningful cross-correlation. To achieve these two important objectives we require an accurate estimate of the compressional stress wave radiated by the vibrator into the ground. In this paper a simple method (subject of a patent application) is developed for predicting the compressional stress waves radiated by a vertical vibrator. The main feature of the proposed method is that it involves the field measurement of the acceleration of the reaction mass and the baseplate, respectively. The method is illustrated by computing the compressional stress waves generated by a typical vertical vibrator radiating into ice, chalk, sand, and mud. It is shown that for a seismic vibrator radiating into hard ground the pressure of the downgoing P-wave is 180° out of phase with the baseplate velocity. It is also shown that when the driving force of the seismic vibrator has a flat amplitude spectrum, the amplitude spectrum of the downgoing P-wave falls off by 6 dB/octave towards low frequencies.     

ENHANCED SERVOVALVE TECHNOLOGY FOR SEISMIC VIBRATORS1

The Pelton DR^TM Servovalve Enhancement causes the natural output of a vibrator to resemble the desired output more closely. This simplifies the control problem and reduces harmonic distortion. The traditional type of servovalve used on seismic vibrators is a flow-control servovalve. Flow is proportional to a vibrator's baseplate velocity, with respect to its reaction mass. The new servovalve control parameter is pressure rather than flow. The differential pressure applied to a vibrator's actuator piston, multiplied by the area of the piston, equals the force applied to the vibrator's baseplate structure. This may be defined as actuator force. There is a simpler and more linear relationship between actuator force and ground force than between actuator velocity and ground force. Thus, it is better for the servovalve to control pressure into the actuator rather than flow. A flow-control servovalve can be made to control pressure by sensing the differential pressure across a vibrator's actuator piston and applying it as a negative feedback around the servovalve main stage. This has been carried out and tested. The result is more accurate vibrator control and reduced harmonic distortion.     

Interaction of an axisymmetric body with obliquely incident seismic waves by global local finite elements

Asymmetric steady-state structure-media interaction due to obliquely incident body waves is investigated via a version of the global local finite element method. In the present version, a local region that houses an axisymmetric structure is modelled by conventional finite elements, while the behaviour in the remaining portion of the homogeneous semi-infinite medium is presented by the spherical harmonics that are the eigensolutions of the entire space problem. The solution scheme involves (1) full displacement and traction continuity along the boundary between the local and the exterior regions and (2) satisfaction of the traction-free requirement on the surface of the half-space beyond the discretized region by virtue of a sequence of integral constraints of the non-zero weighted surface tractions of the spherical harmonics. The numerical results presented are for a perfectly bonded rigid circular foundation resting on the surface of the half-space and subjected to obliquely incident body waves. Dependence of the displacement response of the footing upon incident angles and dimensionless wave numbers is thoroughly studied.     

TWO METHODS FOR CONTINUOUS MONITORING OF HARMONIC DISTORTION IN VIBROSEIS SIGNALS1

The quality of Vibroseis survey data can be improved by continuously monitoring the vibrator's baseplate and reaction mass accelerations. Equipment failures can be detected as they occur, rather than relying on similarity trials at the beginning and end of the day's production. Equipment faults can then be corrected as they happen and thus would not have a detrimental effect on the quality of the survey data. Source efficiency can be optimized by monitoring the amount of harmonic distortion generated by the vibrator at different drive levels on the different surfaces which may be encountered during a survey. Phase problems introduced by poor coupling of the baseplate to the ground can also be identified and addressed in the field. Rapid analysis of vibrator signals is required if continuous monitoring is to be useful. Frequency-time (f-t) analyses of vibrator signals are often used in processing centres, but are slow and require a large storage capacity which makes the technique unsuitable for a field analysis system. The two methods proposed to analyse vibrator signals entail the use of hodograms and time-varying notch filters. Hodograms provide a qualitative analysis of harmonic distortion and vibrator performance. A fast, time-varying notch filter gives quantitative and qualitative information about the harmonic distortion present in the signal and can be used to identify problems with vibrator behaviour. Both the hodogram and fast, time-varying notch filter methods can analyse the vibrator's reaction mass and baseplate accelerations as it progresses through its sweep and can present automatically interpreted results to the operator before moving to the next vibrator point.     

