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.     

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.     

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.     

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.     

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.     

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.     

Sparsity‐enhanced wavelet deconvolution

We propose a three‐step bandwidth enhancing wavelet deconvolution process, combining linear inverse filtering and non‐linear reflectivity construction based on a sparseness assumption. The first step is conventional Wiener deconvolution. The second step consists of further spectral whitening outside the spectral bandwidth of the residual wavelet after Wiener deconvolution, i.e., the wavelet resulting from application of the Wiener deconvolution filter to the original wavelet, which usually is not a perfect spike due to band limitations of the original wavelet. We specifically propose a zero‐phase filtered sparse‐spike deconvolution as the second step to recover the reflectivity dominantly outside of the bandwidth of the residual wavelet after Wiener deconvolution. The filter applied to the sparse‐spike deconvolution result is proportional to the deviation of the amplitude spectrum of the residual wavelet from unity, i.e., it is of higher amplitude; the closer the amplitude spectrum of the residual wavelet is to zero, but of very low amplitude, the closer it is to unity. The third step consists of summation of the data from the two first steps, basically adding gradually the contribution from the sparse‐spike deconvolution result at those frequencies at which the residual wavelet after Wiener deconvolution has small amplitudes. We propose to call this technique “sparsity‐enhanced wavelet deconvolution”. We demonstrate the technique on real data with the deconvolution of the (normal‐incidence) source side sea‐surface ghost of marine towed streamer data. We also present the extension of the proposed technique to time‐varying wavelet deconvolution.     

长周期地震动参数与隔震结构响应参数的相关性研究

从Chi-Chi地震动数据中选取20条近场长周期地震记录和20条远场长周期地震记录,再从汶川地震渭河地震动数据中选取20条远场长周期地震记录作为输入,研究各个地震动记录相对应的地震动强度参数及其之间的相关性,筛选出了适合于长周期地震动的地震动强度指标,采用Pearson相关系数对筛选出的地震动强度指标与隔震体系的隔震层位移响应之间的相关性进行分析。结果表明:①在近、远场长周期地震动作用下,中长周期隔震结构的隔震层位移响应与频谱特征参数的相关性比较好,在进行中长周期隔震结构的抗震性能研究时,PGD、Sd_avg及DSI与隔震结构的相关性较好,地震动强度指标在集集近场建议选取PGD和Sd_avg,集集远场建议选取DSI和D/V,渭河远场建议选取Sd_avg和DSI;②在强相关范围内考虑相关性的高低,近场和远场的长周期地震动强度指标建议分别选取PGD和DSI。     

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.     

The simulation of far-field wavelets using frequency-domain air-gun array near-field wavelets

Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.     

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.     

Estimate of input energy for elasto‐plastic SDOF systems during earthquakes based on discrete wavelet coefficients

The response of an elasto‐plastic single degree of freedom (SDOF) system to ground motion is estimated based on wavelet coefficients calculated by discrete wavelet transform. Wavelet coefficients represent both the time and frequency characteristics of input ground motion, and thus can be considered to be directly related to the dynamic response of a non‐linear system. This relationship between the energy input into an elastic SDOF system and wavelet coefficients is derived based on the assumption that wavelets deliver energy to the structure instantaneously and the quantity of energy is constant regardless of yielding. These assumptions are shown to be valid when the natural period of the system is in the predominant period range of the wavelet, the most common scenario for real structures, through dynamic response analysis of a single wavelet. The wavelet‐based estimation of elastic and plastic energy transferred by earthquake ground motion is thus shown to be in good agreement with the dynamic response analysis when the natural period is in the predominant range of the input. Copyright © 2005 John Wiley & Sons, Ltd.     

