Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain...Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration （LSRTM） （also known as linearized refleetivity inversion） aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional （4D） seismic images compared to traditional RTM and Fourier finite difference （FFD） migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.展开更多
The problems involving periodic contacting surfaces have different practical applications. An inverse heat conductionproblem for estimating the periodic Thermal Contact Conductance (TCC) between one-dimensional, const...The problems involving periodic contacting surfaces have different practical applications. An inverse heat conductionproblem for estimating the periodic Thermal Contact Conductance (TCC) between one-dimensional, constantproperty contacting solids has been investigated with conjugate gradient method (CGM) of function estimation.This method converges very rapidly and is not so sensitive to the measurement errors. The advantage of thepresent method is that no a priori information is needed on the variation of the unknown quantities, since the solutionautomatically determines the functional form over the specified domain. A simple, straight forward techniqueis utilized to solve the direct, sensitivity and adjoint problems, in order to overcome the difficulties associatedwith numerical methods. Two general classes of results, the results obtained by applying inexact simulatedmeasured data and the results obtained by using data taken from an actual experiment are presented. In addition,extrapolation method is applied to obtain actual results. Generally, the present method effectively improves theexact TCC when exact and inexact simulated measurements input to the analysis. Furthermore, the results obtainedwith CGM and the extrapolation results are in agreement and the little deviations can be negligible.展开更多
This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of sec...This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.展开更多
基金sponsored by The National Natural Science Fund(No.41574098)Sinopec Geophysical Key Laboratory Open Fund(No.wtyjy-wx2016-04-2)
文摘Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration （LSRTM） （also known as linearized refleetivity inversion） aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional （4D） seismic images compared to traditional RTM and Fourier finite difference （FFD） migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.
文摘The problems involving periodic contacting surfaces have different practical applications. An inverse heat conductionproblem for estimating the periodic Thermal Contact Conductance (TCC) between one-dimensional, constantproperty contacting solids has been investigated with conjugate gradient method (CGM) of function estimation.This method converges very rapidly and is not so sensitive to the measurement errors. The advantage of thepresent method is that no a priori information is needed on the variation of the unknown quantities, since the solutionautomatically determines the functional form over the specified domain. A simple, straight forward techniqueis utilized to solve the direct, sensitivity and adjoint problems, in order to overcome the difficulties associatedwith numerical methods. Two general classes of results, the results obtained by applying inexact simulatedmeasured data and the results obtained by using data taken from an actual experiment are presented. In addition,extrapolation method is applied to obtain actual results. Generally, the present method effectively improves theexact TCC when exact and inexact simulated measurements input to the analysis. Furthermore, the results obtainedwith CGM and the extrapolation results are in agreement and the little deviations can be negligible.
基金Project supported by the 973 Program of STM, MCME, RFDP, PMC Key Lab of EM of China S. S. Chern Foundation, CEC of Tianjin, and Nankai University.
文摘This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.
