A typical electronic communication system, such as GPS receiver, unmanned aerial vehicle's (UAV's) data link, and radar, faces multi-dimensional and complicated electromagnetic interference in operating environmen...A typical electronic communication system, such as GPS receiver, unmanned aerial vehicle's (UAV's) data link, and radar, faces multi-dimensional and complicated electromagnetic interference in operating environment. To measure the anti- interference performance of the electronic communication system in the complicated electromagnetic interference environment, a method of multi-dimensional and complicated electromagnetic interference hardware-in-the-loop simulation in an anechoic room is proposed. It takes into account the characteristics of interference signals and the positional relationship among interference, the receiver and the transmitter of the electronic communication system. It uses the grey relational method and the angular domain mapping error correction method to control the relevant parameters, the microwave switch and so on, thus achieving the approximately actual mapping of the outdoor multi-dimensional and complicated electromagnetic interference in the anechoic room. To verify the effectiveness of this method, the multi-dimensional and complicated electromagnetic interference of the UAV's data link is simulated as an example. The results show that the degree of correlation between the calculated signal to interference ratio of the data link receiver in the actual scene and the measured signal to interference ratio of the data link receiver simulated with this method in the anechoic room is 0.968 1, proving that the method is effective for simulating the complicated electromagnetic interference.展开更多
In order to study the distribution of shale gas reservoir in the Babaoshan Basin of Eastern Kunlun,the wide-field electromagnetic(WFEM)survey was carried out to obtain the spatial distribution characteristics of the u...In order to study the distribution of shale gas reservoir in the Babaoshan Basin of Eastern Kunlun,the wide-field electromagnetic(WFEM)survey was carried out to obtain the spatial distribution characteristics of the underground electrical volume resistivity based on the delineation of the scope of the Babaoshan Basin by regional gravity data.The basic characteristics of the basement,basin framework,and extension,vertical change,burial depth of dark mud shale in this area were identified,and the electrical distribution of the Babaoshan mud shale horizon was revealed,which has been proved to be a good geological effect by drilling.The exploration results show that the WFEM has significant effects on the exploration of shale gas occurrence strata,which meets the needs of investigation and evaluation of multi-layered and large-scale shale gas,and plays a good demonstration role in the follow-up shale gas exploration.展开更多
In large loop transient electromagnetic method(TEM),the late time apparent resistivity formula cannot truly reflect the geoelectric model,thus it needs to define the all-time apparent resistivity with the position inf...In large loop transient electromagnetic method(TEM),the late time apparent resistivity formula cannot truly reflect the geoelectric model,thus it needs to define the all-time apparent resistivity with the position information of measuring point.Utilizing very fast simulated annealing(VFSA) to fit the theoretical electromagnetic force(EMF) and measured EMF could obtain the all-time apparent resistivity of the measuring points in rectangular transmitting loop.The selective cope of initial model of VFSA could be confirmed by taking the late time apparent resistivity of transient electromagnetic method as the prior information.For verifying the correctness,the all-time apparent resistivities of the geoelectric models were calculated by VFSA and dichotomy,respectively.The results indicate that the relative differences of apparent resistivities calculated by these two methods are within 3%.The change of measuring point position has little influence on the tracing pattern of all-time apparent resistivity.The first branch of the curve of all-time apparent resistivity is close to the resistivity of the first layer medium and the last branch is close to the resistivity of the last layer medium,which proves the correctness of the arithmetics proposed.展开更多
The electromagnetic detection satellite (EDS) is a type of earth observation satellites (EOSs). The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The...The electromagnetic detection satellite (EDS) is a type of earth observation satellites (EOSs). The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The scheduling of EDSs is a complex combinatorial optimization problem. Current research mainly focuses on the scheduling of imaging satellites and SAR satellites, but little work has been done on the scheduling of EDSs for its specific characteristics. A multi-satellite scheduling model is established, in which the specific constrains of EDSs are considered, then a scheduling algorithm based on the genetic algorithm (GA) is proposed. To deal with the specific constrains of EDSs, a penalty function method is introduced. However, it is hard to determine the appropriate penalty coefficient in the penalty function. Therefore, an adaptive adjustment mechanism of the penalty coefficient is designed to solve the problem, as well as improve the scheduling results. Experimental results are used to demonstrate the correctness and practicability of the proposed scheduling algorithm.展开更多
