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    • 4. 发明申请
    • Accelerating Full Wavefield Inversion with Nonstationary Point-Spread Functions
    • 用非稳态点扩散函数加速全波场反演
    • US20150073755A1
    • 2015-03-12
    • US14330767
    • 2014-07-14
    • Yaxun TangSunwoong Lee
    • Yaxun TangSunwoong Lee
    • G01V99/00G06F17/50
    • G01V1/28G01V2210/66G06F17/5009G06F2217/16
    • Method for reducing computational time in inversion of geophysical data to infer a physical property model (91), especially advantageous in full wavefield inversion of seismic data. An approximate Hessian is pre-calculated by computing the product of the exact Hessian and a sampling vector composed of isolated point diffractors (82), and the approximate Hessian is stored in computer hard disk or memory (83). The approximate Hessian is then retrieved when needed (99) for computing its product with the gradient (93) of an objective function or other vector. Since the approximate Hessian is very sparse (diagonally dominant), its product with a vector may therefore be approximated very efficiently with good accuracy. Once the approximate Hessian is computed and stored, computing its product with a vector requires no simulator calls (wavefield propagations) at all. The pre-calculated approximate Hessian can also be reused in the subsequent steps whenever necessary.
    • 减少地球物理数据反演中的计算时间推断物理性质模型的方法(91),在地震数据的全波场反演中特别有利。 通过计算确切的Hessian和由孤立点衍射器(82)组成的采样矢量的乘积,预先计算近似的Hessian,并将近似Hessian存储在计算机硬盘或存储器(83)中。 然后,当需要(99)用于使用目标函数或其他向量的梯度(93)计算其乘积时,检索近似的Hessian。 由于近似的Hessian是非常稀疏的(对角占优势的),因此可以非常有效地逼近具有向量的乘积。 一旦计算和存储近似的Hessian,用矢量计算其乘积就不需要模拟器调用(波场传播)。 预先计算的近似黑森西也可以在随后的步骤中重复使用。
    • 9. 发明申请
    • FREQUENCY-DOMAIN AUGMENTED TIME-DOMAIN FULL WAVEFIELD INVERSION
    • 频域支持时域全波形反演
    • US20150293246A1
    • 2015-10-15
    • US14656389
    • 2015-03-12
    • Thomas A. DickensSunwoong LeeYaxun Tang
    • Thomas A. DickensSunwoong LeeYaxun Tang
    • G01V1/28G01V1/30
    • G01V1/282G01V1/303G01V1/306G01V1/307G01V2210/614G01V2210/622G01V2210/665G01V2210/673G01V2210/675
    • A basically time-domain method for performing full wavefield inversion of seismic data to infer a subsurface physical property model (61), where however at least one quantity required for the inversion, such as the Hessian of the cost function, is computed in the frequency domain (64). The frequency-domain quantity or quantities may be obtained at only a few discrete frequencies (62), preferably low frequencies, and may be computed on a coarse spatial grid, thus saving computing time with minimal loss in accuracy. For example, the simulations of predicted data and the broadband gradient of the objective function may be computed in the time domain (67), and the Hessian matrix, approximated by its diagonal, may be computed in the frequency domain. It may be preferable to use time-domain and the frequency-domain solvers that employ different numerical schemes, such as finite-difference method, one-way wave equation, finite-element method (63).
    • 用于执行地震数据的全波场反演以推断地下物理属性模型(61)的基本时域方法(61),然而,在频率中计算反演所需的至少一个数量,例如成本函数的Hessian 域(64)。 可以仅在几个离散频率(62),优选低频率处获得频域量或量,并且可以在粗略的空间网格上计算,从而以最小的精度损失节省计算时间。 例如,可以在时域(67)中计算目标函数的预测数据和宽带梯度的模拟,并且可以在频域中计算由其对角线近似的Hessian矩阵。 使用有限差分法,单向波动方程,有限元法(63),采用不同数值方案的时域优化和频域求解器。