The full-waveform inversion method is a high-precision inversion method based on the minimization of the misfit between the synthetic seismograms and the observed data. However, this method suffers from cycle skipping in the time domain or phase wrapping in the frequency because of the inaccurate initial velocity or the lack of low-frequency information. furthermore, the object scale of inversion is affected by the observation system and wavelet bandwidth, the inversion for large-scale structures is a strongly nonlinear problem that is considerably difficult to solve. In this study, we modify the unwrapping algorithm to obtain accurate unwrapped instantaneous phase, then using this phase conducts the inversion for reducing the strong nonlinearity. The normal instantaneous phases are measured as modulo 2π, leading the loss of true phase information. The path integral algorithm can be used to unwrap the instantaneous phase of the seismograms having time series and one-dimensional (1D) signal characteristics. However, the unwrapped phase is easily affected by the numerical simulation and phase calculations, resulting in the low resolution of inversion parameters. To increase the noise resistance and ensure the inversion accuracy, we present an improved unwrapping method by adding an envelope into the path integral unwrapping algorithm for restricting the phase mutation points, getting accurate instantaneous phase. The objective function constructed by unwrapping instantaneous phase is less affected by the local minimum, thereby making it suitable for full-waveform inversion. Further, the corresponding instantaneous phase inversion formulas are provided. Using the improved algorithm, we can invert the low-wavenumber components of the underneath structure and ensure the accuracy of the inverted velocity. Finally, the numerical tests of the 2D Marmousi model and 3D SEG/EAGE salt model prove the accuracy of the proposed algorithm and the ability to restore large-scale low-wavenumber structures, respectively.

中文翻译：

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基于展开算法的瞬时相位反转

全波形反演方法是基于最小化合成地震图和观测数据之间的失配的高精度反演方法。但是，由于初始速度不正确或缺乏低频信息，该方法存在时域跳频或频率相位回绕的问题。此外，反演的目标尺度受观测系统和小波带宽的影响，大型结构的反演是一个强烈的非线性问题，很难解决。在本研究中，我们修改了展开算法以获得准确的展开瞬时相位，然后使用该相位进行反演以减小强非线性。正常瞬时相位被测量为模2π，导致真实相位信息的丢失。路径积分算法可用于解开具有时间序列和一维（1D）信号特征的地震图的瞬时相位。但是，展开的相位很容易受到数值模拟和相位计算的影响，导致反演参数的分辨率较低。为了提高抗噪声能力并确保反演精度，我们提出了一种改进的解包方法，在路径积分解包算法中添加一个包络以限制相位突变点，从而获得准确的瞬时相位。通过解开瞬时相位而构造的目标函数受局部最小值的影响较小，从而使其适合于全波形反演。此外，提供了相应的瞬时相位反转公式。使用改进的算法，我们可以反转下层结构的低波数分量，并确保反转速度的准确性。最后，通过2D Marmousi模型和3D SEG / EAGE盐模型的数值测试，分别证明了该算法的准确性和恢复大规模低波数结构的能力。