Magnetic anomalies are often disturbed by the magnetization direction, so we can＇t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insen...Magnetic anomalies are often disturbed by the magnetization direction, so we can＇t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index （expressing the geometry） by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.展开更多
We propose a new automatic method for the interpretation of potential fi eld data, called the RDAS–Euler method, which is based on Euler＇s deconvolution and analytic signal methods. The proposed method can estimate ...We propose a new automatic method for the interpretation of potential fi eld data, called the RDAS–Euler method, which is based on Euler＇s deconvolution and analytic signal methods. The proposed method can estimate the horizontal and vertical extent of geophysical anomalies without prior information of the nature of the anomalies（structural index）. It also avoids inversion errors because of the erroneous choice of the structural index N in the conventional Euler deconvolution method. The method was tested using model gravity anomalies. In all cases, the misfi t between theoretical values and inversion results is less than 10%. Relative to the conventional Euler deconvolution method, the RDAS–Euler method produces inversion results that are more stable and accurate. Finally, we demonstrate the practicability of the method by applying it to Hulin Basin in Heilongjiang province, where the proposed method produced more accurate data regarding the distribution of faults.展开更多
Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the mag...Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the magnetic gradient tensor is not easily interfered from the tilting magnetization,but it can infer the range of the fi eld source more accurately.However,the analytic signal strength decays faster with depth,making it diffi cult to identify deep fi eld sources.Balanced-boundary recognition can eff ectively overcome this disadvantage.We present here a balanced-boundary identifi cation technique based on the normalization of three-directional analytic signals from aeromagnetic gradient tensor data.This method can eff ectively prevent the fast attenuation of analytic signals.We also derive an Euler inversion algorithm of three-directional analytic signal derivative.By combining magnetic-anomaly model testing with the traditional magnetic anomaly interpretation method,we show that the boundary-recognition technology based on a magnetic gradient tensor analytic signal has a greater advantage in identifying the boundaries of the geological body and can better refl ect shallow anomalies.The characteristics of the Euler equation based on the magnetic anomaly direction to resolve the signal derivative have better convergence,and the obtained solution is more concentrated,which can obtain the depth and horizontal range information of the geological body more accurately.Applying the above method to the measured magneticanomaly gradient data from Baoding area,more accurate fi eld source information is obtained,which shows the feasibility of applying this method to geological interpretations.展开更多
The aim of this study is to characterize the subsoil in the southern region of the North-Kivu province (DR Congo). Gravity and geomagnetic data were used in this study. Five different filters—the horizontal gradient ...The aim of this study is to characterize the subsoil in the southern region of the North-Kivu province (DR Congo). Gravity and geomagnetic data were used in this study. Five different filters—the horizontal gradient magnitude, the analytic signal, the tilt derivative, the horizontal derivative of tilt derivative and the tilt angle of horizontal gradient—enabled us to delineate the gravity and magnetic anomaly sources present in the shallow subsurface of the study area. The plains of the Rutshuru territory are dominated by sources of weak gravity anomalies and sources of very weak magnetic anomalies located almost in the same places. The southern part of Rutshuru territory and a large part of Masisi territory are underlain by shallow sources of high gravity and magnetic anomalies. Gravity and magnetic anomaly sources are almost identical in the study area. The shallow sources of gravity and magnetic anomalies encountered in our study area are more or less linear and connected. The numerous gravity and magnetic lineaments present in our study region have three major directions: oriented East-West, North-South and North-East-South-West.展开更多
High-resolution airborne-magnetic data acquired over the Yola extension of the northern Benue Trough,northeastern Nigeria,were analyzed to delineate rock distribution,define basement geometry,determine sedimentary thi...High-resolution airborne-magnetic data acquired over the Yola extension of the northern Benue Trough,northeastern Nigeria,were analyzed to delineate rock distribution,define basement geometry,determine sedimentary thicknesses,and highlight structural framework among others for the hydrocarbon prospect evaluation of sub-basins in the extension.Filtered and refined magnetic intensity data were subjected to Analytic Signal,Horizontal and Vertical Tilt Derivatives and Euler deconvolution depth weighting analyses to enhance various geological features requisite for petroleum prospect evaluation.Sedimentary rock units flanked the northeast and south widely occur in the central part with volcanic rock intrusions delineated within the sedimentary terrain.Extracted lineaments(less than 5 km and up to 45 km)were observed to dominantly follow the established Benue Trough and Yola sub-basin evolutionary trend along the NEeSW and ESEeWNW directions,respectively.Three prominent subbasins with sedimentary thicknesses in excess of 3 km and width of more than 60 km,separated by basement highs of mostly volcanic intrusions origin,were identified.The occurrence of relatively thick and extensive sub-basins which are underlain by structurally active basement rocks suggests relatively high geothermal gradient for generation of hydrocarbon from organic matter rich source rocks while the generated oil and gas are preserved within intra-sedimentary structural traps created when the basement fractures were reactivated.展开更多
