Transient Green’s Tensor for a Layered Solid Half-Space With Different Interface Conditions

Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical basis for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green’s tensor for such a structure is explicitly derived from the three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a “generalized ray” and each is a definite line integral along a fixed path which can be easily computed numerically. Willis’ method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, along with the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code is developed for computation of the Green’s tensor when both the source and the detector are located on the top surface. The Green’s tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions have a great influence on the transient displacements. For example, when the interface bonding conditions vary, some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be used to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration.