Elastic Wave Radiation from a Pressurized Spherical Cavity

Elastic waves radiated from a pressurized spherical cavity embedded within a homogeneous and isotropic wholespace are described by closed-form mathematical formulae, in both the time-domain and the frequency-domain. For this spherically symmetric problem, only radially polarized compressional waves are generated. All near-field and far-field terms are included in the solution, and the expressions are valid for arbitrary source pressure waveforms. Analogous formulae are developed for the elastic wavefield produced by a uniform radial particle displacement imposed at the cavity wall. These closed-form mathematical solutions facilitate rapid and accurate forward modeling, and hence are particularly useful for (i) performing order-of-magnitude estimations of various cavity-source elastic radiation phenomena, and (ii) validating purely numerical (i.e., finite-element or finite-difference) algorithms designed to solve similar problems. The formulae also indicate that the inverse source characterization problem is well posed: the source activation wavelet (pressure, traction, displacement, velocity, etc.) is obtained by performing a deterministic deconvolution of the response observed at a remote receiver. Numerical examples verify that the source signature is accurately recovered, provided the elastic parameters, recording geometry, and cavity radius are known.