Full waveform inversion (FWI) is a nonlinear data fitting process that can derive high-resolution model parameters through iteration. In this process, step length is related to inversion accuracy and computational efficiency. It can be calculated efficiently with the inexact line search method, which does not require a misfit function to achieve the exact minimum. This method is aimed toward obtaining the appropriate descent using evaluation conditions and initial step length. Moreover, it does not depend on the form of the misfit function. In the inexact line search method, the evaluation condition and initial step length are obviously important factors. In this work, the classical Armijo, Wolfe, and Goldstein evaluation conditions in solving optimization problems in mathematics are studied and compared in detail. Numerical examples from the synthetic data of the overthrust model show that the convergence characteristics of Armijo and Goldstein are similar and that the computational efficiency is high and conducive to seismic FWI. In addition, the adaptive Barzilai-Borwein (ABB) method is adopted in FWI. The ABB method maximizes the changes in model parameters and gradients to adaptively calculate the initial step length. The threshold value of the ABB method for the initial step length estimation is also studied to explore a suitable threshold value that can ensure that large and small step lengths are frequently adopted in FWI. Numerical examples from the synthetic data of the overthrust model demonstrate the validity of the ABB method. Moreover, the inversion is superior when the threshold value is less than 0.5.

全波形反演（FWI）是一种非线性数据拟合过程，可以通过迭代推导出高分辨率模型参数。在这个过程中，步长与反演精度和计算效率有关。它可以用不精确的线搜索方法有效地计算，它不需要失配函数来实现精确的最小值。该方法旨在使用评估条件和初始步长获得适当的下降。此外，它不依赖于失配函数的形式。在不精确线搜索方法中，评价条件和初始步长显然是重要的因素。在这项工作中，详细研究和比较了解决数学优化问题的经典 Armijo、Wolfe 和 Goldstein 评估条件。反推模型合成数据的数值算例表明，Armijo和Goldstein的收敛特性相似，计算效率高，有利于地震FWI。此外，FWI 中采用了自适应 Barzilai-Borwein (ABB) 方法。ABB 方法最大化模型参数和梯度的变化以自适应地计算初始步长。还研究了 ABB 方法用于初始步长估计的阈值，以探索合适的阈值，以确保 FWI 中经常采用大步长和小步长。来自逆推模型合成数据的数值例子证明了 ABB 方法的有效性。此外，当阈值小于 0.5 时，反演效果更佳。