GOCE卫星重力测量中有色噪声滤波器设计

本文根据卫星重力梯度测量的有色噪声特性,设计了Wiener、AR、FIR三种滤波器,并利用模拟的有色噪声数据对其滤波效果进行了测试,结果表明:对于文中采用的有色噪声数据,AR的滤波效果最好,其次为Wiener滤波器,FIR的滤波效果最差;三种滤波器均可用于GOCE卫星重力测量中有色噪声数据滤波,但其实用性尚需利用实测数据进行检验;可以利用不同的滤波器对含有色噪声的卫星重力梯度数据进行多次滤波,以进一步减弱有色噪声对卫星重力梯度测量精度的影响.     

Median filter behaviour with seismic data1

Median filters may be used with seismic data to attenuate coherent wavefields. An example is the attenuation of the downgoing wavefield in VSP data processing. The filter is applied across the traces in the ‘direction’ of the wavefield. The final result is given by subtracting the filtered version of the record from the original record. This method of median filtering may be called ‘median filtering operated in subtraction’. The method may be extended by automatically estimating the slowness of coherent wavefields on a record. The filter is then applied in a time- and-space varying manner across the record on the basis of the slowness values at each point on the record. Median filters are non-linear and hence their behaviour is more difficult to determine than linear filters. However, there are a number of methods that may be used to analyse median filter behaviour: (1) pseudo-transfer functions to specific time series; (2) the response of median filters to simple seismic models; and (3) the response of median filters to steps that simulate terminating wavefields, such as faults on stacked data. These simple methods provide an intuitive insight into the behaviour of these filters, as well as providing a semiquantitative measurement of performance. The performance degradation of median filters in the presence of trace-to-trace variations in amplitude is shown to be similar to that of linear filters. The performance of median filters (in terms of signal distortion) applied obliquely across a record may be improved by low-pass filtering (in the t-dimension). The response of median filters to steps is shown to be affected by background noise levels. The distortion of steps introduced by median filters approaches the distortion of steps introduced by the corresponding linear filter for high levels of noise.     

基于区域滤波的GOCE稳态海面动力地形和地转流

基于频域法,利用最新的GOCE卫星重力场模型和卫星测高数据计算了稳态海面动力地形.结合海洋表层漂流浮标的观测结果,对稳态海面动力地形进行了最优空间滤波尺度分析,给出了区域、纬度带和全球稳态海面动力地形的最优空间滤波尺度因子.在此基础上,给出了全球和区域地转流.结果表明:在中高纬度和全球区域,可以分别获得空间尺度优于102km和127km的稳态海面动力地形信息.与海洋表层漂流浮标对比可知,在强流区域,采用稳态海面动力地形得到的地转流速可以解释观测浮标流速的70%;在中高纬度区域,由GOCE重力场得到的地转流略优于对应的GRACE结果;在近赤道区域,由GOCE重力场得到的地转流精度略低于对应的GRACE结果;在北大西洋和阿古拉斯强流区域,由GOCE得到的地转流场明显优于对应的GRACE结果,其精度分别提高了16%和24%.     

Comparison of Factorial Kriging Analysis Method and Upward Continuation Filter to Recognize Subsurface Structures — A Case Study: Gravity Data from a Hydrocarbon Field in the Southeast Sedimentary Basins of the East Vietnam Sea

To interpret geophysical anomaly maps, it is necessary to filter out regional and sometimes noise components. Each measured value in a gravity survey consists of different components. Upward continuation (UC) is one of the most widely used filters. The shortcoming of this filter is not to consider the spatial structure of the data, and also the fact that the trial and error approach and expert’s judgment are needed to adjust it. This study aims to compare the factorial kriging analysis (FKA) and UC filters for separation of local and regional anomalies in the gravity data of a hydrocarbon field in the southeast sedimentary basins of the East Vietnam Sea. As shown in this paper, FKA method permits to filter out all of the identified structures, while the UC filter does not possess this capability. Therefore, beside general and classic filtering methods, the FKA method can be used as a strong method in filtering spatial structures and anomaly component.     

