{'fraction_non_alphanumeric': 0.012259194395796848, 'fraction_numerical': 0.0, 'mean_word_length': 5.891566265060241, '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}}
An exact analytical procedure to evaluate Sommerfeld integrals in layered media problems

In this work, we develop a comprehensive numerical method to evaluate the Sommerfeld Integrals appearing in layered media problems using simple algebraic functions which enable closed form integration. The resulting algorithm is much simpler than the conventional discrete complex image method. Detailed mathematical steps are enumerated for evaluating Sommerfeld integrals involving zero-order and first-order Bessel functions and can be extended to higher-order functions easily.