The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, th...The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.展开更多
In this paper,a linear optimization method(LOM)for the design of terahertz circuits is presented,aimed at enhancing the simulation efficacy and reducing the time of the circuit design workflow.This method enables the ...In this paper,a linear optimization method(LOM)for the design of terahertz circuits is presented,aimed at enhancing the simulation efficacy and reducing the time of the circuit design workflow.This method enables the rapid determination of optimal embedding impedance for diodes across a specific bandwidth to achieve maximum efficiency through harmonic balance simulations.By optimizing the linear matching circuit with the optimal embedding impedance,the method effectively segregates the simulation of the linear segments from the nonlinear segments in the frequency multiplier circuit,substantially improving the speed of simulations.The design of on-chip linear matching circuits adopts a modular circuit design strategy,incorporating fixed load resistors to simplify the matching challenge.Utilizing this approach,a 340 GHz frequency doubler was developed and measured.The results demonstrate that,across a bandwidth of 330 GHz to 342 GHz,the efficiency of the doubler remains above 10%,with an input power ranging from 98 mW to 141mW and an output power exceeding 13 mW.Notably,at an input power of 141 mW,a peak output power of 21.8 mW was achieved at 334 GHz,corresponding to an efficiency of 15.8%.展开更多
Facing the problems lack of considering the non-uniform distribution of the static bias magnetic field and computing the panicle displacements in the simulation model of electromagnetic acoustic transducer (EMAT), a...Facing the problems lack of considering the non-uniform distribution of the static bias magnetic field and computing the panicle displacements in the simulation model of electromagnetic acoustic transducer (EMAT), a multi-field coupled model was established and the finite element method (FEM) was presented to calculate the entire transduction process. The multi-field coupled model included the static magnetic field, pulsed eddy current field and mechanical field. The FEM equations of the three fields were derived by Garlerkin FEM method. Thus, the entire transduction process of the EMAT was calculated through sequentially coupling the three fields. The transduction process of a Lamb wave EMAT was calculated according to the present model and method. The results show that, by the present method, it is valid to calculate the particle displacement under the given excitation signal and non-uniformly distributed static magnetic field. Calculation error will be brought about if the non-uniform distribution of the static bias magnetic field is neglected.展开更多
Airborne electromagnetic transient method enjoys the advantages of high-efficiency and the high resolution of electromagnetic anomalies,especially suitable for mining detection around goaf areas and deep exploration o...Airborne electromagnetic transient method enjoys the advantages of high-efficiency and the high resolution of electromagnetic anomalies,especially suitable for mining detection around goaf areas and deep exploration of minerals.In this paper,we calculated the full-wave airborne transient electromagnetic data,according to the result of numerical research,the advantage of switch-off time response in electromagnetic detection was proofed via experiments.Firstly,based on the full-wave airborne transient electromagnetic system developed by Jilin University(JLU-ATEMI),we proposed a method to compute the full-waveform electromagnetic(EM)data of 3D model using the FDTD approach and convolution algorithm,and verify the calculation by the response of homogenous half-space.Then,through comparison of switch-off-time response and off-time response,we studied the effect of ramp time on anomaly detection.Finally,we arranged two experimental electromagnetic detection,the results indicated that the switch-off-time response can reveal the shallow target more effectively,and the full-waveform airborne electromagnetic system is an effective technique for shallow target detection.展开更多
