Target-oriented modelling and inversion using Recursive Patched Green Functions

SUMMARY We develop the mathematical framework of the recursive Patched Green Functions (RPGF) method. This target-oriented approach enables precise calculation of the wavefield at both the target area and the receivers, entirely in the frequency domain with reduced computational cost when compared with the conventional wave propagation method. The method works by dividing the entire model into subsets for both inside and outside-target areas, then recursively constructing the Green’s Functions by connecting these subsets until the full domain is covered. In this work, we derive the recursive equations from the Dyson equation and present a robust algorithm for their implementation. To demonstrate the effectiveness and accuracy of our approach, we show that: (1) The wavefields computed at the target and receivers are numerically identical to those obtained via conventional full-domain simulations. (2) The RPGF method significantly reduces computational time, offering a major advantage in large-scale simulations. This approach provides a natural foundation for a target-oriented full waveform inversion workflow, enabling localized and efficient inversion strategies. Finally, we validate the versatility of the RPGF method by applying it successfully to both 2-D and 3-D wave propagation problems.