A generalized derivative operator for potential field data‡

The enhancement of potential field data using filters based on horizontal and vertical derivatives is common. As well as the direct use of the gradients themselves they are used in filters such as sunshading, total horizontal derivative, analytic signal, horizontal and vertical tilt angles, the Theta map and other filters. These techniques are high‐pass filters of different types and so enhance noise as well as detail in the data. A new derivative operator is introduced in this paper, which generalizes the effects of some of the previously mentioned filters. This filter is a linear combination of the horizontal and vertical field derivatives, normalized by the analytic signal amplitude. The filter is demonstrated on aeromagnetic and gravity data from South Africa.     

分离重磁区域场与局部场的维纳滤波器

本文从最佳线性滤波理论出发,对目前重磁资料数据处理中分离区域场与局部场的两种滤波器——匹配滤波和维纳滤波的频率响应特性作了分析比较,指出了匹配滤波只是一般维纳滤波的一个特例。将该两种滤波器与一般情况的维纳滤波器的误差作了对比,并通过简单的理论试例,说明它们的局限性和应用范围。     

分离重磁区域场与局部场的维纳滤波器

本文从最佳线性滤波理论出发,对目前重磁资料数据处理中分离区域场与局部场的两种滤波器--匹配滤波和维纳滤波的频率响应特性作了分析比较,指出了匹配滤波只是一般维纳滤波的一个特例。将该两种滤波器与一般情况的维纳滤波器的误差作了对比,并通过简单的理论试例,说明它们的局限性和应用范围。     

THE QUALITY OF SOME TWO-DIMENSIONAL FILTERS IN SEPARATING REGIONAL AND LOCAL GRAVITY ANOMALIES *

The separation of regional from local gravity anomalies by means of the application of two-dimensional linear filters is analyzed. It was found that optimization of the filter in the least squares sense leads to filters that produce strong localized concentrations of the error, which may erroneously be interpreted as anomalies. For this reason the maximum absolute value of the error is a more important criterion for the quality of the filter than the root mean square error. This maximum absolute error is minimized by the minimax filter. Intermediate filters are derived which give a transition zone which comes appreciably closer to that of the optimal filter at only a small price in terms of increase of the maximum absolute error.     

The 3-D Truncation Filtering Methodology Defined for Planar and Spherical Models: Interpreting Gravity Data Generated by Point Masses

This paper focuses on one particular way of linear filtering the gravity data to facilitate gravity inversion or interpretation. With the use of integral transforms the gravity anomalies are transformed into new quantities that allow an easier interpretation with the help of pattern recognition. As the integral transforms are in fact filters, and as the regions of integration are caps with a variable radius, which can be systematically changed as a free parameter, we refer to such methodology as the truncation filtering. Such filters may be understood as weighted spherical windows moving over the surface, on which the gravity anomaly is defined, the kernel of the transform being the weight function. The objective of this paper is to define and deploy the truncation filtering for a planar model, i.e. for a homogenous horizontally infinite layer with embedded anomalous masses, and for a spherical model, i.e., for a homogenous massive sphere with embedded anomalous masses. Instead of the original gravity anomaly, the quantities resulting from the truncation filtering are interpreted/inverted. As we shall see, this approach has certain benefits. The fundamental concept of the truncation filtering methodology is demonstrated here in terms of the model consisting of one point mass anomaly.The relationship between the depth of the point mass and the instant of the onset of the dimple pattern observed in sequences produced by truncation filtering the synthetic gravity data generated by point masses is, for both the planar and spherical models, compiled by computer simulations, as well as derived analytically. It is shown, that the dimple pattern is a consequence of truncating the domain of the filter and is free of the choice of the kernel of the filter. It is shown, that in terms of the mean earth and depths of point masses no greater than some 100 km the spherical model may be replaced by a planar model from the perspective of the truncation filtering methodology. It is also shown, that from the viewpoint of the truncation filtering methodology the rigorous gravity anomaly may be approximated by the vertical component of the gravity disturbance. The relationship between the instant of the dimple onset and the depth of the point mass thus becomes linear and independent of the magnitude (mass) of the point mass.     

