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The utilization of a reverberant shear-wave field in shear-wave elastography has emerged as a promising technique for achieving robust shear-wave speed (SWS) estimation. However, many types of estimators cannot accurately measure SWS within such a complicated 3D wave field. This study introduces an advanced autocorrelation estimator based on angular integration known as the angular integral autocorrelation (AIA) approach to address this issue. The AIA approach incorporates all the autocorrelation data from various angles during measurements, resulting in enhanced robustness to both noise and imperfect distributions in SWS estimation. The effectiveness of the AIA estimator for SWS estimation is first validated using a k-Wave simulation of a stiff branching tube in a uniform background. Furthermore, the AIA estimator is applied to ultrasound elastography experiments, magnetic resonance imaging (MRI) experiments, and optical coherence tomography (OCT) studies across a range of different excitation frequencies on tissues and phantoms, including in vivo scans. The results verify the capacity of the AIA approach to enhance the accuracy of SWS estimation and the signal-to-noise ratio (SNR), even within an imperfect reverberant shear-wave field. Compared to simple autocorrelation approaches, the AIA approach can also successfully visualize and define lesions while significantly improving the estimated SWS and SNR in homogeneous background materials and providing improved elastic contrast between structures within the scans. These findings demonstrate the robustness and effectiveness of the AIA approach across a wide range of applications, including ultrasound elastography, magnetic resonance elastography (MRE), and optical coherence elastography (OCE), for accurately identifying the elastic properties of biological tissues in diverse excitation scenarios.