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1.
We discuss the Hankel transforms related to a particular application, i.e. the dipole antenna radiation in conductive media, such as the antenna radiation in sea-bed electromagnetic applications. In this application, the electromagnetic wavefields decay very rapidly with distance. A good filter means that it can be used to evaluate weak fields. Exponential sampling transforms a Hankel transform into a convolution equation, which must be solved to obtain the filter coefficients. Here, we use a direct matrix inversion method to solve the convolution equation in the sample domain, instead of the Fourier transform method and the Wiener–Hopf method, previously used to solve the convolution equation. This direct method is conceptually simple and is suitable for our optimization process: by using the Sommerfeld identity, we search for the optimum sampling interval, which corresponds to the minimum wavefield, evaluated for a given length filter. The performances of the new filters obtained are compared with some well-known filters. We find that our filters perform better for our application; that is, for the same length filters, our filters are able to calculate weaker fields. For users working in similar applications, three sets of filters with lengths 61, 121, 241 are available from the author.  相似文献   

2.
The numerical evaluation of certain integral transforms is required for the interpretation of some geophysical exploration data. Digital linear filter operators are widely used for carrying out such numerical integration. It is known that the method of Wiener–Hopf minimization of the error can be used to design very efficient, short digital linear filter operators for this purpose. We have found that, with appropriate modifications, this method can also be used to design longer filters. Two filters for the Hankel J0 transform (61-point and 120-point operators), and two for the Hankel J1 transform (47-point and 140-point operators) have been designed. For these transforms, the new filters give much lower errors compared to all other known filters of comparable, or somewhat longer, size. The new filter operators and some results of comparative performance tests with known integral transforms are presented. These filters would find widespread application in many numerical evaluation problems in geophysics.  相似文献   

3.
The accuracy of short length digital linear filter operators can be substantially increased if the sampling interval as well as the abscissa shift are properly adjusted. This may be done by a trial and error process of adjustment of these parameters until the error made by the filter operator, applied to a suitably chosen test function, is smallest. As an illustration of the application of this method, 7-, 11- and 19-point filters for the calculation of Schlumberger apparent resistivity from a known resistivity transform are designed. Errors with the new 7-point filter are seen to be less than those with a 19-point filter of conventional design. The errors with the new 19-point filter are two to three orders of magnitude smaller than those made by the conventional 19-point filter. The new method should provide digital linear operators that allow significant improvements in accuracy for comparable computation efforts, or substantial reduction in computation for comparable accuracy of results, or something of both.  相似文献   

4.
A new approach has been developed for the design of cross-equalization filters by the least-squares method. The filters estimated by this new exact method are subject to only two types of error: bias and random error. Cross-equalization filters estimated by a more conventional least-squares method are further subject to “transient error”. This type of error becomes important when designing filters from a data gate of a length comparable with the length of the filter, i.e., less than four times the length of the filter. The effect of altering various design parameters has been investigated for the new method. It has been found that the proportion of bias in the filter decreases as the effective filter length increases, whereas the random error in the filter decreases with increase in either the signal-to-noise ratio of the data or the ratio of the data duration to the filter length. The level of whitening applied to the auto-correlation matrix before inversion was not found to be a critical design parameter. Also, two techniques have been tested for reducing any anomalous d.c. component in the calculated filter.  相似文献   

5.
Short filters for calculating Hankel-transformations, with special attention to the d.c.-sounding problem, have been published in recent years. These filters, with a typical length of less than 25 coefficients, have made it possible to implement, e.g., VES-interpretation programs on microcomputers and 3-D electric and electromagnetic modeling programs on minicomputers. Initially the performance of the short filters was rather poor, but with the introduction of short optimized filters there has been a considerable improvement in the accuracy. An optimization procedure is applied to design a 20-point filter for the Fourier sine-transformation. This filter may be useful in electromagnetic prospecting theory, e.g., in the calculation of the electric and magnetic field from a line source.  相似文献   

6.
This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities. Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.  相似文献   