The wide-field electromagnetic method is widely used in hydrocarbon exploration,mineral deposit detection,and geological disaster prediction.However,apparent resistivity and normalized field amplitude exceeding 2048 H...The wide-field electromagnetic method is widely used in hydrocarbon exploration,mineral deposit detection,and geological disaster prediction.However,apparent resistivity and normalized field amplitude exceeding 2048 Hz often exhibit upward warping in data,making geophysical inversion and interpretation challenging.The cumulative error of the crystal oscillator in signal transmission and acquisition contributes to an upturned apparent resistivity curve.To address this,a high-frequency information extraction method is proposed based on time-domain signal reconstruction,which helps to record a complete current data sequence;moreover,it helps estimate the crystal oscillator error for the transmitted signal.Considering the recorded error,a received signal was corrected using a set of reconstruction algorithms.After processing,the high-frequency component of the wide-field electromagnetic data was not upturned,while accurate high-frequency information was extracted from the signal.Therefore,the proposed method helped effectively extract high-frequency components of all wide-field electromagnetic data.展开更多
In this paper, propagated δ pulses through different distance of plasma are calculated,and their time-frequency characteristics are studied using CWD (Choi-William distribution). It is found that several horizontal s...In this paper, propagated δ pulses through different distance of plasma are calculated,and their time-frequency characteristics are studied using CWD (Choi-William distribution). It is found that several horizontal spectra appear at early arrival time like discrete spectrum, at last time a hyperbolic curve lies in the time-frequency spectrum which corresponds to the frequency-group delay curve of plasma. To understand the time-frequency the property of a signal is helpful for obtaining the plasma parameters.展开更多
An efficient and real-time simulation method is proposed for the dynamic electromagnetic characteristics of cluster targets to meet the requirements of engineering practical applications.First,the coordinate transform...An efficient and real-time simulation method is proposed for the dynamic electromagnetic characteristics of cluster targets to meet the requirements of engineering practical applications.First,the coordinate transformation method is used to establish a geometric model of the observation scene,which is described by the azimuth angles and elevation angles of the radar in the target reference frame and the attitude angles of the target in the radar reference frame.Then,an approach for dynamic electromagnetic scattering simulation is proposed.Finally,a fast-computing method based on sparsity in the time domain,space domain,and frequency domain is proposed.The method analyzes the sparsity-based dynamic scattering characteristic of the typical cluster targets.The error between the sparsity-based method and the benchmark is small,proving the effectiveness of the proposed method.展开更多
As a new-style stochastic algorithm, the electromagnetism-like mechanism(EM) method gains more and more attention from many researchers in recent years. A novel model based on EM(NMEM) for multiobjective optimizat...As a new-style stochastic algorithm, the electromagnetism-like mechanism(EM) method gains more and more attention from many researchers in recent years. A novel model based on EM(NMEM) for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.展开更多
Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density (TCD). Formulations II and {I1 are based on inc...Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density (TCD). Formulations II and {I1 are based on incomplete and complete equations for source current density (SCD), respectively. Using the weak form of finite element method (FEM), three formulations were applied in a spiral coil electromagnetic acoustic transducer (EMAT) example to solve magnetic vector potential (MVP). The input impedances calculated by Formulation III are in excellent agreement with the experimental measurements. Results show that the errors for Formulations I & II vary with coil diameter, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin & proximity effects. And the current distribution across the coil conductor also follows the same trend. It is better to choose Formulation I instead of Formulation Ili to solve MVP when the coil diameter is less than twice the skin depth for Formulation I is a low cost and high efficiency calculation method.展开更多