Incorporation of a Non-linear Image Filtering Technique for Noise Reduction in Seismic Data

Seismic noise is a fundamental part of seismic data which cannot be avoided when conducting any seismic survey. It consists of coherent and random noise. Noise removal or filtering is one of the major concerns in the field of seismic processing. In this paper, we introduce an image filtering technique based on a detection-estimation algorithm for Gaussian and random noise removal in seismic data, namely the trilateral filter, based on a statistic called rank-ordered absolute differences. The non-linear and adaptive behaviour of this filter makes it very robust in the presence of random and coherent noise, in addition to its computational simplicity and its ability to automatically identify noise in data. We have modified the strategy of trilateral filtering by adapting the rank-ordered absolute differences formula in order to extract the signal component. We have successfully used this filter for the removal of surface waves and random spiky noise from synthetic and field data. Results are very encouraging and show the superiority of this filter compared with other filters, particularly when used recursively.     

Inversion-based data-driven time-space domain random noise attenuation method

Conventional time-space domain and frequency-space domain prediction filtering methods assume that seismic data consists of two parts, signal and random noise. That is, the so-called additive noise model. However, when estimating random noise, it is assumed that random noise can be predicted from the seismic data by convolving with a prediction error filter. That is, the source-noise model. Model inconsistencies, before and after denoising, compromise the noise attenuation and signal-preservation performances of prediction filtering methods. Therefore, this study presents an inversion-based time-space domain random noise attenuation method to overcome the model inconsistencies. In this method, a prediction error filter (PEF), is first estimated from seismic data; the filter characterizes the predictability of the seismic data and adaptively describes the seismic data’s space structure. After calculating PEF, it can be applied as a regularized constraint in the inversion process for seismic signal from noisy data. Unlike conventional random noise attenuation methods, the proposed method solves a seismic data inversion problem using regularization constraint; this overcomes the model inconsistency of the prediction filtering method. The proposed method was tested on both synthetic and real seismic data, and results from the prediction filtering method and the proposed method are compared. The testing demonstrated that the proposed method suppresses noise effectively and provides better signal-preservation performance.     

OPTIMUM DIGITAL FILTERS FOR SIGNAL TO NOISE RATIO ENHANCEMENT*

One of the main objectives of seismic digital processing is the improvement of the signal-to-noise ratio in the recorded data. Wiener filters have been successfully applied in this capacity, but alternate filtering devices also merit our attention. Two such systems are the matched filter and the output energy filter. The former is better known to geophysicists as the crosscorrelation filter, and has seen widespread use for the processing of vibratory source data, while the latter is. much less familiar in seismic work. The matched filter is designed such that ideally the presence of a given signal is indicated by a single large deflection in the output. The output energy filter ideally reveals the presence of such a signal by producing a longer burst of energy in the time interval where the signal occurs. The received seismic trace is assumed to be an additive mixture of signal and noise. The shape of the signal must be known in order to design the matched filter, but only the autocorrelation function of this signal need be known to obtain the output energy filter. The derivation of these filters differs according to whether the noise is white or colored. In the former case the noise autocorrelation function consists of only a single spike at lag zero, while in the latter the shape of this noise autocorrelation function is arbitrary. We propose a novel version of the matched filter. Its memory function is given by the minimum-delay wavelet whose autocorrelation function is computed from selected gates of an actual seismic trace. For this reason explicit knowledge of the signal shape is not required for its design; nevertheless, its performance level is not much below that achievable with ordinary matched filters. We call this new filter the “mini-matched” filter. With digital computation in mind, the design criteria are formulated and optimized with time as a discrete variable. We illustrate the techniques with simple numerical examples, and discuss many of the interesting properties that these filters exhibit.     

二维最佳线性数字滤波器的设计原理

针对如何在干扰场的背景上区分出低缓异常,以及在位场的向下延拓一类计算中如何限制因误差的高频放大所导至的解的不稳定性等问题,本文探讨了在“最小二乘”意义下的最佳线性数字滤波器的设计原理,并将它转化为下述数学问题,即在L₂线性赋范函数空间中如何选取最佳滤波函数的问题。在空间域中直接解这个问题是十分复杂和困难的,我们发现在波数域中用变分法中的等周问题的解法直接选取最佳线性滤波器的传输函数（或波数响应）,则在数学方法上既简单又严格。这样选取的最佳线性滤波器的传输函数L（f,k）其表达式也很简单,即L（f,k）=|S_i（f,k）|²/{|S_i（f,k）|²+λ|N_i（f,k）|²}。式中,|S_i（f,k）|²及|N_i（f,k）|²分别代表滤波器输入端讯号和干扰的能谱（或功率谱）,f、k分别代表x、y方向上的波数,λ为大于零的常数。 对上述两类问题以及相关的两种最佳线性滤波器而言,L（f,k）的表达式是相同的,而区别仅在于其参变量λ的选取条件不同而已。 有了最佳线性滤波器的传输函数L（f,k）的理论公式,就可以在最小二乘的意义下分析和评价国内外所发表的解决上述两类问题的各种线性滤波方法,并能指出在不同的讯号与干扰条件下,在理论上线性滤波可能达到的最佳效果,从而为设计二维线性数字滤波器时,提供一个理论上的准则。 对位     

