  Surface acoustic waves at frequencies beyond a few GHz are promising
components for quantum technology applications. Applying scanning X-ray
diffraction microcopy we directly map the locally resolved components of the
three-dimensional strain field generated by a standing surface acoustic wave on
GaAs with wavelength $\lambda\simeq500\,$nm corresponding to frequencies near 6
GHz. We find that the lattice distortions perpendicular to the surface are
phase-shifted compared to those in propagation direction. Model calculations
based on Rayleigh waves confirm our measurements. Our results represent a break
through in providing a full characterization of a radio frequency surface
acoustic wave beyond plain imaging.
