{'fraction_non_alphanumeric': 0.023076923076923078, 'fraction_numerical': 0.0, 'mean_word_length': 5.285024154589372, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Optimum and standard beam widths for numerical modeling of interface scattering problems

Gaussian beams provide a useful insonifying field for surface or interface scattering problems such as encountered in electromagnetics, acoustics and seismology. Gaussian beams have these advantages: (i) They give a finite size for the scattering region on the interface. (ii) The incident energy is restricted to a small range of grazing angles. (iii) They do not have side lobes. (iv) They have a convenient mathematical expression. The major disadvantages are: (i) Insonification of an interface is nonuniform. The scattered field will depend on the location of the scatterers within the beam. (ii) The beams spread, so that propagation becomes an integral component of the scattering problem. A standard beam parameterization is proposed which keeps propagation effects uniform among various models so that the effects of scattering only can be compared. In continuous wave problems, for a given angle of incidence and incident amplitude threshold, there will be an optimum Gaussian beam which keeps the insonified area as small as possible. For numerical solutions of pulse beams, these standard parameters provide an estimate of the smallest truncated domain necessary for a physically meaningful result.