The potential of digital filtering of generic topographic data for geomorphological research

High resolution terrain models generated from widely available Interferometric Synthetic Aperture Radar (IfSAR) and digital photogrammetry are an exciting resource for geomorphological research. However, these data contain error, necessitating pre‐processing to improve their quality. We evaluate the ability of digital filters to improve topographic representation, using: (1) a Gaussian noise removal filter; (2) the proprietary filters commonly applied to these datasets; and (3) a terrain sensitive filter, similar to those applied to laser altimetry data. Topographic representation is assessed in terms of both absolute accuracy measured with reference to independent check data and derived geomorphological variables (slope, upslope contributing area, topographic index and landslide failure probability) from a steepland catchment in northern England. Results suggest that proprietary filters often degrade or fail to improve precision. A combination of terrain sensitive and Gaussian filters performs best for both IfSAR and digital photogrammetry datasets, improving the precision of photogrammetry digital elevation models (DEMs) by more than 50 per cent relative to the unfiltered data. High‐frequency noise and high‐magnitude gross errors corrupt geomorphological variables derived from unfiltered photogrammetry DEMs. However, a terrain sensitive filter effectively removes gross errors and noise is minimized using a Gaussian filter. These improvements propagate through derived variables in a landslide prediction model, to reduce the area of predicted instability by up to 29 per cent of the study area. Interferometric Synthetic Aperture Radar is susceptible to removal of topographic detail by oversmoothing and its errors are less sensitive to filtering (maximum improvement in precision of 5 per cent relative to the raw data). Copyright © 2008 John Wiley and Sons, Ltd.     

基于f-x域流式预测滤波器的地震随机噪声衰减方法

随机噪声的影响在地震勘探中是不可避免的,常规的随机噪声压制方法在处理中往往会破坏具有时空变化特征的非平稳有效地震信号,影响地震数据的准确成像.当前油气勘探的目标已经转变为“两宽一高”,随着数据量的增大,对去噪方法的处理效率也提出了更高的要求.因此,开发高效的非平稳地震数据随机噪声压制方法具有重要意义.预测滤波技术广泛用于地震随机噪声的衰减,本文基于流式处理框架提出一种新的f-x域流式预测滤波方法,通过在频率域建立预测自回归方程,运用直接复数矩阵逆运算代替迭代算法求解非平稳滤波器系数,实现时空变地震同相轴预测,提高自适应预测滤波的计算效率.通过与工业标准的FXDECON方法和f-x域正则化非平稳自回归(RNA)方法进行对比,理论模型和实际数据的测试结果表明,提出的f-x域流式预测滤波方法能更好地平衡时空变有效信号保护、随机噪声压制和高效计算三者之间的关系,获得合理的处理效果.     

基于混合时频分析技术的地震数据噪声压制(英文)

针对复杂地质结构、陡倾角相干噪声、空间采样不均匀等情况下F-x域反褶积去噪技术的不足,提出首先应用具有时-频聚集性度量准则的广义S变换将时间-空间域的地震数据变换至时间-频率-空间域(t-f-x)的数据,在t-f-x域中对每一个频率切片应用经验模态分解(EMD),移除噪声占主导地位的本征模态函数以压制相干和随机噪声的滤波方法。模型分析表明第一本征模态函数表征的高频信息以噪声为主,移除第一本证模态函数可以达到压制噪声的目的。经广义S变换后形成t-f-x域中EMD滤波方法等效于具有依赖于空间位置、频率、高波数截断特征的自适应f-k滤波。此滤波方法考虑了数据的局部时-频特征,且具有执行简单的特点。与AR预测滤波方法比较,此法滤除的成分包含较少的低波数的信息,滤除的成分非常的局部化,且获得结果没有表现出过度平滑的特征。实际资料的应用表明在经广义S变换后形成t-f-x域中运用EMD滤波方法能够有效地压制随机和陡倾角相干噪声。     

Suppression of near‐surface scattered body‐to‐surface waves: a steerable and nonlinear filtering approach