Application of balanced edge detection filters to estimate the location parameters of the causative sources using potential field data

Balanced edge detection filters can recognize the edges of the shallow and deep bodies simultaneously, and are commonly used in the edge detection of potential field data. In this paper, we present using the balanced edge detection filters to estimate source locations, and derive two linear equations based on the balanced edge detection filters that can estimate the locations of the source without any priori information about the nature (structural index) of the source. The proposed methods are demonstrated on synthetic gravity anomalies, and the inversion results show that the proposed methods can successfully estimate location parameters of the sources. I also apply the proposed methods to real magnetic data, and the inversion results estimated by the proposed methods are consistent with the results estimated by the other similar method.     

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.     

基于Theta法改进的均衡滤波器在位场边界识别中的应用--以庐枞矿集区为例

利用观测数据确定地质体的边界位置是位场数据解译中的一项重要工作,传统的边界识别滤波器通常不能均衡深、浅部的地质体边界,近些年相关研究开始致力于发展均衡边界滤波器.本文基于Theta图法定义了新的边界识别滤波器,详述了滤波器波数域及空间域的主要计算公式,通过模型验证,该滤波器显著压制了Theta图法对深部地质体边界的放大作用,较好地平衡了深部和浅部边界.通过与传统的边界识别滤波器对比,本文定义的滤波器能够清晰且更加收敛地圈定出地质体的水平边界位置.以长江中下游成矿带庐枞矿集区为例,开展了1：5万重磁数据的处理分析,并结合物性资料进行了讨论,结果表明：重磁数据的检测结果精确刻画了郯庐断裂带的位置;庐枞盆地的磁力数据检测边界整体与盆地的地质边缘一致,明确了边界断裂在深部倾向盆地内部;识别出庐枞盆地外围一系列环形边界,这些边界封闭区域与最新勘探发现的深部岩体及铁铜矿化体相对应,对于指导区域深部找矿工作有着重要的意义.

     

利用重力异常匹配技术实现潜艇导航

潜艇的惯性导航误差是随时间积累的,利用重力异常数据进行辅助导航可以对惯性导航的漂移误差进行校正.首先利用2′×2′重力异常数据库作为基础信息,结合Kalman滤波算法对某区域进行了模拟计算,模拟过程采用了增益系数和信息更新序列的新方法进行Kalman 滤波的处理,结果表明在重力异常变化幅度较大的地区,重力异常可以进行潜艇的辅助导航.     

航空重力数据无限脉冲响应低通数字滤波器设计与试验研究

采用巴特沃思(Butterworth)和切比雪夫(Chebyshev)逼近,设计无限脉冲响应(Infinite Impulse Response, IIR)低通数字滤波器,对GT-1A航空重力勘查系统的测量数据进行了滤波试验研究,结果表明,通过选择合适的通带和阻带衰减等滤波参数,IIR低通数字滤波器在航空重力数据的低通滤波处理中可以发挥重要作用,获得与GT-1A系统滤波结果几乎同样满意的滤波效果.     

Wavelet approach to the determination of gravity tide parameters

A new approach is proposed for the determination of gravity tide parameters.Three pairs of compactly supported wavelet filters are introduced in the approach.They can efficiently extract the objective tides from the gravity observation series.The new approach guarantees a direct and precise analysis on the tidal gravity records of any sampling length.The new approach is applied to the harmonic analysis on Wuhan superconducting gravimeter records.The results clearly show the resonant effects of the Earth Nearly Diurnal Free Wobble (NDFW).     

A refined method of recovering potential coefficients from surface gravity data

Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained. Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the error data propagation is, consequently, maximally suppressed.     

