25
На правах рукописи
Разработка методики анализа результатов геодезических измерений при
наблюдении за осадками и смещениями крупных инженерных сооружений
спутниковыми методами
Специальность: 25.00.32 – Геодезия
АВТОРЕФЕРАТ
диссертации на соискание ученой степени
кандидата технических наук
ОБЩАЯ ХАРАКТЕРИСТИКА РАБОТЫ
Актуальность темы
Разработка эффективных методов выявления и прогнозирования деформаций
инженерных сооружений является актуальной, поскольку ее успешное решение
и последующее развитие вносят важный вклад в обеспечение надежности,
долговечности и безопасности эксплуатации ответственных сооружений.
Решение этой задачи создает условия для повышения эффективности
использования капитальных вложений в строительство, помогает рационально
планировать различные регламентные работы, в том числе геодезические
наблюдения за деформацией сооружений, а также приносит определенный
социальный эффект.
Строительство больших технических структурных сооружений типа плотин,
мостов и высотных зданий является существенным для развития любой нации.
Значительные деформации инженерных сооружений, близких к критическим,
потенциально может вызывать гибель большого количества людей и сильные
разрушения. Сохранность и долговечность сооружений – важнейшая
народнохозяйственная задача, и она зависит не только от
научно-обоснованной конструкции этих сооружений, но также во многом и от
полноты исследования грунтов, на которых возводятся сооружения, от учета
влияния на сооружения внешней среды и, особенно, от своевременной
постановки и правильного выполнения систематических наблюдений за
состоянием сооружений. Следовательно, безопасность этих работ, особенно
в случаях с плотинами, требует периодического контроля и всестороннего
анализа их структурного состояния, основанного на большом наборе
переменных, которые вносят свой вклад в эти деформации. Деформацию
данных структур определяют несколько факторов. Самые важные из них – это
результаты переменных усилий и напряжений, развитых в структуре из-за
эффектов местных движений земной коры. Движения земной коры вызывают
изменения в относительном местоположении пунктов, расположенных на самой
плотине или около нее. Другие определяющие факторы включают в себя: тип
материалов строительства, силу ветра, изменение температур, усадку почв
и колебания из-за движения транспорта. Результаты наблюдений за осадками
и смещениями инженерных сооружений геодезическими методами должны
удовлетворять предъявляемым требованиям в отношении их полноты,
своевременности и точности.
С момента появления ГЛОНАСС и GPS, а также на основе непрерывного
процесса совершенствования технологии спутниковых измерений проблемы
прогнозирования деформаций инженерных сооружений стали решаться на
качественно новой основе. При использовании спутниковых методов точность
координатных определений в сочетании с оперативностью получения конечных
результатов определяются степенью необходимой детальности исследований,
а также экономическими возможностями организации данного вида работ.
Развитие высокоэффективных спутниковых методов координатных определений
на основе применения глобальных навигационных систем ГЛОНАСС и GPS
принципиальным образом изменяют технологию и точность определения
геодезических координат и принципы построения геодезических сетей,
являющихся фактической реализацией систем координат. По результатам
спутниковых измерений одновременно определяются точные значения
координат как в плане, так и по высоте. Поэтому современные спутниковые
методы координатных определений на основе применения глобальных
навигационных систем GPS и ГЛОНАСС создают условия для создания плановой
и высотной основы в виде единой совокупности геодезических пунктов.
Сложность решения этой проблемы состоит в том, что по спутниковым
измерениям непосредственно определяется геодезическая (эллипсоидальная)
высота, т.е. высота точки земной поверхности над отсчетным эллипсоидом.
При использовании спутниковых методов геодезические высоты определяются
непосредственно по результатам измерений. Обработка спутниковых данных
не требует редукции на поверхность эллипсоида.
Внедрение новых методов и средств геодезических измерений должно
сопровождаться и новой методикой обработки результатов измерений. Только
комплексное решение задачи позволит добиться максимальной эффективности
и будет отвечать современным требованиям.
Цель работы:
Основной целью работы является разработка методики анализа результатов
наблюдений за осадками и смещениями крупных электроэнергетических
объектов, расположенных в Мексике, с применением спутниковых методов
измерений, научное обоснование методики и определение путей их
практической реализации.
Научная новизна работы:
В результате выполненного анализа особенностей построения локальных
геодезических сетей спутниковыми методами, обеспечивающих оперативность
выполнения необходимых измерений и требуемый высокий уровень точности:
1. Выполнена теоретическая и экспериментальная проверка эффективности
предложенных математических методов оценки точности спутниковых
координатных определений.