We present an approach based on local‐slope estimation for the separation of scattered surface waves from reflected body waves. The direct and scattered surface waves contain a significant amount of seismic energy. They present great challenges in land seismic data acquisition and processing, particularly in arid regions with complex near‐surface heterogeneities (e.g., dry river beds, wadis/large escarpments, and karst features). The near‐surface scattered body‐to‐surface waves, which have comparable amplitudes to reflections, can mask the seismic reflections. These difficulties, added to large amplitude direct and back‐scattered surface (Rayleigh) waves, create a major reduction in signal‐to‐noise ratio and degrade the final sub‐surface image quality. Removal of these waves can be difficult using conventional filtering methods, such as an filter, without distorting the reflected signal. The filtering algorithm we present is based on predicting the spatially varying slope of the noise, using steerable filters, and separating the signal and noise components by applying a directional nonlinear filter oriented toward the noise direction to predict the noise and then subtract it from the data. The slope estimation step using steerable filters is very efficient. It requires only a linear combination of a set of basis filters at fixed orientation to synthesize an image filtered at an arbitrary orientation. We apply our filtering approach to simulated data as well as to seismic data recorded in the field to suppress the scattered surface waves from reflected body waves, and we demonstrate its superiority over conventional techniques in signal preservation and noise suppression.     

EFFICIENT MULTICHANNEL FILTERING OF SEISMIC DATA1

Multichannel filters are used to eliminate coherent noise from surface seismic data, for wavefield separation from VSP stacks, and for signal enhancement. Their success generally depends on the choice of the filter parameters and the domain of application. Multichannel filters can be applied to shots (monitors), common-receiver traces, CDP traces and stacked sections. Cascaded applications in these domains are currently performed in the seismic industry for better noise suppression and for signal enhancement. One-step shot-domain filtering is adequate for some applications. However, in practice, cascaded applications in shot-and common-receiver domains usually give better results when the S/N ratio is low. Multichannel filtering after stacking (especially after repeated applications in shot and/or receiver domains) may create undesirable results such as artificial continuations, or smearing and smoothing of small features such as small throw faults and fine stratigraphic details. Consequently, multichannel filtering after stacking must be undertaken with the utmost care and occasionally only as a last resort. Multichannel filters with fan-shaped responses (linear moveout filters) should be applied after NMO correction. These are the filters commonly used in the seismic industry where they have such names as velocity filters, moveout filters, f-k filters and coherency filters. Filtering before NMO correction may result in break-up and flattening especially of those shallow reflection events with relatively higher curvatures and diffractions. NMO correction is needed prior to wavefield separation from VSP stacks for the same practical reasons outlined above whenever source-receiver offsets are involved. Creation of artificial lineup and smearing at the outputs of multichannel filters is presently the common practical concern. Optimum multichannel filters with well-defined pass, reject and transition bands overcome the latter problems when applied before stacking and after NMO correction. The trace dimension of these filters must be kept small to avoid such lineups and the smoothing of small structures. Good results can be obtained with only five traces, but seven traces seems to be a better compromise both in surface and well seismic applications. The so-called f-k filtering and τ-p domain filtering are no exceptions to the above practical considerations. Residual static computations after multichannel filtering also need special consideration. Since multichannel filtering improves spatial continuity, residual static algorithms using local correlation, i.e. nonsurface-consistent algorithms, may be impractical especially after multichannel filtering.     

分数维约束下的自适应对消技术研究

介绍了自适应对消技术的基本原理,分析了自适应对消技术的优缺点,针对一些缺点提出了相应的改进方法。由于常规自适应对消技术是通过迭代技术实现的,需要迭代一定次数后才能确定最佳参数,所以在信号起始位置和有效信号尾部收敛效果不好,从而影响滤波效果。引入hausdorff维数来约束地震信号,首先求取原始地震信号的hausdorff维数谱,利用有效信号与随机噪音维数的不同,将有效信号以外的随机噪音滤除,并将自适应对消中的参考噪声对应位置的随机噪音去除;然后将更新后的地震信号和参考噪声进行自适应滤波,从而得到一个优化的自适应对消滤波器。     

Nonlinear structure‐enhancing filtering using plane‐wave prediction*

Attenuation of random noise and enhancement of structural continuity can significantly improve the quality of seismic interpretation. We present a new technique, which aims at reducing random noise while protecting structural information. The technique is based on combining structure prediction with either similarity‐mean filtering or lower‐upper‐middle filtering. We use structure prediction to form a structural prediction of seismic traces from neighbouring traces. We apply a non‐linear similarity‐mean filter or an lower‐upper‐middle filter to select best samples from different predictions. In comparison with other common filters, such as mean or median, the additional parameters of the non‐linear filters allow us to better control the balance between eliminating random noise and protecting structural information. Numerical tests using synthetic and field data show the effectiveness of the proposed structure‐enhancing filters.     