The area covered by this study is the county of Kakobola and its surroundings. Previous studies show that those related to the study of depths by the gravity method, using other techniques, are not always carried out ...The area covered by this study is the county of Kakobola and its surroundings. Previous studies show that those related to the study of depths by the gravity method, using other techniques, are not always carried out until now. The main goal of this article is the gravimetric characterization of our area by other approach. The interest is not only to map the lineaments and to know their dip, but also to estimate the depths of these different anomalies. The methods used for this study are the first total horizontal derivative (FTHDT), tilt angle (TA), analytical signal (AS) and horizontal gradient magnitude (HGM). The processing of the complete Bouguer anomalies (CBA) data was done mainly through software. Data analysis using the semi-finished body depth method shows depths ranging from 7.49 m to 224.6 m. Data analysis using the AS method shows values ranging from 41.7 mGal/m to 510 mGal/m. The fractures and/or geological contacts in our study area show dips ranging from -73.73° to 68.16° and North-South orientation according to the tilt angle method. The FTHDT shows several lineaments, a NE oriented fracture of Kakobola and low dip values which suggest a tabular structure of the subsurface in our study area. According to the HGM, the study area shows several preferential directions of fractures and/or geological contacts whose the most frequent directions are the NNE-SSW and WNW.展开更多
Magnetic survey is one of the most successful techniques for locating buried unexploded ordnances( UXO). For the location and identification of buried UXO in Jinshan area,a total-field magnetic survey is applied. The ...Magnetic survey is one of the most successful techniques for locating buried unexploded ordnances( UXO). For the location and identification of buried UXO in Jinshan area,a total-field magnetic survey is applied. The analytic signal of magnetic field is widely used to outline the boundaries of geology bodies,slightly dependent on the magnetization direction. In order to locate the UXO position,the analytic signal is applied to process the magnetic UXO data,which performs better than the conventional magnetic data. Then a typical UXO anomaly is extracted from the original data to invert for its depth by an improved Euler method proposed.The calculated depth is close to the real buried depth.展开更多
This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selec...This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.展开更多
One of the measurement geophysical methods to investigate kimberlite pipes is by using the magnetic method. The acquired field data in this study uses <span style="font-family:Verdana;">two proton-prec...One of the measurement geophysical methods to investigate kimberlite pipes is by using the magnetic method. The acquired field data in this study uses <span style="font-family:Verdana;">two proton-precession magnetometers for the mapping of magnetic anomalies</span><span style="font-family:Verdana;"> due to kimberlites. Three different magnetic maps are obtained from the result of total magnetic field data processing on Oásis Montaj software programme. These maps include magnetic anomaly maps through statistical analyses, total magnetic field intensity map and map of the analytic signal. Based on the interpretation of these maps a structure is identified with SWW-NEE directions in which magnetic signatures that indicate the presence of kimberlite pipes are observed. As the interpretation of the magnetic anomalies is a complicated process due to their dipolar nature, the analytic signal is generated, where is possible to observe the typical shape of these anomalies.</span>展开更多
A dissolution method with robust high performance liquid chromatographic （HPLC） analysis for im- mediate release tablet formulation was developed and validated to meet the requirement as per Inter- national Conferen...A dissolution method with robust high performance liquid chromatographic （HPLC） analysis for im- mediate release tablet formulation was developed and validated to meet the requirement as per Inter- national Conference on Harmonization （ICH） and United States Food and Drug Administration （USFDA） guidelines. The method involved the use of Agilent ZORBAX Eclipse XDB C18 column, and temperature was maintained at 30 ℃. After optimization, the mobile phase was selected as phosphate buffer （KH2PO4, 30 mM） ： ACN （60：40, v/v） with pH 3.0, and retention time Rt was found as 3.24, 4.16, and 2.55 min for paracetamol （PCM）, chlorpheniramine maleate （CPM） and phenylephrine hydrochloride （PH） respec- tively at 265 nm and at a flow rate of 1 mL/min. The relative standard deviation （%RSD） for 6 replicate measurements was found to be less than 2%. Furthermore net analyte signal standard addition method （NASSAM） with spectrophotometer was performed for standard and liquid oral suspension. On the basis of selectivity, sensitivity and accuracy analysis, it was confirmed that this novel method could be useful for simultaneous estimation of the given drug combinations. Two-way analysis of variance （ANOVA） was applied for evaluating the statistical difference between the assay results obtained via both NASSAM and RP-HPLC methods and ultimately no significant difference was found between both the methods. All the methods and results were acceptable and confirmed that the method was suitable for intended use.展开更多
Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition,...Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and efficiently extracted out.展开更多
Gravity anomalies illuminate subsurface lithology and geological structure in three dimensions,which is vital for studies of concealed faults,sedimentary basins,basement lithology,and other geological targets.Although...Gravity anomalies illuminate subsurface lithology and geological structure in three dimensions,which is vital for studies of concealed faults,sedimentary basins,basement lithology,and other geological targets.Although not all geological contacts correspond to lithological contacts,the contact mapping provides key information on structural regimes,deformation styles and trends.Many techniques for contact mapping have been developed.Here,we evaluate five methods applied to gridded data.The first two are the horizontal gradient magnitude of the gravity field （GFhgm）,and tilt （TIhgm）.The third and fourth rely on locating maxima of the analytic signal （AS） and the 3D local wavenumber （LW）.The fifth is normalized standard deviation （NSTD） method.In this article,we evaluate the use of these five methods for mapping contacts and compare the results.First,synthetic vertically-sided models are used to quantify the offsets of maxima from the true contact location due to the source effects of finite source thickness,central depth,and width.Second,the effects of contact dip are discussed.Finally,a real data set is used to evaluate the ability of each method to produce maps of coherent contact trends in the presence of noise and gridding artifacts.展开更多
基金supported by the Special Investigation and Assessment of Geological Mineral Resources of the China Geological Survey(No.GZH003-07-03)
文摘Magnetic anomalies are often disturbed by the magnetization direction, so we can＇t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index （expressing the geometry） by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.
基金supported by the National High Technology Research and Development Program of China(No.2006AA06A208)
文摘We propose a new automatic method for the interpretation of potential fi eld data, called the RDAS–Euler method, which is based on Euler＇s deconvolution and analytic signal methods. The proposed method can estimate the horizontal and vertical extent of geophysical anomalies without prior information of the nature of the anomalies（structural index）. It also avoids inversion errors because of the erroneous choice of the structural index N in the conventional Euler deconvolution method. The method was tested using model gravity anomalies. In all cases, the misfi t between theoretical values and inversion results is less than 10%. Relative to the conventional Euler deconvolution method, the RDAS–Euler method produces inversion results that are more stable and accurate. Finally, we demonstrate the practicability of the method by applying it to Hulin Basin in Heilongjiang province, where the proposed method produced more accurate data regarding the distribution of faults.
基金supported by the National Key R&D Program of China (No. 2017YFC0602204)。
文摘Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the magnetic gradient tensor is not easily interfered from the tilting magnetization,but it can infer the range of the fi eld source more accurately.However,the analytic signal strength decays faster with depth,making it diffi cult to identify deep fi eld sources.Balanced-boundary recognition can eff ectively overcome this disadvantage.We present here a balanced-boundary identifi cation technique based on the normalization of three-directional analytic signals from aeromagnetic gradient tensor data.This method can eff ectively prevent the fast attenuation of analytic signals.We also derive an Euler inversion algorithm of three-directional analytic signal derivative.By combining magnetic-anomaly model testing with the traditional magnetic anomaly interpretation method,we show that the boundary-recognition technology based on a magnetic gradient tensor analytic signal has a greater advantage in identifying the boundaries of the geological body and can better refl ect shallow anomalies.The characteristics of the Euler equation based on the magnetic anomaly direction to resolve the signal derivative have better convergence,and the obtained solution is more concentrated,which can obtain the depth and horizontal range information of the geological body more accurately.Applying the above method to the measured magneticanomaly gradient data from Baoding area,more accurate fi eld source information is obtained,which shows the feasibility of applying this method to geological interpretations.
