Geophysical analyses are often performed in spherical geometry and require the use of spherical harmonic functions to express observables or physical quantities. When expanded to high degree, the accuracy and speed of the spherical harmonic transforms and reconstructions are of paramount importance. SHTools is a time and user‐tested open‐source archive of both Fortran 95 and Python routines for performing spherical harmonic analyses. The routines support all spherical‐harmonic normalization conventions used in the geosciences, including 4π‐normalized, Schmidt seminormalized, orthonormalized, and unnormalized harmonics, along with the option of employing the Condon‐Shortley phase factor of (−1)m. Data on the sphere can be sampled on a variety of grid formats, including equally spaced cylindrical grids and grids appropriate for integration by Gauss‐Legendre quadrature. The spherical‐harmonic transforms are proven to be fast and accurate for spherical harmonic degrees up to 2800. Several tools are provided for the geoscientist, including routines for performing localized spectral analyses and basic operations related to global gravity and magnetic fields. In the Python environment, operations are very simple to perform as a result of three class structures that encompass all operations on grids, spherical harmonic coefficients, and spatiospectral localization windows. SHTools is released under the unrestrictive BSD 3‐clause license.

S U M M A R YWe examine focusing of seismic waves at the antipode of large terrestrial meteorite impacts, using the Chicxulub impact as our case study. Numerical simulations are based on a spectralelement method, representing the impact as a Gaussian force in time and space. Simulating the impact as a point source at the surface of a spherically symmetric earth model results in deceptively large peak displacements at the antipode. Earth's ellipticity, lateral heterogeneity and a spatially distributed source limit high-frequency waves from constructively interfering at the antipode, thereby reducing peak displacement by a factor of 4. Nevertheless, for plausible impact parameters, we observe peak antipodal displacements of ∼4 m, dynamic stresses in excess of 15 bar, and strains of 2 × 10 −5 . Although these values are significantly lower than prior estimates, mainly based on a point source in a spherically symmetric earth model, wave interference en route to the antipode induces 'channels' of peak stress that are five times greater than in surrounding areas. Underneath the antipode, we observed 'chimneys' of peak stress, strain and velocity, with peak values exceeding 50 bar, 10 −5 and 0.1 m s −1 , respectively. Our results put quantitative constraints on the feasibility of impact-induced antipodal volcanism and seismicity, as well as mantle plume and hotspot formation.