Numerical calculation for two integral transforms in 2.5-D transient electromagnetic forward is a difficult and key task, namely, the inverse Fourier transform and the inverse Laplace transform. Some effective algorit...Numerical calculation for two integral transforms in 2.5-D transient electromagnetic forward is a difficult and key task, namely, the inverse Fourier transform and the inverse Laplace transform. Some effective algorithms for them were described. Based on the known algorithms in DC resistivity on wave-number distribution and selection, we proposed a principle on how to choose the least wave-number concerning the central-loop transient electromagnetic method. First, observe the behavior of transformation function curve with regard to wave-number in Fourier domain. In the light of its asymptote, ascertain the coverage scope of wave-number. Compared with analytic solution, the least wave-number in Fourier domain can be derived. Furthermore, the Laplace numerical inversion algorithm which needs only a few Laplace variables in pure real domain was also introduced here. The procedure was applied to forward modeling on transient electromagnetic field of a vertical magnetic dipole over uniform half-space to demonstrate them effectiveness and general applicability.展开更多
基金supported by the National Natural Science Foundation of China(61571368)the certain Ministry Foundation(2014607B006)
文摘A typical electronic communication system, such as GPS receiver, unmanned aerial vehicle's (UAV's) data link, and radar, faces multi-dimensional and complicated electromagnetic interference in operating environment. To measure the anti- interference performance of the electronic communication system in the complicated electromagnetic interference environment, a method of multi-dimensional and complicated electromagnetic interference hardware-in-the-loop simulation in an anechoic room is proposed. It takes into account the characteristics of interference signals and the positional relationship among interference, the receiver and the transmitter of the electronic communication system. It uses the grey relational method and the angular domain mapping error correction method to control the relevant parameters, the microwave switch and so on, thus achieving the approximately actual mapping of the outdoor multi-dimensional and complicated electromagnetic interference in the anechoic room. To verify the effectiveness of this method, the multi-dimensional and complicated electromagnetic interference of the UAV's data link is simulated as an example. The results show that the degree of correlation between the calculated signal to interference ratio of the data link receiver in the actual scene and the measured signal to interference ratio of the data link receiver simulated with this method in the anechoic room is 0.968 1, proving that the method is effective for simulating the complicated electromagnetic interference.
基金Project(2019-SF-141)supported by Science and Technology Program of Qinghai Province,ChinaProjects(2017042105kc055,2017042014ky014)supported by Geological Exploration Foundation of Qinghai Province,China。
文摘In order to study the distribution of shale gas reservoir in the Babaoshan Basin of Eastern Kunlun,the wide-field electromagnetic(WFEM)survey was carried out to obtain the spatial distribution characteristics of the underground electrical volume resistivity based on the delineation of the scope of the Babaoshan Basin by regional gravity data.The basic characteristics of the basement,basin framework,and extension,vertical change,burial depth of dark mud shale in this area were identified,and the electrical distribution of the Babaoshan mud shale horizon was revealed,which has been proved to be a good geological effect by drilling.The exploration results show that the WFEM has significant effects on the exploration of shale gas occurrence strata,which meets the needs of investigation and evaluation of multi-layered and large-scale shale gas,and plays a good demonstration role in the follow-up shale gas exploration.
基金Projects(40804027,41074085) supported by the National Natural Science Foundation of ChinaProject(09JJ3048) supported by the Natural Science Foundation of Hunan Province,ChinaProject(200805331082) supported by the Research Fund for the Doctoral Program of Higher Education,China
文摘In large loop transient electromagnetic method(TEM),the late time apparent resistivity formula cannot truly reflect the geoelectric model,thus it needs to define the all-time apparent resistivity with the position information of measuring point.Utilizing very fast simulated annealing(VFSA) to fit the theoretical electromagnetic force(EMF) and measured EMF could obtain the all-time apparent resistivity of the measuring points in rectangular transmitting loop.The selective cope of initial model of VFSA could be confirmed by taking the late time apparent resistivity of transient electromagnetic method as the prior information.For verifying the correctness,the all-time apparent resistivities of the geoelectric models were calculated by VFSA and dichotomy,respectively.The results indicate that the relative differences of apparent resistivities calculated by these two methods are within 3%.The change of measuring point position has little influence on the tracing pattern of all-time apparent resistivity.The first branch of the curve of all-time apparent resistivity is close to the resistivity of the first layer medium and the last branch is close to the resistivity of the last layer medium,which proves the correctness of the arithmetics proposed.
