We extend the Kirchhoff-Helmholtz integral method to calculate acoustic potentials which transmit through three-dimensional warped boundaries. We specify the potentials on an arbitrary surface with Snell's law and plane-wave transmission coefficients and numerically integrate their contributions at a receiver via the scalar integral representation theorem. The method is appropriate for modeling precritical transmitted potentials. Results from test models compare well with optical solutions for transmissions through a flat interface. We model the effect of several idealized crust-mantle boundary structures on teleseismic P wave generated by explosion sources. The structures are all upwarps and are designed to produce travel-time residuals as a function of delta and azimuth which have the same magnitude as residuals observed for NTS tests within Pahute Mesa. These structures consistently cause complicated low amplitude waveforms which arrive early and simple high amplitude waveforms which arrive late. Thus, they cause systematic amplitude variations with azimuth, delta, and source location. The magnitude of this variation is less than or equal to . This factor is somewhat less than the observed ab amplitude variation with azimuth of Pahute Mesa tests; however, it is approximately the same magnitude as the observed ab variation at a given station as a function of test location within the mesa.