文摘The aim of this study is to characterize the subsoil in the southern region of the North-Kivu province (DR Congo). Gravity and geomagnetic data were used in this study. Five different filters—the horizontal gradient magnitude, the analytic signal, the tilt derivative, the horizontal derivative of tilt derivative and the tilt angle of horizontal gradient—enabled us to delineate the gravity and magnetic anomaly sources present in the shallow subsurface of the study area. The plains of the Rutshuru territory are dominated by sources of weak gravity anomalies and sources of very weak magnetic anomalies located almost in the same places. The southern part of Rutshuru territory and a large part of Masisi territory are underlain by shallow sources of high gravity and magnetic anomalies. Gravity and magnetic anomaly sources are almost identical in the study area. The shallow sources of gravity and magnetic anomalies encountered in our study area are more or less linear and connected. The numerous gravity and magnetic lineaments present in our study region have three major directions: oriented East-West, North-South and North-East-South-West.
文摘High-resolution airborne-magnetic data acquired over the Yola extension of the northern Benue Trough,northeastern Nigeria,were analyzed to delineate rock distribution,define basement geometry,determine sedimentary thicknesses,and highlight structural framework among others for the hydrocarbon prospect evaluation of sub-basins in the extension.Filtered and refined magnetic intensity data were subjected to Analytic Signal,Horizontal and Vertical Tilt Derivatives and Euler deconvolution depth weighting analyses to enhance various geological features requisite for petroleum prospect evaluation.Sedimentary rock units flanked the northeast and south widely occur in the central part with volcanic rock intrusions delineated within the sedimentary terrain.Extracted lineaments(less than 5 km and up to 45 km)were observed to dominantly follow the established Benue Trough and Yola sub-basin evolutionary trend along the NEeSW and ESEeWNW directions,respectively.Three prominent subbasins with sedimentary thicknesses in excess of 3 km and width of more than 60 km,separated by basement highs of mostly volcanic intrusions origin,were identified.The occurrence of relatively thick and extensive sub-basins which are underlain by structurally active basement rocks suggests relatively high geothermal gradient for generation of hydrocarbon from organic matter rich source rocks while the generated oil and gas are preserved within intra-sedimentary structural traps created when the basement fractures were reactivated.
文摘The area covered by this study is the county of Kakobola and its surroundings. Previous studies show that those related to the study of depths by the gravity method, using other techniques, are not always carried out until now. The main goal of this article is the gravimetric characterization of our area by other approach. The interest is not only to map the lineaments and to know their dip, but also to estimate the depths of these different anomalies. The methods used for this study are the first total horizontal derivative (FTHDT), tilt angle (TA), analytical signal (AS) and horizontal gradient magnitude (HGM). The processing of the complete Bouguer anomalies (CBA) data was done mainly through software. Data analysis using the semi-finished body depth method shows depths ranging from 7.49 m to 224.6 m. Data analysis using the AS method shows values ranging from 41.7 mGal/m to 510 mGal/m. The fractures and/or geological contacts in our study area show dips ranging from -73.73° to 68.16° and North-South orientation according to the tilt angle method. The FTHDT shows several lineaments, a NE oriented fracture of Kakobola and low dip values which suggest a tabular structure of the subsurface in our study area. According to the HGM, the study area shows several preferential directions of fractures and/or geological contacts whose the most frequent directions are the NNE-SSW and WNW.