Scattering of seismic waves by cracks in multi-layered geological regions: I. Mechanical model

In this work, a hybrid boundary integral equation method (BIEM) is developed, based on both displacement and hypersingular traction formulations, for the analysis of time-harmonic seismic waves propagating through cracked, multi-layered geological regions with surface topography and under plane strain conditions. Specifically, the displacement-based BIEM is used for a multi-layered deposit with interface cracks, while the regularized, traction-based BIEM is used when internal cracks are present within the layers. The standard uni-dimensional boundary element with parabolic shape functions is employed for discretizing the free surface and the layer interfaces, while special discontinuous boundary elements are placed near the crack tips to model the asymptotic behaviour of both displacements and tractions. This formulation yields displacement amplitudes and phase angles on the free surface of a geological deposit, as well as stress intensity factors near the tips of the cracks. Finally, in the companion paper, numerical results are presented which show that both scattered wave and stress concentration fields are sensitive to the incidence seismic wave parameters and to specific site conditions such as surface topography, layering, the presence of cracks and crack interaction.     

Review of vibroseis data acquisition and processing for better amplitudes: adjusting the sweep and deconvolving for the time-derivative of the true groundforce

The goal of vibroseis data acquisition and processing is to produce seismic reflection data with a known spatially-invariant wavelet, preferably zero phase, such that any variations in the data can be attributed to variations in geology. In current practice the vibrator control system is designed to make the estimated groundforce equal to the sweep and the resulting particle velocity data are cross-correlated with the sweep. Since the downgoing far-field particle velocity signal is proportional to the time-derivative of the groundforce, it makes more sense to cross-correlate with the time-derivative of the sweep. It also follows that the ideal amplitude spectrum of the groundforce should be inversely proportional to frequency. Because of non-linearities in the vibrator, bending of the baseplate and variable coupling of the baseplate to the ground, the true groundforce is not equal to the pre-determined sweep and varies not only from vibrator point to vibrator point but also from sweep to sweep at each vibrator point. To achieve the goal of a spatially-invariant wavelet, these variations should be removed by signature deconvolution, converting the wavelet to a much shorter zero-phase wavelet but with the same bandwidth and signal-to-noise ratio as the original data. This can be done only if the true groundforce is known. The principle may be applied to an array of vibrators by employing pulse coding techniques and separating responses to individual vibrators in the frequency domain. Various approaches to improve the estimate of the true groundforce have been proposed or are under development; current methods are at best approximate.     

利用有限单元计算地应力时的边界条件处理

本文借助于弹性力学中的弹性约束方法,利用了物理学上的镜像法,对边界条件进行了特殊处理,从而把整体结构表面上未知的分布面力转化成边界单元的节点力,解决了未知边界条件的约束问题。通过实例论证了本文提出的边界处理方法是可靠的和有效的     

Axisymmetric soil–structure interaction by global–local finite elements

A version of the global–local finite element method is presented for studying dynamic steady-state soil–structure interaction wherein the soil medium extends to infinity. Herein, only axisymmetric behaviour is considered. In this approach, conventional finite elements are used to model the structure and some portion of the surrounding soil medium considered to be homogeneous and isotropic. A complete set of outgoing waves in the form of spherical harmonics for the entire space is used to represent the behaviour in the half-space beyond the finite element mesh and these are termed the global functions. Full traction and displacement continuity is enforced at the finite element mesh interface with the outer region. On the free surface of the half-space in the outer field, traction-free surface conditions are enforced by demanding that a sequence of integrals of the weighted-average tractions must vanish. Numerical examples are presented for the response of different shaped foundations, resting on the free surface or at various submerged levels, due to a normal seismic plane compressional wave. Plots of differential scattering cross-sections show the angular distribution of the energy (its directional nature) of the scattered field.     

