As internal tides propagate in the ocean, they carry and dissipate energy over hundreds and even thousands of kilometers. In relatively shallow seas the low vertical mode internal tide can evolve to form solitary waves whose surface signature can be detected by satellites as regions of high and low reflectance where the surface is roughened or smoothed respectively by horizontally convergent and divergent flows induced by the waves. To gain insight into what processes lead to the observation of internal solitary waves by satellites, we perform fully nonlinear simulations in three dimensions to examine the evolution of horizontally propagating, vertical mode-1 internal tides as it depends on wave amplitude, ocean depth, and the spanwise extent of the waves. The background stratification is set up according to measurements in the South China Sea. The spanwise evolution of the 3D waves is examined in terms of the lateral spreading, radius of curvature, and sea surface signature corresponding to a threshold in the surface horizontal convergent and divergent flow. The evolution of sea surface signature compares favorably to a satellite image in the South China Sea, particularly for waves initially having spanwise extent comparable to their horizontal wavelength.