Kirchhoff Integral Forward Modeling Algorithm

The Kirchhoff integral forward modeling algorithm is a fundamental technique in seismic exploration, primarily used to simulate seismic wave propagation through subsurface media. This algorithm is based on the mathematical principles of Kirchhoff integration, which calculates wavefield integrals over interfaces to model seismic wave propagation paths and amplitudes. The core concept of forward modeling involves using known seismic source parameters and subsurface physical properties to predict wave propagation behaviors, including reflection, refraction, and scattering phenomena. Through forward modeling simulations, synthetic seismograms can be generated, providing theoretical foundations for subsequent seismic data interpretation and migration processing. In code implementation, this typically involves discretizing the Kirchhoff integral formula using numerical integration methods and calculating wavefield contributions from each subsurface point. A key advantage of the Kirchhoff integral forward modeling algorithm lies in its computational efficiency, particularly suitable for wavefield simulation under complex geological conditions. The algorithm can be optimized through parallel computing techniques when handling large-scale models. However, the method relies on simplified medium assumptions, typically treating media as homogeneous or layered structures, which may present limitations when dealing with strongly heterogeneous media. Code implementations often incorporate smoothing filters to mitigate these limitations. The Kirchhoff migration algorithm mentioned in the current article has not yet been implemented – this represents another crucial component in seismic data processing. Migration algorithms aim to reposition wavefield data obtained from forward modeling to their actual subsurface locations, thereby more accurately reflecting subsurface structures. The integration of forward modeling and migration algorithms provides comprehensive technical support for seismic exploration. A typical migration implementation would involve back-propagating wavefields using Green's functions and applying imaging conditions. Overall, the Kirchhoff integral forward modeling algorithm plays a foundational role in seismic wave simulation, establishing the basis for developing migration algorithms and optimizing seismic data processing workflows. Future code enhancements could focus on incorporating more accurate Green's function calculations and adaptive mesh refinement techniques.