Pushing the vibrator ground-force envelope towards low frequencies

Several mechanical and hydraulic limitations hinder the ground-force energy output of a seismic vibrator at low frequencies. The hydraulic pump flow, pump response time, reaction mass stroke, servo valve stroke, engine horsepower, accumulator size, harmonic distortion and vehicle chassis isolation each play a role in limiting the ground-force energy output of vibrators. In addition, the peak-decoupling force – which is defined as the smaller value of either the maximum peak force or the hold-down weight – also plays a role in limiting ground-force energy production. A model useful for simulating seismic vibrator dynamics is developed to evaluate the impact of these parameters on the vibrator fundamental force envelope at low frequencies. Model data show that among these factors the reaction mass stroke and the peak-decoupling force are key parameters for setting the target fundamental force that can be achieved at low frequencies. Formulas are derived to estimate fundamental force, peak force and the reaction mass displacement. These formulas can serve as guidelines for sweep designers who plan to design low frequency sweeps with considerable dwell time in the lower frequency ranges. Test data show that formulas can be used to profile the vibrator envelope at low frequencies.     

Application of a perfectly matched layer in seismic wavefield simulation with an irregular free surface

Recently, an effective and powerful approach for simulating seismic wave propagation in elastic media with an irregular free surface was proposed. However, in previous studies, researchers used the periodic condition and/or sponge boundary condition to attenuate artificial reflections at boundaries of a computational domain. As demonstrated in many literatures, either the periodic condition or sponge boundary condition is simple but much less effective than the well‐known perfectly matched layer boundary condition. In view of this, we intend to introduce a perfectly matched layer to simulate seismic wavefields in unbounded models with an irregular free surface. We first incorporate a perfectly matched layer into wave equations formulated in a frequency domain in Cartesian coordinates. We then transform them back into a time domain through inverse Fourier transformation. Afterwards, we use a boundary‐conforming grid and map a rectangular grid onto a curved one, which allows us to transform the equations and free surface boundary conditions from Cartesian coordinates to curvilinear coordinates. As numerical examples show, if free surface boundary conditions are imposed at the top border of a model, then it should also be incorporated into the perfectly matched layer imposed at the top‐left and top‐ right corners of a 2D model where the free surface boundary conditions and perfectly matched layer encounter; otherwise, reflections will occur at the intersections of the free surface and the perfectly matched layer, which is confirmed in this paper. So, by replacing normal second derivatives in wave equations in curvilinear coordinates with free surface boundary conditions, we successfully implement the free surface boundary conditions into the perfectly matched layer at the top‐left and top‐right corners of a 2D model at the surface. A number of numerical examples show that the perfectly matched layer constructed in this study is effective in simulating wave propagation in unbounded media and the algorithm for implementation of the perfectly matched layer and free surface boundary conditions is stable for long‐time wavefield simulation on models with an irregular free surface.     

Break through the limits of vibroseis data quality

The vibroseis method has become the principal data acquisition method in land seismic exploration. It seems that this method has been extended to its limits as the search for energy resources continues. Many practical issues arising from field operations have remained theoretically unexplained, for example, variations in wavelet arrival time, inaccurate wavelet estimation and harmonics in the wavelet itself. The focus of this paper is the proposal of a new model, which is referred to as the vibrator‐coupled ground model, to simulate the filtering effects of a complex coupling system consisting of the coupling between the baseplate and the ground as well as the coupling between the captured ground mass near the vibrator baseplate and the surrounding earth. With this vibrator‐coupled ground model many of the practical issues mentioned above were reasonably addressed. Furthermore, it was demonstrated from experimental tests that both the pilot sweep and the weighted‐sum groundforce, when filtered by the vibrator‐coupled ground model, are proportional to the far‐field particle velocity whereas the unfiltered signals are not. The harmonics on the filtered weighted‐sum groundforce successfully maintain a proportional relationship with the harmonics seen in the far‐field signal.     

