Application Of Kalman Filtering In The Gravity Field Data Processing

The gravity field data processing is an important part in the gravity prospecting, along with science technique of continuously development and data collect accuracy continuously to raise,the study of method and technology for high- precision data processing of gravity anomalies seem to very important.Gravity anomaly without data processing can be seen as different depths underground,different scale,different physical parameters of the geological bodies stacking up at the ground effect,and the weight does not change over time with the smooth characteristics.Whether through a filtering method is more reasonable,in accordance with this stack depth anomaly(or wavelength) to open the whole decomposition,thereby to determine a more accurate or underground geological structure of the distribution and morphology.Therefore,the choice of what kind of filtering method is a very important job.This article is based on this theory,combined with Kalman filtering technology to Bouguer gravity anomaly data for processing. Through a variety of theoretical models of the spreadsheet shows that the better,more adaptable,free from interference with useful information and the relevance of information and the impact of the same phase.For the observed potential field anomaly profile,after some necessary preprocessing,we can consider that it is underground at different depths,different scale,different physical parameters of the geological bodies in the ground on the superposition effect,and the weight has not changed over time smooth features, whether through a more reasonable filtering method,this superposition of anomalies in accordance with the depth(or wavelength) decomposition generally open,thus more accurate to judge the underground geological structure or the distribution and morphology.Therefore,the selection of what kind of filtering method is a very important job.This article is on this theoretical foundation,combined with Kalman filtering technology on the gravitational potential field measurement data for processing.Through a variety of theoretical models of the spreadsheet shows that the effect of better adapted,from the useful information and interference information of relevance and impact of the same phase.Kalman filter since its inception in early 60s,one after another in many areas, been widely used.Although the Kalman filter with the Wiener filtering criteria are minimum variance filter,but they are required by the known conditions,the calculation method and the scope of application,such as not the same.At present,the separation of the regional market with the local field in the "Wiener filtering",Wiener filter in the signal and interference are not relevant under the conditions of a special case,the so-called separation of the regional market with the local field of "matched filtering",Wiener filter is essentially at the same phase signal and interference under the conditions of a special case.About Kalman filter in the application of geophysical applications,currently limited to seismic data processing.In this paper,using Kalman filter for potential field data processing,and discussed the separation of gravity anomalies in the application problem.Regional market with the local field separation of the regional gravity field data are an important aspect of treatment.At the actual data interpretation also has important significance.Judging from the spectral analysis,regional market and the local field frequency components are different.Regional market to low-frequency components of the main local market dominated by high frequency components. Extracted using different wave number components of the field to complete the separation field.1.Window functionPlace at the actual conduct of field separation treatment are often required to observe the time limit for the signal at a certain time interval,only select a period of time required to analyze the signal.In this way,take a finite number of data,signal data is about to cut off the process,it means that the signal window function add to the operation.This operation later,usually occurs from the normal weight spectrum spread spectrum open to the situation,namely the so-called "spectral leakage." When carried out Discrete Fourier Transform,the time domain of the cut-off is necessary, therefore,the leakage effect is also a Discrete Fourier Transform(DFT) inherent in the need for suppression.In order to carry out suppression of spectral leakage can be inhibited through the window function weighted equivalent DFT filter sidelobe amplitude characteristics,or the weighted window function so that the limited length of the input signal cycle after the extension at the border to minimize the extent of discontinuous Ways of implementation.In addition,power spectrum estimation of the weighted window function also encountered problem.This shows that the weighted window function in power field separation technology to the important status of treatment.Digital signal processing field of the window function used in the main are: rectangular window function,the triangular window function,Hanning window function,Chebyshev window function.2.Matched FilteringMatched filter response to the wave number reflects the regional market extract matched filter is a low-pass filter.Local field and extract the matched filter is a high-pass filter.But it downward continuation and derivation of the wave