基金supported by the National Natural Science Foundation of China(6110118461174159)
文摘The electromagnetic detection satellite (EDS) is a type of earth observation satellites (EOSs). The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The scheduling of EDSs is a complex combinatorial optimization problem. Current research mainly focuses on the scheduling of imaging satellites and SAR satellites, but little work has been done on the scheduling of EDSs for its specific characteristics. A multi-satellite scheduling model is established, in which the specific constrains of EDSs are considered, then a scheduling algorithm based on the genetic algorithm (GA) is proposed. To deal with the specific constrains of EDSs, a penalty function method is introduced. However, it is hard to determine the appropriate penalty coefficient in the penalty function. Therefore, an adaptive adjustment mechanism of the penalty coefficient is designed to solve the problem, as well as improve the scheduling results. Experimental results are used to demonstrate the correctness and practicability of the proposed scheduling algorithm.
文摘The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.
基金Supported by the Beijing Municipal Science&Technology Commission(Z211100004421012),the Key Reaserch and Development Pro⁃gram of China(2022YFF0605902)。
文摘In this paper,a linear optimization method(LOM)for the design of terahertz circuits is presented,aimed at enhancing the simulation efficacy and reducing the time of the circuit design workflow.This method enables the rapid determination of optimal embedding impedance for diodes across a specific bandwidth to achieve maximum efficiency through harmonic balance simulations.By optimizing the linear matching circuit with the optimal embedding impedance,the method effectively segregates the simulation of the linear segments from the nonlinear segments in the frequency multiplier circuit,substantially improving the speed of simulations.The design of on-chip linear matching circuits adopts a modular circuit design strategy,incorporating fixed load resistors to simplify the matching challenge.Utilizing this approach,a 340 GHz frequency doubler was developed and measured.The results demonstrate that,across a bandwidth of 330 GHz to 342 GHz,the efficiency of the doubler remains above 10%,with an input power ranging from 98 mW to 141mW and an output power exceeding 13 mW.Notably,at an input power of 141 mW,a peak output power of 21.8 mW was achieved at 334 GHz,corresponding to an efficiency of 15.8%.
基金Project(10974115) supported by the National Natural Science Foundation of China
文摘Facing the problems lack of considering the non-uniform distribution of the static bias magnetic field and computing the panicle displacements in the simulation model of electromagnetic acoustic transducer (EMAT), a multi-field coupled model was established and the finite element method (FEM) was presented to calculate the entire transduction process. The multi-field coupled model included the static magnetic field, pulsed eddy current field and mechanical field. The FEM equations of the three fields were derived by Garlerkin FEM method. Thus, the entire transduction process of the EMAT was calculated through sequentially coupling the three fields. The transduction process of a Lamb wave EMAT was calculated according to the present model and method. The results show that, by the present method, it is valid to calculate the particle displacement under the given excitation signal and non-uniformly distributed static magnetic field. Calculation error will be brought about if the non-uniform distribution of the static bias magnetic field is neglected.
基金Project(41674109) supported by the National Natural Science Foundation of China
文摘Airborne electromagnetic transient method enjoys the advantages of high-efficiency and the high resolution of electromagnetic anomalies,especially suitable for mining detection around goaf areas and deep exploration of minerals.In this paper,we calculated the full-wave airborne transient electromagnetic data,according to the result of numerical research,the advantage of switch-off time response in electromagnetic detection was proofed via experiments.Firstly,based on the full-wave airborne transient electromagnetic system developed by Jilin University(JLU-ATEMI),we proposed a method to compute the full-waveform electromagnetic(EM)data of 3D model using the FDTD approach and convolution algorithm,and verify the calculation by the response of homogenous half-space.Then,through comparison of switch-off-time response and off-time response,we studied the effect of ramp time on anomaly detection.Finally,we arranged two experimental electromagnetic detection,the results indicated that the switch-off-time response can reveal the shallow target more effectively,and the full-waveform airborne electromagnetic system is an effective technique for shallow target detection.