7.
Bias aware Kalman filters: Comparison and improvements   总被引：1，自引：0，他引：1  
This paper reviews two different approaches that have been proposed to tackle the problems of model bias with the Kalman filter: the use of a colored noise model and the implementation of a separate bias filter. Both filters are implemented with and without feedback of the bias into the model state. The colored noise filter formulation is extended to correct both time correlated and uncorrelated model error components. A more stable version of the separate filter without feedback is presented. The filters are implemented in an ensemble framework using Latin hypercube sampling. The techniques are illustrated on a simple one-dimensional groundwater problem. The results show that the presented filters outperform the standard Kalman filter and that the implementations with bias feedback work in more general conditions than the implementations without feedback.  相似文献   

8.
基于非因果滤波器的多次波匹配相减方法(英文)   总被引：1，自引：0，他引：1  
在常规多道匹配滤波方法中的滤波器是物理可实现的因果滤波器,只能实现地震信号序列延迟的滤波。本文提出了最小二乘意义下的非因果多道输入多道输出维纳滤波方法,通过比较多道匹配相减中因果和非因果滤波方法之间的差别,验证了方法的有效性,解决了模型数据滞后于实际数据的情况。而且,通过定义长度随偏移距和层速度变化的滑动时窗,解决了匹配时窗内同相轴数量随偏移距增大而增加的问题。并将上述方法应用到改进的扩展多道匹配相减去除多次波的方法中,利用Pluto1.5理论模拟数据,对非因果滤波器和变长度时窗的匹配相减方法进行测试,取得了很好的去除多次波后的地震数据。  相似文献   

9.
以ADS1281为例,介绍新一代地震数据采集器后级滤波器设计。该后级滤波器包括变抽样率的梳状滤波器、有限脉冲响应(FIR1)4抽1滤波器和有限脉冲响应(FIR2)2抽1滤波器。其中,FIR1 4抽1滤波器和FIR2 2抽1又分为最小相位、线性相位和瞬态3种滤波器,文中使用设计的最小相位滤波抽取器对仿真的正弦波进行滤波验证,结果表明,通带波动和阻带衰减满足中国数字测震台网技术规程的要求。  相似文献   

10.
It was found in Part I of this paper that approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length M produced a characteristic whose slope on a linear frequency scale was proportional to the length of impulse response, but whose maximum overshoot of ±9% was independent of this length (Gibbs' phenomenon). Weighting functions, based on frequency tapering or arbitrarily chosen, were used in Part II to modify the truncated impulse response of the sharp cut-off frequency characteristic, and thereby obtain a trade-off between the value of maximum overshoot and the sharpness of the resulting characteristic. These weighting functions, known as apodising functions, were dependent on the time-bandwidth product Mξ, where 2ξ, corresponded to the tapering range of frequencies. Part III now deals with digital filters where the number 2N–1 of coefficients is directly related to the finite length M of the continuous impulse response. The values of the filter coefficients are taken from the continuous impulse response at the sampling instants, and the resulting characteristic is approximately the same as that derived in Part II for the continuous finite length impulse response. Corresponding to known types of frequency tapering, we now specify a filter characteristic which is undefined in the tapering range, and determine the filter coefficients according to a mean square criterion over the rest of the frequency spectrum. The resulting characteristic is dependent on the time bandwidth product Mξ= (N–1/2)ξ up to a maximum value of 2, beyond which undesirable effects occur. This optimum partially specified characteristic is an improvement on the previous digital filters in terms of the trade-off ratio for values of maximum overshoot less than 1%. Similar to the previous optimum characteristic is the optimum partially specified weighted digital filter, where greater “emphasis is placed on reducing the value of maximum overshoot than of maximum undershoot”. Such characteristics are capable of providing better trade-off ratios than the other filters for maximum overshoots greater than 1/2%. However these filters have critical maximum numbers 2.NC–1 of coefficients, beyond which the resulting characteristics have unsuitable shapes. This type of characteristic differs from the others in not being a biassed odd function about its cut-off frequency.  相似文献   

11.
The purpose of this paper is to study the possibility of performing practically stable and efficient frequency‐space (f?x) wavefield extrapolation for the application of seismic imaging and datuming via infinite impulse response (IIR) filters. The model reduction control theory was adopted to design such IIR f?x extrapolation filters. The model reduction theory reduces the order of a given order system which, in this case, involves reducing a finite impulse response (FIR) f?x extrapolation filter system into an IIR f?x extrapolation filter system. This theory relies on decomposing the states of the given filter system into strong and weakly coupled sub‐systems, and then eliminating the weakly coupled states via singular value decomposition of the Hankel and the impulse response Gramian matrices. Simulation results indicate that IIR f?x filters can be obtained, which are stable from an IIR filter design point of view. Simulations also indicate that stable seismic impulse responses and synthetics can be obtained with a reduced system model order and, hence, less computational efforts with respect to the number of complex multiplications and additions per output sample. It is hoped that this study will open new possibilities for researchers to reconsider designing IIR f?x explicit depth extrapolation filters due to their expected computational savings and wavenumber response accuracy, when compared to the FIR f?x explicit depth extrapolation filters.  相似文献   

