Monitoring spatiotemporal variations in the properties of Earth’s subsurface is fundamental to understanding its dynamic behavior and associated geological hazards. Coda wave interferometry （CWI） is a powerful branch of seismic interferometry that utilizes multiply scattered seismic waves, or coda waves. Owing to their prolonged and complex trajectories, coda waves exhibit exceptional sensitivity to subtle changes in the subsurface medium, enabling the detection of weak seismic velocity variations that are often undetectable by direct waves. This provides an efficient, economical, and environmentally sustainable approach for imaging dynamic subsurface processes. This paper presents a comprehensive review of the principles, applications, and prospects of CWI for monitoring both temporal and spatial seismic velocity changes.

The review begins by detailing the fundamental principles of established CWI methods for monitoring temporal velocity changes in subsurface media. These include the moving window cross-correlation method, the stretching method, the sliding window cross-spectral method, dynamic time warping, and the wavelet cross-spectrum analysis method. Each technique is designed to measure travel-time shifts between a reference waveform and a perturbed waveform, which are then translated into relative velocity changes. The moving window cross-correlation method determines time shifts by maximizing correlation coefficients within sliding windows, with quantifiable error bounds. The stretching method applies a linear stretch to the perturbed waveform to optimize its correlation with the reference, directly yielding the relative velocity change. Operating in the frequency domain, the sliding window cross-spectral method derives time shifts from the phase slope of cross-spectra, offering potentially greater stability. Dynamic time warping identifies an optimal non-linear alignment path between two time series, thereby acommodating non-uniform velocity changes. The wavelet cross-spectrum analysis employs time-frequency analysis to provide measurements across multiple frequency bands over the entire coda, facilitating the discrimination of changes occurring at different depths.

The application of these temporal monitoring methods across diverse geological settings is extensively summarized. In volcanology, CWI has successfully detected precursory velocity drops caused by magma pressurization prior to eruptions, as well as seasonal variations linked to hydrological cycles. Studies at volcanoes such as Piton de la Fournaise and Merapi demonstrate its utility for eruption forecasting and elucidating magma migration processes. For fault zone studies, CWI has been instrumental in delineating co-seismic damage, post-seismic healing, and the dynamics of slow slip events. Research on the San Andreas fault and investigations following the Wenchuan earthquake revealed pronounced co-seismic velocity reductions and their subsequent logarithmic recovery, illuminating stress accumulation and release mechanisms. In hydrogeology, CWI offers a non-invasive means to monitor groundwater storage changes by detecting velocity variations induced by alterations in pore pressure and fluid saturation. Correlations established between seismic velocity and well data or precipitation records underscore its potential for aquifer management. Furthermore, in industrial contexts such as CO₂ geological storage and geothermal reservoir operations, CWI monitors reservoir responses to fluid injection, aiding in the assessment of induced seismicity risks and reservoir compaction. Case studies from the Basel and Salton Sea geothermal fields exemplify its effectiveness in tracking stimulation effects and production-induced changes.

While early applications often presumed spatially uniform velocity changes, a significant advancement in CWI involves incorporating sensitivity kernel theory to resolve the spatial distribution of these changes. The review elaborates on two primary classes of sensitivity kernels. The diffusion approximation kernel, based on the assumption of isotropic energy diffusion, provides a computationally efficient framework for locating perturbations. In contrast, the radiative transfer kernel offers a more rigorous physical model by accounting for the angular distribution of energy flux, thereby improving accuracy in anisotropic scattering media. The development of these kernels has enabled CWI to evolve from a tool measuring averaged changes to one capable of 4D imaging. Applications include locating pre-eruptive changes around volcanoes, imaging co-seismic damage zones following large earthquakes such as the 2008 Wenchuan event, and visualizing the propagation of hydrological changes in the subsurface. Recent innovations, such as adaptive imaging with Voronoi tessellation and coupled body-surface wave kernels, are further enhancing spatial resolution and applicability in complex media.

Despite its successes, CWI faces several challenges. Theoretically, the inverse problem for spatial imaging can be non-unique, and accurately modeling wave propagation in complex 3D heterogeneous media remains difficult. Practically, interpretations can be confounded by environmental noise, seasonal effects, and the difficulty in discriminating the physical mechanisms （e.g., crack density versus fluid saturation） behind observed velocity changes. The method’s sensitivity is also depth-dependent, often resulting in lower resolution at greater depths. The paper concludes by outlining promising avenues for future research to address these limitations and expand CWI’s capabilities. These include leveraging new sensing technologies like Distributed Acoustic Sensing （DAS） on fiber-optic cables for unprecedented spatial sampling; developing high-precision 3D inversion and imaging techniques; integrating artificial intelligence for automated data processing, noise suppression, and pattern recognition; and establishing multi-parameter real-time monitoring systems that integrate seismic velocity with other geophysical data to build comprehensive hazard early warning systems and improve resource management. In summary, CWI stands as a vital and rapidly evolving geophysical tool, whose continued development promises deeper insights into the dynamic processes shaping Earth’s interior.