Perturbation Analysis of Travel-Time Accuracy for Core Phases Reconstructed from Seismic Interferometry

Correlating late coda waves from large earthquakes produces stable waveforms that approximate inter-station core phases. However, the properties of these coda waves often violate the strict assumptions underlying classical Green's function retrieval, raising doubts about the physical correspondence of the reconstructed arrivals to true inter-station phases and limiting their utility in seismic imaging. In this study, we present a perturbation analysis of core-phase interferometry and show that accurate travel-time information can be recovered under locally uniform wave incidence along the inter-station path. We introduce a dimensionless parameter – defined as the ratio of the seismic wave period to the inter-station travel time – which establishes a critical angular threshold. Our perturbation analysis reveals that the travel-time reconstruction accuracy scales with the cube of this threshold, allowing high-precision recovery of core phases, particularly those associated with small threshold values. Numerical simulations validate the theoretical predictions. By applying the proposed framework to real coda correlation data, we demonstrate that core phases can be reliably reconstructed using a sufficiently large number of global earthquakes – even without the traditionally assumed uniform source distribution. These results establish a rigorous theoretical foundation for extracting high-precision core-phase travel times from coda correlations, enhancing the reliability of seismological imaging of Earth's deep interior.