ЧИСЛЕННОЕ РЕШЕНИЕ ОБРАТНОЙ КОЭФФИЦИЕНТНОЙ ЗАДАЧИ АКУСТИКИ С ПРИМЕНЕНИЕМ ПРЕОБРАЗОВАНИЯ ЛАПЛАСА И МЕТОДА ДИФФЕРЕНЦИАЛЬНОЙ ЭВОЛЮЦИИ

В данной статье рассматривается решение обратной коэффициентной задачи для волнового уравнения, направленной на восстановление пространственного распределения скорости звука в неоднородной среде. Для решения прямой задачи применяется преобразование Лапласа, позволяющее исключить временную зависимость и перейти к обыкновенным дифференциальным уравнениям в частотной области, что существенно снижает вычислительные затраты. Обратная задача формулируется как оптимизационная: минимизация функционала невязки между рассчитанными и измеренными значениями акустического давления осуществляется с помощью стохастического метода глобальной оптимизации, дифференциальной эволюции. Численные эксперименты проводились на модели многослойной среды (песок, грунт, камень, вода, воздух) с использованием синтетических данных, зашумленных случайным образом. Предложен адаптивный комбинированный метод восстановления, позволяющий снизить влияние ошибок на границах сред. Результаты показывают высокую точность метода: относительная погрешность восстановления профиля скорости звука составила около от 2,5 до 4,3%, что подтверждает эффективность подхода для задач акустической диагностики и томографии.

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