Nonlinear analysis on the coupling process of electromagnetic vibrator and earth

Vibrator is an excitation equipment of the vibratory source in the seismic exploration[1―3]. In order to ap-proach the δ function, dynamite can be used to release high energy in an instantaneous explosion and form the seismic wavelet. On the other hand, a portable vi-brator sweeps a low energy signal for a long time to simulate the function of an explosion source. The re-flection signal of the portable vibrator is estimated for time-delay by digital cross correlation technology, and the disp…     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

SEISMIC VIBRATOR MODELLING1

The wavefield in, and at the surface of, a homogeneous, isotropic, perfectly elastic half-space, excited by a traction distribution at the surface of the medium is investigated. The emitted wavefield is a spatial convolution of the surface tractions and the spatial impulse response. The properties of the wavefield in the far-field of the medium are derived and it is shown that the far-field particle velocity is essentially equal to a weighted sum of the time derivative of the integrated surface tractions, that is, of the components of the ‘ground force’. The theory is valid for an arbitrary geometry and orientation of the surface tractions, and is independent of the boundary conditions at the surface of the medium. The surface tractions are related to a source that consists of a mass distribution with an arbitrary force distribution imposed upon it. A boundary condition is introduced that accounts for the mass load and the forces applied to it but neglects vibrations within the mass. The boundary condition follows from the equation of motion of the surface mass load. The theory is applied to the Vibroseis configuration, using a P-wave vibrator model with a uniformly distributed force imposed on top of the baseplate, and assuming that horizontal surface traction components are absent. The distribution of displacement and stress directly underneath the baseplate of a single vibrator and an array of vibrators is investigated. Three different boundary conditions are used: (1) assuming uniform pressure, (2) assuming uniform displacement, (3) using the equation of motion of the baseplate as a boundary condition. The calculations of the distribution of stress and displacement over the plate for different elastic media and several frequencies of operation show that only the results obtained with the mixed boundary condition agree with measurements made in the field. The accuracy of three different phase-feedback signals is compared using synthetic data. Baseplate velocity phase-feedback leads to huge deviations in the determination of the far-field wavelet; reaction mass acceleration phase-feedback looks stable but neglects the differentiating earth filter; and phase-feedback to a weighted sum of baseplate and reaction mass accelerations becomes unstable with increasing frequency. The instability can be overcome using measurements over the whole baseplate. The model can be extended to a lossy layered earth.     

基于重构激发信号的电磁式可控震源相关检测参考信号方法研究

针对电磁式可控震源地震数据的相关检测,研究发现,在地下结构复杂、基板-大地耦合不佳时,常规方法——基于震源控制信号或基板附近信号作为参考信号检测得到的地震记录中,存在子波到时误差和虚假多次波问题.本文分析了上述问题的理论原因,并提出基于重构激发信号的相关检测参考信号方法(Correlation Detection Reference Signal Based on the Reconstructed Excitation Signal,CDRSBRES).首先,利用直达波与其他地震波到时不一致的特点,从震源基板附近信号中分离、提取直达波.然后,利用直达波重构震源激发信号并作为参考信号对地震数据进行相关检测.最后,应用谱白化技术提高检测结果质量.数值模拟研究表明,重构激发信号与理想激发信号的相关系数为0.9869,达到高度线性相关,CDRSBRES方法检测的地震记录在子波到时和波形特征上均与模型相符.随后,在某金属矿区开展了可控震源对比实验.与液压式可控震源MiniVib T15000检测结果相比,电磁式可控震源PHVS 500的检测结果中:基于震源控制信号的检测结果存在子波到时误差约0.012s,对应垂向精度误差约11.16m;基于基板附近信号的检测结果部分区域出现虚假多次波,信噪比降低;而CDRSBRES方法的检测结果子波到时误差约0.001s,对应垂向精度误差约0.93m,波形特征一致,相同区域无虚假多次波.综上,本方法适用于电磁式可控震源地震数据的高精度检测,尤其对于地下结构复杂区域的高分辨率地震勘探具有重要意义.     

Elimination of ghost noise in vibroseis data by deconvolution

A deconvolution approach is presented to process uncorrelated vibroseis data. The recorded ground force signal, known to be a better correlator for the vibrogram than the pilot sweep itself, is used to deconvolve rather than to correlate the vibrogram. In such a way the ghost sweep (correlation noise), produced by severe harmonic distortions in the ground force signal both at negative and positive correlation times if such a signal is used as the correlator, is eliminated automatically. This type of deconvolution can eliminate the ghost sweep caused by both the upsweep or by the downsweep signal. Synthetic and real data are used to demonstrate the application of the deconvolution procedure. The results are compared with the traditional correlation procedure and show the superiority of the deconvolution approach.     

