Elastic full-waveform inversion (EFWI) updates high-resolution model parameters by minimizing the misfit function between the observed and modeled data. EFWI possesses strong nonlinearity and is likely to converge to a local minimum when the inversion begins with inaccurate initial models. Elastic reflection waveform inversion (ERWI) recovers the low-wavenumber components of P- and S-wave velocities along the “rabbit ear” wavepaths to provide initial velocity models for EFWI. However, every iteration of ERWI requires six times as many forward calculations with elastic-wave equations, which can be computationally expensive. Hence, we have developed a pure-wave reflection waveform inversion (PRWI) approach, which sequentially inverts low-wavenumber components of P- and S-wave velocity models. In our PRWI, we decompose elastic-wave operators into background and perturbed pure-wave parts and derive PRWI gradients using pure-wave operators. The background and perturbed wavefields in PRWI gradients are vector wavefields with a single wave mode. PRWI can remove the high-wavenumber noise caused by S-wave stress decomposition and reduce the computational cost of ERWI by almost 70%. Under the framework of PRWI, we have further developed the pure-wave reflection traveltime inversion (PRTI) approach to alleviate the issue of cycle skipping caused by waveform mismatch. To ensure the recovery of low-wavenumber components, we mute out the contribution of wavefields with small opening angles to PRTI gradients. Numerical examples have demonstrated that our PRTI method can efficiently provide good initial velocity models for EFWI.

中文翻译：

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使用纯波传播器进行弹性反射旅行时反演

弹性全波形反演 (EFWI) 通过最小化观测数据和建模数据之间的错配函数来更新高分辨率模型参数。EFWI 具有很强的非线性，当反演以不准确的初始模型开始时，很可能收敛到局部最小值。弹性反射波形反演 (ERWI) 沿“兔耳”波路径恢复 P 波和 S 波速度的低波数分量，为 EFWI 提供初始速度模型。然而，ERWI 的每次迭代都需要六倍的弹性波方程前向计算，这在计算上可能很昂贵。因此，我们开发了一种纯波反射波形反演 (PRWI) 方法，该方法依次反演 P 波和 S 波速度模型的低波数分量。在我们的 PRWI 中，我们将弹性波算子分解为背景和扰动纯波部分，并使用纯波算子推导出 PRWI 梯度。PRWI 梯度中的背景波场和扰动波场是具有单波模式的矢量波场。PRWI 可以去除 S 波应力分解引起的高波数噪声，将 ERWI 的计算成本降低近 70%。在PRWI框架下，我们进一步发展了纯波反射走时反演（PRTI）方法，以缓解波形失配引起的跳周期问题。为了确保低波数分量的恢复，我们消除了具有小张角的波场对 PRTI 梯度的贡献。数值例子表明，我们的 PRTI 方法可以有效地为 EFWI 提供良好的初始速度模型。