文摘Magnetic survey is one of the most successful techniques for locating buried unexploded ordnances( UXO). For the location and identification of buried UXO in Jinshan area,a total-field magnetic survey is applied. The analytic signal of magnetic field is widely used to outline the boundaries of geology bodies,slightly dependent on the magnetization direction. In order to locate the UXO position,the analytic signal is applied to process the magnetic UXO data,which performs better than the conventional magnetic data. Then a typical UXO anomaly is extracted from the original data to invert for its depth by an improved Euler method proposed.The calculated depth is close to the real buried depth.
基金supported in part by the Science and Technology Development Fund,Macao SAR FDCT/085/2018/A2the Guangdong Basic and Applied Basic Research Foundation(2019A1515111185)。
文摘This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.
文摘One of the measurement geophysical methods to investigate kimberlite pipes is by using the magnetic method. The acquired field data in this study uses <span style="font-family:Verdana;">two proton-precession magnetometers for the mapping of magnetic anomalies</span><span style="font-family:Verdana;"> due to kimberlites. Three different magnetic maps are obtained from the result of total magnetic field data processing on Oásis Montaj software programme. These maps include magnetic anomaly maps through statistical analyses, total magnetic field intensity map and map of the analytic signal. Based on the interpretation of these maps a structure is identified with SWW-NEE directions in which magnetic signatures that indicate the presence of kimberlite pipes are observed. As the interpretation of the magnetic anomalies is a complicated process due to their dipolar nature, the analytic signal is generated, where is possible to observe the typical shape of these anomalies.</span>
文摘A dissolution method with robust high performance liquid chromatographic （HPLC） analysis for im- mediate release tablet formulation was developed and validated to meet the requirement as per Inter- national Conference on Harmonization （ICH） and United States Food and Drug Administration （USFDA） guidelines. The method involved the use of Agilent ZORBAX Eclipse XDB C18 column, and temperature was maintained at 30 ℃. After optimization, the mobile phase was selected as phosphate buffer （KH2PO4, 30 mM） ： ACN （60：40, v/v） with pH 3.0, and retention time Rt was found as 3.24, 4.16, and 2.55 min for paracetamol （PCM）, chlorpheniramine maleate （CPM） and phenylephrine hydrochloride （PH） respec- tively at 265 nm and at a flow rate of 1 mL/min. The relative standard deviation （%RSD） for 6 replicate measurements was found to be less than 2%. Furthermore net analyte signal standard addition method （NASSAM） with spectrophotometer was performed for standard and liquid oral suspension. On the basis of selectivity, sensitivity and accuracy analysis, it was confirmed that this novel method could be useful for simultaneous estimation of the given drug combinations. Two-way analysis of variance （ANOVA） was applied for evaluating the statistical difference between the assay results obtained via both NASSAM and RP-HPLC methods and ultimately no significant difference was found between both the methods. All the methods and results were acceptable and confirmed that the method was suitable for intended use.
基金supported by Cultivation Program for Oustanding Young Teachers of Guangdong Province (Grant No. Yq2014060)Macao Science Technology Fund (Grant No. FDCT/099/ 2014/A2)
文摘Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and efficiently extracted out.
基金supported by the Ph.D. Program Foundation of Ministry of Education of China for Distinguished Young Scholars (No. 200804911523)the Research Foundation for Outstanding Young Teachers,China University of Geosciences (No. CUGQNL0726)
文摘Gravity anomalies illuminate subsurface lithology and geological structure in three dimensions,which is vital for studies of concealed faults,sedimentary basins,basement lithology,and other geological targets.Although not all geological contacts correspond to lithological contacts,the contact mapping provides key information on structural regimes,deformation styles and trends.Many techniques for contact mapping have been developed.Here,we evaluate five methods applied to gridded data.The first two are the horizontal gradient magnitude of the gravity field （GFhgm）,and tilt （TIhgm）.The third and fourth rely on locating maxima of the analytic signal （AS） and the 3D local wavenumber （LW）.The fifth is normalized standard deviation （NSTD） method.In this article,we evaluate the use of these five methods for mapping contacts and compare the results.First,synthetic vertically-sided models are used to quantify the offsets of maxima from the true contact location due to the source effects of finite source thickness,central depth,and width.Second,the effects of contact dip are discussed.Finally,a real data set is used to evaluate the ability of each method to produce maps of coherent contact trends in the presence of noise and gridding artifacts.