基于无分裂复频移卷积完全匹配层边界的黏弹介质勒夫波模拟

本文建立了无分裂复频移卷积完全匹配层(CFS-CPML)吸收边界条件,利用交错网格下的高精度有限差分格式对黏弹性介质中的勒夫波场进行了数值模拟;分析了松弛机制个数对品质因子拟合精度的影响,验证了CFS-CPML边界条件对大角度掠射波的吸收效果．数值结果表明:本文方法所使用的5个松弛机制和空间4阶差分精度,即可在保证计算效率的前提下满足目前理论研究的需要;随着品质因子的减小,频散特征曲线的相速度逐渐向增高的方向偏离理论频散特征曲线的相速度,且各模式的高频能量也随之减弱．本文结果可为发展高精度的面波反演方法提供必要的理论依据．      

A hybrid modelling of soil–structure interaction problems for deeply embedded structures in A multilayered medium

Dynamic response of deeply embedded structures, such as underground tunnels and deep foundations, in a multilayered elastic half-space are analysed when the structure is excited by a plane P or SV wave propagating at some angle. The scattered field is represented by the sum of three Green's functions, corresponding to two oscillating forces and one oscillating moment at the centroid position of the buried structure. The amplitudes of these two forces and one moment are a priori unknown and are obtained by satisfying displacement and stress continuity conditions across the near-field/far-field boundary. The distinguishing feature of this technique from direct or indirect boundary integral techniques is that in these techniques a distribution of sources of unknown amplitude are considered at the near-field/far-field boundary, and a large number of sources are needed for different combinations of source-receiver arrangements. But in this technique the sources of unknown amplitude are placed at the location of the structure, not at the near-field/far-field boundary and, using the Saint Venant's principle, the scattered field is modelled. Thus, the number of sources required is reduced to only three. Two example problems are solved. The first one is for a deeply embedded footing in a three-layer soil mass and the second one is for a rectangular tunnel in a two-layer soil mass.     

Topography on the D′′ region from analysis of a thin dense layer beneath a convecting cell

In this study, we examine the development of topography on a thin dense layer at the base of the lower mantle. The effect of the convecting mantle above is represented as a traction acting on the upper surface of the layer. Topography on the layer boundaries is predicted by a balance of dynamic flow stress and external traction. The nature of boundary topography depends on the magnitude of the driving tractions and the density variation within the layer. If we assume that the layer density is greatest beneath areas of mantle downwelling and decreases to a minimum beneath areas of mantle upwelling (the layer is thermally coupled to the convection in the overlying mantle) then its upper boundary develops a cusp-like peak beneath the upwelling mantle. The height of this peak is potentially much greater than the layer thickness. If, however, the layers are effectively coupled by viscous shear then internal density gradients of the opposite sign may be established. In this case, we observe solutions where the layer is completely swept away beneath areas of mantle downwelling leaving steep-sided ‘islands’ of dense material. This mechanism therefore provides a possible explanation for steep-sided anomalously slow regions at the base of the mantle observed by seismic methods (e.g. beneath south Africa) or for discrete ultralow velocity zones detected at the core-mantle boundary beneath locations of surface hotspots. The magnitude of the upper boundary driving tractions compared to the density gradient within the layer is the key parameter that determines the nature of flow in, and consequently boundary topography of, the layer. The deflection of the core-mantle boundary is small compared with that of the top of the dense layer, but a change in sign of the ratio of these deflections is observed as the magnitude of the driving tractions changes relative to the magnitude of the internal density gradient. We compare seismic measurements of core-mantle boundary topography and D′′ topography with the predictions of this model in an attempt to constrain model parameters, but no clear correlation seems to exist between D′′ thickness and CMB topography.     

适用于结构时程分析法的输入地震波

本文对建筑结构抗震设计时程法所需的输入地震波提出一种基于规范反应谱的、与设防烈度、场地条件、设计近震或远震、结构自振特性有关的选择原则和方法。按远、近震和四类场地标定了反应谱、延性谱和积累损伤谱。通过对六幢不同高度的剪切和弯曲型结构模型的弹塑性分析,表明离差很小。建议在进行结构时程法分析时,按地震加速度反应谱特定的分布规律选择4条加速度记录作为输入计算。两个实际的例子表明按上述方法计算的结果与按底部剪力法计算的结果基本相符。