Borehole reflection waveform inversion based on subarray decomposition

High-resolution imaging of near-borehole structures and quantitative inversion is crucial for reservoir characterization. However, conventional acoustic logging is dominated by direct waves, limiting its investigation depth to the near-borehole invasion zone. Full-waveform inversion is a waveform-fitting inversion technique that offers high resolution and is not constrained by assumptions of homogeneity. To reconstruct deep formation properties and structures, we apply the method of borehole reflection waveform inversion to array acoustic logging data. By dividing the array into subarrays and exploiting the spatial correlation of adjoint wavefields, this approach implicitly suppresses crosstalk artifacts in the adjoint-state method under the framework of elastic waves. Additionally, energy weighting and anisotropic diffusion filtering are applied to precondition the gradient, effectively mitigating severe illumination imbalances and high-wavenumber noises. A frequency hierarchy strategy is further integrated to enhance convergence stability. This method provides a theoretical P-wave velocity reconstruction workflow for single-borehole deep acoustic sensing without adding significant computational complexity. Numerical results demonstrate that the proposed method reconstructs complex two-dimensional heterogeneities with high precision.