On selection and scaling of ground motions for analysis of seismically isolated structures

A broader consensus on the number of ground motions to be used and the method of scaling to be adopted for nonlinear response history analysis (RHA) of structures is yet to be reached. Therefore, in this study, the effects of selection and scaling of ground motions on the response of seismically isolated structures, which are routinely designed using nonlinear RHA, are investigated. For this purpose, isolation systems with a range of properties subjected to bidirectional excitation are considered. Benchmark response of the isolation systems is established using large sets of unscaled ground motions systematically categorized into pulse-like, non-pulse-like, and mixed set of motions. Different subsets of seven to 14 ground motions are selected from these large sets using (a) random selection and (b) selection based on the best match of the shape of the response spectrum of ground motions to the target spectrum. Consequences of weighted scaling (also commonly referred to as amplitude scaling or linear scaling) as well as spectral matching are investigated. The ground motion selection and scaling procedures are evaluated from the viewpoint of their accuracy, efficiency, and consistency in predicting the benchmark response. It is confirmed that seven time histories are sufficient for a reliable prediction of isolation system displacement demands, for all ground motion subsets, selection and scaling procedures, and isolation systems considered. If ground motions are selected based on their best match to the shape of the target response spectrum (which should be preferred over randomly selected motions), weighted scaling should be used if pulse-like motions are considered, either of weighted scaling or spectral matching can be used if non-pulse-like motions are considered, and an average of responses from weighted-scaled and spectrum-matched ground motions should be used for a mixed set of motions. On the other hand, the importance of randomly selected motions in representing inherent variability of response is recognized and it is found that weighted scaling is more appropriate for such motions.     

Comparison of the 2010 Chile and 2011 Japan Tsunamis in the Far Field

In this study we analyze water level data from coastal tide gauges and deep-ocean tsunameters to explore the far-field characteristics of two major trans-Pacific tsunamis, the 2010 Chile and the 2011 Japan (Tohoku-oki) events. We focused our attention on data recorded in California (14 stations) and New Zealand (31 stations) as well as on tsunameters situated along the tsunami path and proximal to the study sites. Our analysis considers statistical analyses of the time series to determine arrival times of the tsunami as well as the timing of the largest waves and the highest absolute sea levels. Fourier and wavelet analysis were used to describe the spectral content of the tsunami signal. These characteristics were then compared between the two events to highlight similarities and differences between the signals as a function of the receiving environment and the tsunami source. This study provides a comprehensive analysis of far-field tsunami characteristics in the Pacific Ocean, which has not experienced a major tsunami in nearly 50 years. As such, it systematically describes the tsunami response characteristics of modern maritime infrastructure in New Zealand and California and will be of value for future tsunami hazard assessments in both countries.     

海洋地震资料采集过程中近场检波器的应用

海洋地震资料采集中空气枪震源近场检波器不仅可以较好地进行震源质量实时监控,更重要的是可以较好地预测远场子波.经国外大量的远场子波实测试验与预测结果对比,利用近场检波器预测远场子波,与实测远场子波吻合度很高,因此,利用近场检波器预测远场子波是一项非常关键的技术,然而国内在该技术领域还不是很成熟,目前只用来做一些震源的质量监控和近场子波记录.较为详细地描述了国外的部分试验结果,并根据国外的试验结果和国内的具体使用情况,提出了近场检波器放置位置、记录长度和采样率合理化选取的建议.并建议国内相关领域的专家尽快研发拥有自主知识产权的相关软件,利用近场子波来有效地预测远场子波.     

时变地震谱估计的非参数方法评价及应用

针对工程中常见的非平稳地震动激励,进一步建立了时变功率谱估计的理论框架。首先,在多个样本情形下,采用信号处理中的时频分析方法对非平稳激励的时变谱估计理论进行了讨论。当激励样本数量有限时,对Priestley提出的估计方法进行了介绍。其次,以地震工程中常用的Kanai-Tajimi谱模型为目标,分别对均匀调制与一般调制谱的估计结果以及不同估计方法的精度与收敛性进行评价后,提出了能够方便工程应用的建议。最后,针对SMART-Ⅰ(Strong Motion Array in Taiwan,Phase Ⅰ)密集台阵第45次地震记录的多组三维样本,揭示了EW、NS、UD三个方向时变谱的典型特征以及各方向间的时变相干性。结果表明:与短时Fourier变换相比,复Morlet小波与广义谐和小波估计谱具有较好的精度与收敛性,Priestley方法估计单个样本具有优势;SMART-Ⅰ台阵地震动具有强度和频率的双重非平稳性,三个方向具有弱相干性。研究结论可为拓展谱估计理论的工程应用以及后续大跨结构多维多点非平稳地震响应的分析提供参考。     