Applications of Savitzky-Golay Filter for Seismic Random Noise Reduction

This article utilizes Savitzky–Golay (SG) filter to eliminate seismic random noise. This is a novel method for seismic random noise reduction in which SG filter adopts piecewise weighted polynomial via leastsquares estimation. Therefore, effective smoothing is achieved in extracting the original signal from noise environment while retaining the shape of the signal as close as possible to the original one. Although there are lots of classical methods such as Wiener filtering and wavelet denoising applied to eliminate seismic random noise, the SG filter outperforms them in approximating the true signal. SG filter will obtain a good tradeoff in waveform smoothing and valid signal preservation under suitable conditions. These are the appropriate window size and the polynomial degree. Through examples from synthetic seismic signals and field seismic data, we demonstrate the good performance of SG filter by comparing it with the Wiener filtering and wavelet denoising methods.     

PRINCIPLES OF DIGITAL WIENER FILTERING*

The theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so-called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.     

AFTER-STACK MULTICHANNEL FILTERS WITHOUT MIXING EFFECTS *

Several types of multichannel filters have been introduced in the past with the purpose of rejecting, in a seismic section, coherent noise having a slope different from that of the signal. These filters, generally, tend to introduce a certain amount of mixing and therefore the output trace shows increased horizontal coherence. This is due to the model on which these filters are based, since the hypothesis is posed that the reflectors are continuous. This may be dangerous since it could lead to mistaken interpretations, for example when small faults or breaks are made to disappear in the output section. Other problems that could arise in the application of multichannel filters after-stack are space-aliasing and high-pass filtering. The former occurs when coherent noise is rejected with apparent Velocity V and frequency f_a=V/X, where X is the distance between traces. In this case, the signal also is distorted since it is rejected in the same frequency range. The high pass filtering effect occurs when the multichannel filter is designed to remove low coherent noise with high apparent velocity. In the paper a family of multichannel filters is presented based on a model of the seismic section such that minimum mixing effects appear. The filters are designed to give good results even in the case of low frequency and high velocity coherent noise. Some practical examples are shown.     

Influence of parameters selection in Chebyshev filters on the strong motion data processing

This contribution discusses the application of Chebyshev Type I filter for processing real earthquake records. Consideration is given to the effects of filtering parameters (passband amplitude ripple and order of the filter) on the time series, strong-motion parameters, Fourier Amplitude Spectrum of acceleration, and elastic displacement response spectra. Time histories of five earthquakes with different moment magnitudes have been examined (from stations located close to the epicenters). Data processing is based on application of bandpass Chebyshev filtering over frequency range with substantial signal to noise ratio (level of 3 or approximately 3 dB). Applying different filters, we have monitored several important strong-motion parameters: peak values of acceleration, velocity, and displacement; Arias intensity, acceleration/velocity spectrum intensity, significant duration, etc. Some new results and conclusions concerning the influence of Chebyshev filter in data processing of records have been summarized. The graphical and numerical outcomes obtained, as well as the comparison with a Butterworth causal filter, are included in the work. The results could be potentially useful to engineering seismologists who need to evaluate and better understand the merits of this type of filtering for strong-motion data processing.     

基于ARMA模型非因果空间预测滤波(英文)

常规频域预测滤波方法是建立在自回归(autoregressive,AR)模型基础上的,这导致滤波过程中前后假设的不一致,即首先利用源噪声的假设计算误差剖面,却又将其作为可加噪声而从原始剖面中减去来得到有效信号。本文通过建立自回归-滑动平均(autoregres sive/moving-average,ARMA)模型,首先求解非因果预测误差滤波算子,然后利用自反褶积形式投影滤波过程估计可加噪声,进而达到去除随机噪声目的。此过程有效避免了基于AR模型产生的不一致性。在此基础上,将一维ARMA模型扩展到二维空间域,实现了基于二维ARMA模型频域非因果空间预测滤波在三维地震资料随机噪声衰减中的应用。模型试验与实际资料处理表明该方法在很好保留反射信息同时,压制随机噪声更加彻底,明显优于常规频域预测去噪方法。