基金Project(42004056)supported by the National Natural Science Foundation of ChinaProject(ZR2020QD052)supported by the Natural Science Foundation of Shandong Province,ChinaProject(2019YFC0604902)supported by the National Key Research and Development Program of China。
文摘The wide-field electromagnetic method is widely used in hydrocarbon exploration,mineral deposit detection,and geological disaster prediction.However,apparent resistivity and normalized field amplitude exceeding 2048 Hz often exhibit upward warping in data,making geophysical inversion and interpretation challenging.The cumulative error of the crystal oscillator in signal transmission and acquisition contributes to an upturned apparent resistivity curve.To address this,a high-frequency information extraction method is proposed based on time-domain signal reconstruction,which helps to record a complete current data sequence;moreover,it helps estimate the crystal oscillator error for the transmitted signal.Considering the recorded error,a received signal was corrected using a set of reconstruction algorithms.After processing,the high-frequency component of the wide-field electromagnetic data was not upturned,while accurate high-frequency information was extracted from the signal.Therefore,the proposed method helped effectively extract high-frequency components of all wide-field electromagnetic data.
文摘In this paper, propagated δ pulses through different distance of plasma are calculated,and their time-frequency characteristics are studied using CWD (Choi-William distribution). It is found that several horizontal spectra appear at early arrival time like discrete spectrum, at last time a hyperbolic curve lies in the time-frequency spectrum which corresponds to the frequency-group delay curve of plasma. To understand the time-frequency the property of a signal is helpful for obtaining the plasma parameters.
文摘An efficient and real-time simulation method is proposed for the dynamic electromagnetic characteristics of cluster targets to meet the requirements of engineering practical applications.First,the coordinate transformation method is used to establish a geometric model of the observation scene,which is described by the azimuth angles and elevation angles of the radar in the target reference frame and the attitude angles of the target in the radar reference frame.Then,an approach for dynamic electromagnetic scattering simulation is proposed.Finally,a fast-computing method based on sparsity in the time domain,space domain,and frequency domain is proposed.The method analyzes the sparsity-based dynamic scattering characteristic of the typical cluster targets.The error between the sparsity-based method and the benchmark is small,proving the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(60873099)the Fundamental Research Funds for the Central Universities(2011QNA29)
文摘As a new-style stochastic algorithm, the electromagnetism-like mechanism(EM) method gains more and more attention from many researchers in recent years. A novel model based on EM(NMEM) for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.
基金Project(2014BAF12B01)supported by the Key Projects in the National Science&Technology Pillar Program during the Twelfth Five-year Plan Period,ChinaProject(51405520)supported by the National Natural Science Foundation of ChinaProject(2012CB619505)supported by National Basic Research Program of China
文摘Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density (TCD). Formulations II and {I1 are based on incomplete and complete equations for source current density (SCD), respectively. Using the weak form of finite element method (FEM), three formulations were applied in a spiral coil electromagnetic acoustic transducer (EMAT) example to solve magnetic vector potential (MVP). The input impedances calculated by Formulation III are in excellent agreement with the experimental measurements. Results show that the errors for Formulations I & II vary with coil diameter, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin & proximity effects. And the current distribution across the coil conductor also follows the same trend. It is better to choose Formulation I instead of Formulation Ili to solve MVP when the coil diameter is less than twice the skin depth for Formulation I is a low cost and high efficiency calculation method.
基金Project(40344022) supported by the National Natural Science Foundation of China
文摘Numerical calculation for two integral transforms in 2.5-D transient electromagnetic forward is a difficult and key task, namely, the inverse Fourier transform and the inverse Laplace transform. Some effective algorithms for them were described. Based on the known algorithms in DC resistivity on wave-number distribution and selection, we proposed a principle on how to choose the least wave-number concerning the central-loop transient electromagnetic method. First, observe the behavior of transformation function curve with regard to wave-number in Fourier domain. In the light of its asymptote, ascertain the coverage scope of wave-number. Compared with analytic solution, the least wave-number in Fourier domain can be derived. Furthermore, the Laplace numerical inversion algorithm which needs only a few Laplace variables in pure real domain was also introduced here. The procedure was applied to forward modeling on transient electromagnetic field of a vertical magnetic dipole over uniform half-space to demonstrate them effectiveness and general applicability.