12.
Two distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma-Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.  相似文献   

13.
Approximate deconvolution by means of Wiener filters has become standard practice in seismic data-processing. It is well-known that addition of a certain percentage of noise energy to the autocorrelation of the signal wavelet leads to a filter that does not increase, or even reduces, the noise level on the seismogram. This noise addition will, in general, cause a minimum phase signal to become mixed phase. A technique is presented for the calculation of the optimum-lag shaping filter for a contaminated signal wavelet. The advantages of this method over the more conventional approach are that it needs less arithmetic operations and that it automatically gives the filter with the optimum combination of shaping performance and noise reduction.  相似文献   

14.
The impact of vegetated filter strips (VFS) on sediment removal from runoff has been studied extensively in recent years. Vegetation is believed to increase water infiltration and decrease water turbulence thus enhancing sediment deposition within filter media. In the study reported here, field experiments have been conducted to examine the efficiency of vegetated filter strips for sediment removal from cropland runoff. Twenty filters with varying length, slope and vegetated cover were used under simulated runoff conditions with an average sediment concentration of 2700 mg/L. The filters were 2, 5, 10 and 15 m long with a slope of 2·3 and 5% and three types of vegetation. Three other strips with bare soil were used as a control. The experimental results showed that the average sediment trapping efficiency of all filters was 84% and ranging from 68% in a 2‐m filter to as high as 98% in a 15‐m long filter compared with only 25% for the control. The length of filter has been found to be the predominant factor affecting sediment deposition in VFS up to 10 m. Increasing filter length to 15 m did not improve sediment trapping efficiency under the present experimental conditions. The rate of incoming flow and vegetation cover percentage has a secondary effect on sediment deposition in VFS. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

15.
A simple system was designed using7LiOH-impregnated filters to collect acidic gases from ambient air and from highly concentrated volcanic plumes or gas streams. These filters were developed for analysis using instrumental neutron activation analysis, but other analytical techniques could be used as well. The sampling system was designed to use a series of 1–3 M7LiOH-impregnated filters to collect high concentrations of acidic gases found in gas plumes of active volcanoes. The filters are quantitative for SO2 and the halide acids when sufficient base is present to neutralize the acidic species. Extremely high concentrations of SO2 may not be collected quantitatively since SO2 is a relatively weak Lewis acid compared to the halide acids. The acidic oxides of Sb, As, and Se were also collected quantitatively. A particle filter preceded the impregnated filters in order to remove particles from the fumes. This system has proven effective under difficult sampling conditions and, since it is portable and light weight, it could be used for many volcanological applications where high levels of acidic gaseous phase species need to be collected.  相似文献   

16.
Receiver Functions from Autoregressive Deconvolution   总被引：4，自引：0，他引：4  
Summary Receiver functions can be estimated by minimizing the square errors of Wiener filter in time-domain or spectrum division in frequency domain. To avoid the direct calculation of auto-correlation and cross-correlation coefficients in Toeplitz equation or of auto-spectrum and cross-spectrum in spectrum division equation as well as empirically choosing a damping parameter, autoregressive deconvolution is presented to isolate receiver function from three-component teleseismic P waveforms. The vertical component of teleseismic P waveform is modeled by an autoregressive model, which can be forward and backward, predicted respectively. The optimum length of the autoregressive model is determined by the Akaike criterion. By minimizing the square errors of forward and backward predicting filters, autoregressive filter coefficients can be recursively solved, and receiver function is also estimated in the similar procedure. Both synthetic and real data tests show that autoregressive deconvolution is an effective method to isolate receiver function from teleseismic P waveforms in time-domain.  相似文献   

