PyCalibrAE: An Open-Source Toolbox for Broadband Calibration of Ultrasonic Sensors

Acoustic emission (AE) and ultrasonic sensors are integral for interpreting elastic wave data in laboratory and field experiments. This study introduces a broadband calibration toolbox for absolute sensor calibration using theoretical Hertzian ball impacts on a transfer medium. High-resolution seismic wave propagation is simulated with the spectral-element method (SEM) within the open-source SPECFEM3D framework. By modeling a Heaviside step function on an aluminum plate, Green’s function is obtained at multiple receiver locations, enabling flexible calibration with various source mechanisms. A stitching algorithm combines instrument responses, propagating uncertainties to achieve broadband calibration from 100 Hz up to 1.31 MHz. SEM outperforms generalized ray theory (GRT) by capturing reflections and low-frequency waves, while GRT remains effective for high-frequency calibration. Applying the framework to longitudinal and shear wave sensors reveals effects such as reversed first-arrival polarities, time-series ringing, frequency resonance peaks, slope sensitivities, and calibration uncertainties, particularly below 10 kHz. For large-aperture sensors, a reduced high-frequency sensitivity at shallow angles is critical for nonoptimally aligned sensor arrays. This accessible toolbox enhances AE understanding across diverse fields.