SIMULTANEOUS VIBROSEIS RECORDING1

An experiment was undertaken at BP's Fulbeck Geophysical test site to compare the viability of various simultaneous vibroseis recording techniques, which are often recommended as a means of improving data acquisition production rates for 3D seismic surveys. Of particular interest were: (a) the ability to separate the signals from each source during processing, (b) the generation and suppression of harmonics and (c) the effects of any source interaction. Two vibrators were deployed with a baseplate separation of 10 m, about a borehole containing a vertical array of geophones. Our analysis concentrated on the groundforce signals measured at each vibrator and the far-field signatures measured using a vertical geo-phone at a depth of 204 m. By comparing single vibrator records with similar but separated records from a simultaneous recording sequence, signal separability, harmonic suppression and vibrator interaction could be fully studied. Separated far-field signatures from simultaneous vibroseis methods using combinations of up and downsweeps exhibited unsuppressed harmonics and substantial energy from the undesired source which leaked through the correlation process. The ‘up/down’ method was capable of separating the signal from each source by only 12.7 dB, and is therefore unsuitable as a field technique. The variphase simultaneous vibroseis methods studied afforded some harmonic suppression and gave signal separations of about 30.0 dB. Use of variphase simultaneous vibroseis methods will compromise the quality of the data recorded, when compared with single-source acquisition methods. None of the simultaneous vibroseis methods tested provided adequate signal separation and, therefore, cannot be recommended as data acquisition techniques. The ‘alternate sweeping’ method coupled with multispread recording will give the desired improvement in data acquisition rates, while preserving the necessary quality of our seismic data.     

Improvements of corner frequency and scaling factor for stochastic finite-fault modeling

In this paper, three existing source spectral models for stochastic finite-fault modeling of ground motion were reviewed. These three models were used to calculate the far-field received energy at a site from a vertical fault and the mean spectral ratio over 15 stations of the Northridge earthquake, and then compared. From the comparison, a necessary measure was observed to maintain the far-field received energy independent of subfault size and avoid overestimation of the long-period spectral level. Two improvements were made to one of the three models (i.e., the model based on dynamic corner frequency) as follows: (i) a new method to compute the subfault corner frequency was proposed, where the subfault corner frequency is determined based on a basic value calculated from the total seismic moment of the entire fault and an increment depending on the seismic moment assigned to the subfault; and (ii) the difference of the radiation energy from each subfault was considered into the scaling factor. The improved model was also compared with the unimproved model through the far-field received energy and the mean spectral ratio. The comparison proves that the improved model allows the received energy to be more independent of subfault size than the unimproved model, and decreases the overestimation degree of the long-period spectral amplitude.     

Feasibility of utilizing wavelet phase to map the CO2 plume at the Ketzin pilot site,Germany

Spectral decomposition is a powerful tool that can provide geological details dependent upon discrete frequencies. Complex spectral decomposition using inversion strategies differs from conventional spectral decomposition methods in that it produces not only frequency information but also wavelet phase information. This method was applied to a time‐lapse three‐dimensional seismic dataset in order to test the feasibility of using wavelet phase changes to detect and map injected carbon dioxide within the reservoir at the Ketzin carbon dioxide storage site, Germany. Simplified zero‐offset forward modelling was used to help verify the effectiveness of this technique and to better understand the wavelet phase response from the highly heterogeneous storage reservoir and carbon dioxide plume. Ambient noise and signal‐to‐noise ratios were calculated from the raw data to determine the extracted wavelet phase. Strong noise caused by rainfall and the assumed spatial distribution of sandstone channels in the reservoir could be correlated with phase anomalies. Qualitative and quantitative results indicate that the wavelet phase extracted by the complex spectral decomposition technique has great potential as a practical and feasible tool for carbon dioxide detection at the Ketzin pilot site.