{'fraction_non_alphanumeric': 0.024324324324324326, 'fraction_numerical': 0.005405405405405406, 'mean_word_length': 5.557522123893805, '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}}
Numerical implementation of seismic wavefield operators via path integrals

The seismic imaging problem centers around mathematical and numerical techniques to create an accurate image of the earth's subsurface, using recorded data from geophones that capture reflected seismic waves. Using a path integral approach, a wavefield extrapolater can be expressed as a limit of depth‐sliced path steps through a variable velocity medium. An image is created from the correlation between upward and downward going waves. We report on the mathematical issues that arise in implementing numerical algorithms based on the path integral approach, in particular convergence, stability, and accuracy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)