17.
A spatial filter is often attached to a microphone or microbarometer in order to reduce the noise caused by atmospheric turbulence. This filtering technique is based on the assumption that the coherence length of turbulence is smaller than the spatial extent of the filter, and so contributions from turbulence recorded at widely separated ports will tend to cancel while those of the signal of interest, which will have coherence length larger than the spatial dimensions of the filter, will be reinforced. In this paper, the plane wave response for a spatial filter with an arbitrary arrangement of open ports is determined. It is found that propagation over different port-to-sensor distances causes out-of-phase sinusoids to be summed at the central manifold and can lead to significant amplitude decay and phase delays as a function of frequency. The determined spatial filter plane wave response is superimposed on an array response typical of infrasound arrays that constitute the International Monitoring System infrasound network used for nuclear monitoring purposes. It is found that signal detection capability in terms of the Fisher Statistic can be significantly degraded at certain frequencies. The least-squares estimate of signal slowness can change by up to 1.5° and up to 10 m/s if an asymmetric arrangement of low and high frequency spatial filters is used. However, if a symmetric arrangement of filters is used the least-squares estimate of signal slowness is found to be largely unaffected, except near the predicted null frequency.  相似文献   

18.
Soil and water conservation practices have been promoted for a long time, in order to sustain agricultural activities and prevent environmental pollution. Vegetated filter strips (VFS) have been used to reduce sediment pollution into water bodies at or near the pollutant source. However, factors effecting VFS performance under natural conditions have not been well understood owing to the physical, time and financial limitations of field experiments. The use of well‐validated simulation models to understand the performance of VFS and factors affecting sediment deposition is highly justified. The objective of this research is to investigate sediment trapping in VFS and to study various factors affecting VFS performance using the simulation model VFSMOD, which was developed by researchers at University of North Carolina. Recently, VFSMOD has been validated successfully by using 21 filters with varying length, slope and vegetated cover. A wide range of five parameters was selected for the simulations, namely filter length, filter slope, manning roughness coefficient, soil type and characteristics of incoming sediment from adjacent fields. Computer simulations revealed that the length of filter is the most significant factor affecting sediment trapping in VFS. The relative increase in trapping efficiencies was not linearly related to an increase in filter length. Inflow sediment class also has a major influence on sediment trapping in VFS. The trapping efficiency of clay sediments in a 15 m length VFS was 47% compared with 92% for silt from incoming sediment. Manning roughness coefficient had a moderate effect on sediment trapping and was more significant in short filters. Land slope and soil type of VFS had a minor influence on the performance of VFS. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

19.
Linear relationship between dipole and Schlumberger sounding resistivities leads to the use of digital filters to transform the former to the latter. This transformation is of importance from the viewpoint that Schlumberger interpretational techniques and know-how could then be applied to the pseudo-Schlumberger field curve. Filters for this transformation are presented for the radial, perpendicular, and parallel (30°) dipole method. The characteristics of these filters are similar to the ones for transforming dipole data to the kernel and are favourable in that they do not amplify noise. A sampling interval of (In 10) /6 has been used in determining the filter yielding good accuracy. Like previous filters the present one is handy and fast in operation.  相似文献   

20.
The calculation of dip moveout involves spreading the amplitudes of each input trace along the source-receiver axis followed by stacking the results into a 3D zero-offset data cube. The offset-traveltime (x–t) domain integral implementation of the DMO operator is very efficient in terms of computation time but suffers from operator aliasing. The log-stretch approach, using a logarithmic transformation of the time axis to force the DMO operator to be time invariant, can avoid operator aliasing by direct implementation in the frequency-wavenumber (f–k) domain. An alternative technique for log-stretch DMO corrections using the anti-aliasing filters of the f–k approach in the x-log t domain will be presented. Conventionally, the 2D filter representing the DMO operator is designed and applied in the f–k domain. The new technique uses a 2D convolution filter acting in single input/multiple output trace mode. Each single input trace is passed through several 1D filters to create the overall DMO response of that trace. The resulting traces can be stacked directly in the 3D data cube. The single trace filters are the result of a filter design technique reducing the 2D problem to several ID problems. These filters can be decomposed into a pure time-delay and a low-pass filter, representing the kinematic and dynamic behaviour of the DMO operator. The low-pass filters avoid any incidental operator aliasing. Different types of low-pass filters can be used to achieve different amplitude-versus-offset characteristics of the DMO operator.  相似文献   

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