Linear transformations of anomalous potential fields using <Emphasis Type="Italic">S</Emphasis> and <Emphasis Type="Italic">R</Emphasis> approximations

Methods for linear transformations of anomalous physical fields based on R and S approximations of the elements of the initial field are described. The results of the numerical experiment and analytical extension of the gravity field measured in a detailed gravity survey in two regions of Russia are presented.     

重力潮汐观测资料的改正和异常背景值的显示问题

本文系统地研究了重力潮汐观测的改正和作为地震预报研究的异常背景值的显示问题.文章讨论了仪器弹性系统流变模型改正和惯性改正以及海洋潮汐等的资料精确化问题和气压、地下水等对重力潮汐观测的影响,并给出了相应的结果.文章还讨论了台站重力测量中非潮汐信息的提取问题,从理论上论证并对比了几种滤波器的实质.      

Noise filtering of full-gravity gradient tensor data

In oil and mineral exploration, gravity gradient tensor data include higher-frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry (FTG) data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high-frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.     

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.     

多源布格重力异常数据贝叶斯融合算法及其在川滇地区的应用

布格重力异常数据是研究地壳结构和变形的重要依据,由于观测手段、处理方法等存在差异,不同手段获得的布格重力异常可能存在数据噪声水平及起算基准不一致,从而引起多源布格重力异常数据难以有效融合的难题.为此,本文在传统等效源重力数据融合方法的基础上,通过引入贝叶斯参数优化准则,提出了一种新的多源布格重力异常融合算法.随后对川滇...     

On the correction of gravity tides observation and the indication analysis of gravity anomaly

The problems of correcting gravity tidal observations and indicating of the gravity anomalies used in earthquake prediction in China are systematically studied in this paper. The correcting problems of the rheological model of the instrument, inertia of the earth and the effects of the ocean loading, air pressure, underground water on gravity tidal recording data are also discussed in details, the related results are also given in the paper. The problem of the indicating non-tidal information in stational gravity data is dicussed. The properties of the several different data processing filters are compared in theoretical point of view.     

陕西重力测网起算基准稳定性分析

采用经典平差方法处理重力网数据时,判断起算基准是否稳定是一个关键性问题。本文在精细化处理陕西重力测网观测资料基础上,采用线性回归法,对1992—2011年陕西重力测网起算基准进行了稳定性分析。并以泾阳M_S 4.8地震为例,分析了重力起算基准稳定性对重力网计算的影响及线性回归方法的有效性,结果表明:(1)起算基准重力值随时间变化明显;(2)起算基准扰动影响改正后,地震前后重力场及跨断裂重力段差变化特征更加符合实际情况;(3)处理重力数据及分析重力场变化特征时,必须考虑起算基准稳定性的影响。     

Improving Surface Geostrophic Current from a GOCE-Derived Mean Dynamic Topography Using Edge-Enhancing Diffusion Filtering

With increased geoid resolution provided by the gravity and steady-state ocean circulation explorer (GOCE) mission, the ocean’s mean dynamic topography (MDT) can be now estimated with an accuracy not available prior to using geodetic methods. However, an altimetric-derived MDT still needs filtering in order to remove short wavelength noise unless integrated methods are used in which the three quantities are determined simultaneously using appropriate covariance functions. We studied nonlinear anisotropic diffusive filtering applied to the ocean´s MDT and a new approach based on edge-enhancing diffusion (EED) filtering is presented. EED filters enable controlling the direction and magnitude of the filtering, with subsequent enhancement of computations of the associated surface geostrophic currents (SGCs). Applying this method to a smooth MDT and to a noisy MDT, both for a region in the Northwestern Pacific Ocean, we found that EED filtering provides similar estimation of the current velocities in both cases, whereas a non-linear isotropic filter (the Perona and Malik filter) returns results influenced by local residual noise when a difficult case is tested. We found that EED filtering preserves all the advantages that the Perona and Malik filter have over the standard linear isotropic Gaussian filters. Moreover, EED is shown to be more stable and less influenced by outliers. This suggests that the EED filtering strategy would be preferred given its capabilities in controlling/preserving the SGCs.