Conventional full-waveform inversion (FWI) updates a velocity model by minimizing the data residuals between the predicted and observed data at the receiver positions. We have developed a new FWI to update the velocity model by minimizing virtual source artifacts at the receiver positions in the source-domain FWI (SFWI). Virtual source artifacts are created by replacing the propagating source wavefield by the forward-time observed data at the receiver positions as a data-residual constraint. Therefore, no matter whether the velocity model is correct or not, the data residuals at the receiver positions always are forced to be zero. If the velocity model is correct, this data-residual constraint has no effect on the wavefield because the predicted data are the same as the observed data. However, if the estimated velocity model is incorrect, the mismatch between the replaced forward-time observed data and the incorrect predicted upgoing waves (e.g., the reflected waves) at the receiver positions will produce downgoing artifact waves. Thus, the data-residual constraint behaves as a virtual source to create artifact wavefields. By minimizing the virtual source artifacts (equivalent to producing the artifact wavefield), the velocity model can be iteratively updated toward the true velocity model. Similar to conventional FWI, SFWI can be implemented in either the frequency or time domain, which is unlike previous source-domain solutions which have to be implemented only in the frequency domain to solve the normal equations. SFWI does more overfitting of noisy observed data than conventional FWI does because noise is amplified by the differential operators when calculating the virtual source artifacts. Tests on synthetic data indicate that SFWI inverts for the velocity model more accurately than conventional FWI for noise-free or low-noise data.

中文翻译：

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源域全波形反演

常规的全波形反演（FWI）通过最小化接收器位置处的预测数据与观测数据之间的数据残差来更新速度模型。我们已经开发了一种新的FWI，以通过最小化源域FWI（SFWI）的接收器位置处的虚拟源伪像来更新速度模型。通过用在接收器位置的正时观测数据代替传播源波场来创建虚拟源伪像，作为数据残留约束。因此，无论速度模型是否正确，接收器位置的数据残差总是被迫为零。如果速度模型正确，则此数据残留约束对波场没有影响，因为预测数据与观测数据相同。但是，如果估算的速度模型不正确，替换的正时观测数据与接收机位置处的不正确的预测上行波（例如，反射波）之间的不匹配将产生下行伪像波。因此，数据残差约束充当创建伪影波场的虚拟源。通过最小化虚拟源伪像（相当于产生伪像波场），可以将速度模型朝着真实速度模型迭代更新。与常规FWI相似，SFWI可以在频域或时域中实现，这与以前的源域解决方案不同，以前的源域解决方案只需要在频域中实现以解决正规方程。与传统的FWI相比，SFWI进行的噪点观测数据拟合程度更高，这是因为在计算虚拟源伪像时，差分运算符会放大噪声。对合成数据的测试表明，对于无噪声或低噪声数据，SFWI对速度模型的反演比常规FWI更准确。