Научные статьи \ Математика. Естественные науки \ Математика \ Вычислительная математика. Численный анализ

Применение сеточно-характеристического метода для моделирования распространения упругих волн в геологических средах с наличием трещин с использованием наложенных сеток

Применение сеточно-характеристического метода для моделирования распространения упругих волн в геологических средах с наличием трещин с использованием наложенных сеток

Автор: Митьковец И.А.

Журнал: Труды Московского физико-технического института @trudy-mipt

Рубрика: Математика

Статья в выпуске: 3 (59) т.15, 2023 года.

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Исследование зон геологических разломов важно для определения запасов нефти и газа в месторождениях. Для моделирования рассеяния волн в зонах трещиноватости используют численные методы на структурированных вычислительных сетках для оптимизации вычислительных ресурсов. Однако эти методы позволяют рассчитать рассеяние волн на трещинах только в направлении координатных осей. Чтобы моделировать более реалистичные трещиноватые поля, используют численные методы на неструктурированных вычислительных сетках или структурированных криволинейных вычислительных сетках, требующих больших вычислительных мощностей и важных при решении обратных задач. В данной работе предлагается численный метод с использованием наложенных сеток, где расчеты проводятся на структурированных регулярных вычислительных сетках с наложенными сетками, повернутыми вдоль трещин. Основным фактором является аналитическое задание якобиана вращения объектов, описывающих трещину, и малый локальный размер наложенных вычислительных сеток для экономии вычислительных ресурсов.

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Наложенные сетки, сеточно-характеристический метод, упругие волны, распространение волн, сейсморазведка, трещины, геологические разломы, рассеяние волн

Короткий адрес: https://sciup.org/142239990

IDR: 142239990   |   УДК: 519.633.6

Application of the grid characteristic method for modeling the propagation of elastic waves in geological media with cracks using overset grids approach

The study of geological fault zones is crucial for determining oil and gas reserves in deposits. For modeling wave scattering in fracture zones, numerical methods are used on structured computational grids to optimize computing resources. However, these methods allow us to calculate the scattering of waves on cracks only in the direction of the coordinate axes. For modeling more realistic fractured fields, numerical methods are used on unstructured computational grids or structured curved computational grids that require large computing power and are important for solving inverse problems. In this paper, we propose a numerical method using overset grids approach, where calculations are carried out on structured regular computational grids with overset grids rotated along cracks. The main factor is the analytical assignment of the Jacobian of rotation of the objects describing the crack, and the small local size of the overset computational grids to save computational resources.

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