消除滑动扫描地震数据中谐波干扰的反相关方法(英文)

滑动扫描技术是高效、高保真、环保的可控震源勘探技术之一,是下一组震源不必等待上一组震源震动结束即可开始震动的高效采集方法。该技术由于缩短了相邻两炮的等待时间,使得生产效率得到显著提高。但是后一炮的谐波畸变与前一炮的基波信号混叠在一起,不易分离,在相关后的地震记录上形成了严重的谐波干扰,降低了地震资料的质量。本文提出一种反相关方法来压制滑动扫描地震数据中的谐波干扰。该方法首先把地面力信号分解为基波和各阶谐波分量;然后将后一炮的相关前数据分别与各分量相关,只选取正时间轴中对应分量的自相关部分,利用各分量的反相关算子提取各阶谐波信息;最后从前一炮数据中减去提取出的高阶谐波,得到压制谐波后的地震记录。该方法对有效信号影响小,可同时处理相关前和相关后数据,而且算法简单稳定,计算效率高。本文分别对理论模型和实际数据进行处理,验证了该方法消除谐波干扰的有效性。     

Radiation from flexural vibrations of the baseplate and their effect on the accuracy of traveltime measurements

We analyse the problem of radiation of seismic waves by a vibroseis source when the baseplate is subject to flexure. A theoretical model is proposed to account for baseplate flexure, generalizing the well‐known model of the vibroseis source of Sallas and Weber, which was developed for a rigid plate. Using the model proposed, we analyse the effect of flexure on the properties of seismic waves. We show that the flexure does not contribute to the far‐field and mainly affects the readings of the reference accelerometer that is used to measure the force applied to the ground; these readings generally become dependent on the location of the sensor on the plate. For muddy and sandy soils, the effect of flexure on baseplate‐acceleration measurements is nonetheless pronounced at the high end of the vibroseis frequency band only (～100 Hz), and is negligible at all frequencies for stiffer soils. The corresponding phase lags introduced by the flexural vibrations at high frequencies lead to errors in the traveltime measurements (through the cross‐correlation function) of up to 0.6 ms for muddy soils and less for denser soils. We show the existence of an optimal position of the reference sensor on the baseplate and also propose a general method of eliminating the phase lag due to the baseplate flexure in acceleration measurements.     

检测地震勘探微弱同相轴的混沌振子算法

针对地震勘探资料湮没在随机噪声中的微弱同相轴问题提出基于混沌理论的混沌振子检测算法. 利用修正的Duffing_Holmes方程建立检测微弱同相轴的混沌振子系统,之后经过对同相轴的扫描处理,构成新子波等时间间隔序列W(t),与此同时对随机噪声也进行相同的截断. 截断的随机噪声在混沌振子系统中可以具有与周期信号相同的表现;经过大量仿真实验确定出满足通常地震勘探子波延续时间的使混沌振子检测子波不呈现周期相态的随机噪声截断时间范围. 选用与松辽盆地T1、T2反射层类似的子波函数并构成待检微弱周期信号,经过MATLAB仿真试验成功地检测出该弱信号,信噪比达到约-103dB.     

Weighted sum method for calculating ground force: an evaluation by using a portable vibrator system

Using a lightweight portable vibrator, we have evaluated the accuracy of the 'weighted sum' method for calculating ground force. Experiments in which the vibrator was suspended elastically have shown that, contrary to expectations based on standard theory, the amplitude of the weighted sum ground force was significantly above zero at high frequencies (> 500 Hz). Complementary investigations with load cells confirmed these results. If not accounted for, these deviations may introduce significant 'vibroseis-correlation noise' in processed records. Furthermore, we have demonstrated that ground force and base-plate velocity can be used to estimate the radiation impedance, which describes the interaction of (vibratory) sources with the ground. Using the mechanical characteristics of the system (i.e. maximum displacement, maximum velocity and maximum acceleration of the base-plate) and the radiation impedance, the behaviour of the portable vibrator on typical Dutch soil types was evaluated. We found that for the same sweep, more high-frequency energy could be generated on hard grounds (e.g. concrete) characterized by a higher radiation impedance than on softer grounds (e.g. clay or sand). Knowledge of this behaviour may provide important information for use in data interpretation.     

