Seismic full-waveform inversion (FWI) estimates subsurface velocity structures by reducing data misfit between observed and modeled data. Simultaneous matching of transmitted and reflected waves in seismic FWI causes different updates of different wavenumber components of a given model depending on the diffraction angle between incident and diffracted rays. Motivated by the inverse-scattering imaging condition and elastic FWI, we have applied a diffraction-angle filtering technique in acoustic FWI, which enables us to separate transmission and reflection energy in the partial derivative wavefields. Diffraction-angle filtering is applied to the virtual source, which is the model parameter perturbation acting as a source for the partial derivative wavefields. Diffraction-angle filtering consists of two diffraction-angle filters (DAFs), DAF-I and DAF-II. The former is derived from the particle acceleration of the incident wavefields and suppresses energies at either small or large diffraction angles by changing the sign of the weighting factor. DAF-I is exactly identical to the conventional inverse scattering approach. The DAF-II is derived from the artificial shear strain of the incident P-wave and additionally suppresses energies at intermediate diffraction angles. With this mechanism, we can design various types of diffraction-angle filtering to control the updates of wavenumber components of the misfit gradient with respect to the P-wave velocity. Using the synthetic Marmousi-II data and real ocean-bottom seismic data from the North Sea, we determined that diffraction-angle filtering enables us to control low-, intermediate-, and high-wavenumber components of the gradient direction.

中文翻译：

---

声学全波形反演的梯度衍射角滤波

地震全波形反演（FWI）通过减少观测数据和建模数据之间的数据不匹配来估计地下速度结构。地震FWI中透射波和反射波的同时匹配会导致给定模型的不同波数分量的不同更新，具体取决于入射射线和衍射射线之间的衍射角。受反散射成像条件和弹性FWI的影响，我们在声学FWI中应用了衍射角滤波技术，这使我们能够分离偏导波场中的透射和反射能量。衍射角滤波应用于虚拟源，虚拟源是模型参数摄动，是偏导波场的源。衍射角滤镜由两个衍射角滤镜（DAF）组成，DAF-I和DAF-II。前者源自入射波场的粒子加速度，并通过更改加权因子的符号来抑制大或小衍射角的能量。DAF-1与常规的逆散射方法完全相同。DAF-II来自入射P波的人工剪切应变，并另外抑制了中等衍射角的能量。通过这种机制，我们可以设计各种类型的衍射角滤波来控制失配梯度的波数分量相对于P波速度的更新。利用来自北海的合成Marmousi-II数据和真实的海底地震数据，我们确定了衍射角滤波使我们能够控制低，中，