number has an important response is the difference between the wave number matched filter response to one of its asymptotic lines,it can only play the role of extracting high frequency components will not be enlarged a result of concussion.However,in order to better focus on effective information,in practical work with matched filter extracts the local market when they should be compatible with low-pass filter to suppress high-frequency interference.3.Wiener filtering and Kalman filteringWiener filtering and Kalman filtering are based on minimum mean square error as the criterion of the linear estimator.Kalman filtering and Wiener filtering the difference is:(1) Kalman filtering and Wiener filtering to address the best method of filtering is not the same.Wiener filter is used in frequency domain and transfer function methods,Kalman are using time-domain and state variable methods.(2) Wiener filtering requirements of the process of auto-correlation function and cross-correlation function of simple knowledge,and Kalman filter requires time domain signal status variables and a detailed knowledge of the process.(3) Wiener filter for a smooth,while the Kalman filter is not required.4.Kalman Filter-based sampling data Spline InterpolationSpline interpolation of the basic approach is to use a series of discrete points give the coordinates,using cubic spline function of adjacent contact points,the adjacent spline function at convergence not only has the same function value,but also has the same tangent and curvature,which is very smooth.There is a whole interpolation function of these sub-cubic spline connected.Cubic spline interpolation algorithms are derived equations have unknown,the corresponding equation is only months,it must only determine its solution must also provide two boundary conditions.Boundary conditions usually have the following:(1) second derivative conditions;(2) assumed that the sequence of data points for the cycle sequence;(3) slope conditions;(4) the conditions of virtual nodes;(5) "non-node" conditions;(6) Lagrange - cubic spline interpolation conditions.At the actual interpolation,the above methods there are less than certain.The first three conditions for a narrower scope of application,and in reality often can not meet its conditions,the conditions(4) only depends on the value of subjective judgments,the conditions(5) and(6) did not be able to take full advantage of known data points of information,when a relatively small number of data points on the interpolation accuracy of a greater impact on this use of Kalman filtering method known recursive data type values to estimate the follow-up data,and thus the volume of solution of the unknown method.Kalman filter in real terms are used recursive filtering methods, using linear unbiased minimum variance criteria in order to obtain the optimal estimation process,it can be applied to multi-input,multiple output of non-stationary random process.Through a given measurement of the number of column values to get the estimated state vector,estimated by the prediction,prediction error covariance matrix,the best gain,the filter is estimated that filtering error covariance matrix and the composition of the best initial value. Measurement data obtained after the first data on its pre-processing to a certain extent,reduce the data noise,remove the outlier points.Then at the end of the right to select the number of data points for fitting.At fitting process,generally taking many second-order fitting,fitting because the order of First,excessive,volatile curve,there will be ups and downs of unnecessary so that the lower accuracy;two are at the time only by Kalman prediction to fit within the second-order recursive data.By the nature of Kalman filter,we can see that it can effectively reduce the impact of noise.In addition,at sufficiently long time after iteration,the impact of incorrect initial value will gradually disappear,the best filter will converge to the status,therefore,in reality,when many of enough data points after filtering,Kalman filtering,after The value will be close to true value.5.Kalman filter at yakeshi - Lindian profile applicationYakeshi - Lindian geophysical profiles across the Inner Mongolia Autonomous Region,after Heilongjiang Province,near to the North West.Northwest began in Yakeshi City of Inner Mongolia,and then to the southeast all the way through the avoidance of crossing Ukrainian slave ears.boqueron map Zalantun,Longjiang, Fulaerji,Qiqihar,such as cities and towns until the end of Heilongjiang Lindian total length of 540km.From the Bouguer gravity anomaly profile shows that low-value Daxinganling region against the backdrop of large negative anomalies,and both sides of the Hailar Basin and Songliao Basin is a small negative anomalies.First of all,the use of Kalman filter for denoising of abnormal treatment,then the profile of the Bouguer anomaly separation by yakeshi - Lindian profile regional market and local market.As can be seen isolated from the regional anomaly field in the local field of residual small,isolated completely in line with the Bouguer gravity anomaly shown by the regional anomaly characteristics,and its apparent characteristics of the basin basement structure:local anomaly field noise is basically was removed,reflecting the ups and downs of local basins and surface density of non-uniform characteristics of local structures in the area are carried out to explain the basis for fine.