LINEAR QUADRATIC REGULATOR FOR STRUCTURE UNDER ON-LINE PREDICTED FUTURE SEISMIC EXCITATION

A predictive-adaptive (PA) control algorithm has been developed for a structure under a seismic excitation. This algorithm analyses information of an observed seismic excitation, estimates future structural responses and determines the control force for the structure, based on the linear quadratic regulator. That is, at a given moment t_k: (1) seismic excitation information is converted to an autoregressive model, which forms the state equation for the excitation; (2) the identification model is combined with the structural model to build a state equation in an augmented space; (3) the weighted quadratic norm of the state vector and the future control force is formed as a cost function for estimating future responses; (4) the Ricatti equation is solved to find the optimum value of the cost function; and (5) the optimum gain matrix is obtained, and the control force is determined. The PA algorithm is not restricted to one type of control system, but can be applied to both an active driver system and an active tendon system. Its effectiveness is confirmed by numerical experiments for 1DOF and 3DOF structural models under sine and seismic excitations.     

伪随机编码震源信号的地震响应

常规的可控震源Chirp扫描信号的地震响应存在着相关信号旁瓣大、分辨率低的缺点.本文利用数值模拟技术研究可控震源伪随机编码信号地震响应的规律和特点.伪随机编码信号的地震响应剖面的旁瓣电平与常规的Chirp扫描信号情形相比有明显地降低,但是伪随机编码信号地震响应剖面的相关噪声仍然没有得到有效地压制.利用伪随机编码信号的周期性特点把一个长地震记录以信号周期为间隔进行分时叠加可以提高地震记录的信噪比和地震数据的利用率.     

Effective elimination of subharmonic ghost events from vibroseis data

Harmonic or subharmonic noise is often present in vibroseis data as reverberation‐like, laterally coherent bands occurring parallel to and before or after, the main events. Such periodic noise is typically generated during the standard correlation process when the actual source signal travelling through the subsurface is, for whatever reason, different from the desired source signal, i.e., the pilot‐sweep controlling the baseplate and used for correlation. A typical cause can be that harmonic or subharmonic frequency partials are generated in addition to the vibroseis sweep's desired fundamental frequencies. These harmonics produce strong ‘ghost events’ during correlation of the geophone trace with the pilot‐sweep, originating from additional correlations between the fundamental and harmonic frequencies. Especially subharmonic ‘ghosts’ will overlap with ‘good’ fundamental signals, since for typically used up‐sweeps they are folded to later traveltimes, where the signal/noise‐ratio is already lower, thus aggravating or preventing a reliable interpretation of possible later reflections. Here, a method is introduced to remove these unwanted noise trains (with only negligible impact on the fundamental signal) by transforming the seismogram traces into a so‐called ‘(sub)harmonic domain’. In this domain, the respective harmonic noise portions are focused and separated from the fundamental signals, enabling easier detection and appropriate suppression. After back‐transformation to the x‐T domain, the records are free from the corresponding harmonic contamination and can then be processed as usual. The method operates in a data‐driven fashion, i.e., the traces are not uniformly processed but are processed depending upon their actual (sub)harmonic content. The decontamination procedure can be applied universally, i.e., to uncorrelated/correlated and/or vertically unstacked/stacked data either in a manual, semiautomated or fully automated manner. The method works perfectly for synthetic vibroseis traces with or without harmonic/subharmonic portions. The application to real, crustal‐scale vibroseis records that were acquired in 2006 in the Dead Sea region, Israel and that were severely contaminated by subharmonic ground‐roll ghosts covering reflectivity from the basement to the Moho, shows the robustness and success of the presented method.     

OPTIMAL POLYNOMIAL CONTROL FOR SEISMICALLY EXCITED NON-LINEAR AND HYSTERETIC STRUCTURES

In this paper, we present an optimal polynomial controller for reducing the peak response quantities of seismically excited non-linear or hysteretic building systems. A performance index, that is quadratic in control and polynomial of any order in non-linear states, is considered. The performance index is minimized based on the Hamilton–Jacobi–Bellman equation using a polynomial function of non-linear states, which satisfies all the properties of a Lyapunov function. The resulting optimal controller is a summation of polynomials in non-linear states, i.e. linear, cubic, quintic, etc. Gain matrices for different parts of the controller are determined from Riccati and Lyapunov matrix equations. Numerical simulation results indicate that the percentage of reduction for the selected peak response quantity increases with the increase of the earthquake intensity. Such load adaptive properties are very desirable, since the intensity of the earthquake ground acceleration is stochastic in nature. The proposed optimal polynomial controller is an effective and viable control method for non-linear or hysteretic civil engineering structures. It is an addition to available control methods in the literature.