Keywords: acoustic emission, localization, velocity anisotropy, rock mechanics, fracture, error estimation.

In this paper, an algorithm is discussed for localization based on acoustic emission (AE) data in a transverse isotropic rock. The application of AE provides information on the fracture process in the interior of a sample during rock mechanical testing. If the rock or another brittle material is loaded sufficiently high, micro-fractures develop and generate elastic strain waves that can be recorded by acoustic emission sensors (AE) [1]. By determining the positions of origin of these emissions, the micro-fractures can be mapped in order to analyse the fracture process. This technique is called localization.

Localization is performed by measuring arrival time differences (ATD) from one emission (so-called hit) to several sensors. Multiplying the ATD by the velocity results in a distance difference. This technique is been applied for a long time in isotropic media [2,3]. Here, a localization algorithm is developed for layered rock, which has commonly transverse isotropic properties. Due to the layered structure, the wave velocity is found to be directional dependent. It is assumed that the velocity is constant within each direction.

Theoretically, given an array of sensors with known wave velocities in each direction, the ATD to each pair of sensors can be calculated for every position on a reference grid. Thus, a database of theoretical ATDs for all these positions can be constructed. Then, when a hit is recorded during testing, its position can be estimated by comparing the measured ATDs with the calculated ATDs from the reference grid database. The comparison is done by minimizing the error on ATD. Thus, the reference grid point that has the least sum of squared differences between its ATDs and the set of measured ATDs is determined as the origin of the hit. The least sum of the square differences is defined as the allocation efficiency and can be applied to a certain extent as a quality estimator for the localization.

The algorithm is programmed in Matlab and is tested for validation in a two-dimensional experiment where artificial hits are induced on known positions on the surface of a layered slate rock sample. Comparison of the positions generated by localization with the actual positions shows that the position estimates are good. The algorithm is applied in later three-dimensional applications during loading tests.

Areas of future research on the computational side are the detection of and compensation for systematic localization errors (drift) and optimising the allocation efficiency.

1

A. Lavrov, A. Vervoort, M. Wevers, J.A.L. Napier, "The experimental and numerical study of the Kaiser effect in cyclic Brazilian test with disk rotation", International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 39(3), 287-302, 2003. doi:10.1016/S1365-1609(02)00038-2

2

A. Tobias, "Acoustic-emission source location in two dimensions by an array of three sensors", Nondestructive Testing, 9(1), 9-12, 1976. doi:10.1016/0029-1021(76)90027-X

3

M. Ohtsu, K. Ono, "AE source location and orientation determination of tensile cracks from surface observation", NDT International, 21(3), 143-150, 1988. doi:10.1016/0308-9126(88)90445-2

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