2. Установлено, что в условиях недостаточной геодезической обеспеченной
в некоторых районах Мексики наибольшей оперативностью и экономичностью
для определения деформаций электроэнергетических объектов является метод
спутниковых измерений.
3. Разработан алгоритм определения средних квадратических ошибок
топоцентрических координат и установлена зависимость между малыми
изменениями декартовых топоцентрических координат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,
picscalex1000100090000039d00000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02c00160011200000026060f001a00ffffffff000010000000c0ffffff
3700000020010000f70100000b00000026060f000c004d61746854797065000050001c00
0000fb0240fe0000000000009001000000020002001053796d626f6c00007f140af90cfa
1200d89ff377e19ff3772020f57764096649040000002d01000008000000320a20013200
0100000068790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d00006409664900000a0021008a010000
0000ffffffff28fc1200040000002d01010004000000f0010000030000000000 и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 и
геоцентрических координат.
Практическая значимость работы:
Основные результаты выполненных исследований предложены для
использования в геодезической службе Мексики. Установленная практическая
связь прямоугольных геоцентрических и топоцентрических координат с
зонами деформаций уже сейчас может быть использована для переосмысления
существующего перспективного плана выявления разных видов деформаций в
районах электроэнергетических объектов на территории Мексики.
Разработанные в диссертации принципы применения топоцентрических
прямоугольных координат с использованием современных спутниковых
технологий ориентированы на реализацию в работах по изучению и выявлению
деформационных процессов крупных инженерных сооружений в условиях
Мексики, а также для создания высокоэффективной системы геодезического
обеспечения.
Предложенный метод оценки точности результатов геодезических измерений
для прогнозирования деформаций может служить основой для организации
геодезического мониторинга на территории Мексики, главная цель которого
– выявление до и после наводнений в зоне водохранилищ изменений уровней
воды.
На конкретном объекте (плотина «Саналона», Мексика) был проведен цикл
измерений за деформацией тела плотины, на основе которых с
использованием предложенной методики сделаны выводы об устойчивости
исследуемого объекта.
Публикации:
По результатам выполненных исследований по теме диссертации автором
опубликованы четыре статьи, а также (в соавторстве) тезисы доклада на
международной конференции.
Структура и объем диссертации:
Диссертационная работа состоит из введения, четырех разделов с
подразделами, заключения и списка литературы. Общий объем работы – 120
стр. Диссертация содержит 14 таблиц и 18 рисунков. Список литературы
составляет 52 наименований.
ОСНОВНОЕ СОДЕРЖАНИЕ РАБОТЫ
ВВЕДЕНИЕ
Обоснована актуальность решаемой задачи, сформулированы цель и задачи
исследования, обоснована научная новизна и практическая значимость
работы.
ГЛАВА 1. ДЕФОРМАЦИИ КРУПНЫХ ИНЖЕНЕРНЫХ СООРУЖЕНИЙ И ПРИЧИНЫ ИХ
ВОЗНИКНОВЕНИЯ
Дается общая классификация геодезических задач и обзор традиционных
методов их решения при изучении деформаций крупных инженерных
сооружений. Особое внимание уделяется анализу современных концепций
природы деформаций и причин их возникновения.
При изучении различного рода деформаций, возникающих в земной коре, а
также в основаниях крупных инженерных сооружениях и на других объектах,
появляется необходимость выполнения достаточно частых (а иногда и
непрерывных во времени) измерений. Традиционные геодезические методы в
организации мониторинговых измерений на объектах больших размеров
требуют больших затрат средств и времени. Целесообразность использования
GPS-измерений при изучении деформаций на различных объектах, в первую
очередь, связана с высокой экономической эффективностью спутниковых
методов измерений в сочетании с высокой точностью измерений.
В настоящее время спутниковые методы измерений находят все более и более
широкое применение для изучения и мониторинга деформаций крупных
инженерных сооружений. При этом необходимо учитывать, что нормальная
высота пунктов определятся менее точно, кроме того, точность определения
изменений координат пунктов зависит от широты исследуемого объекта.
Кроме того, недостаточное число наблюдаемых спутников, вызванных
экранировкой сигнала местными предметами, ограничивают возможность
использования спутниковых методов.
ГЛАВА 2. СПУТНИКОВЫЕ МЕТОДЫ ВЫСОКОТОЧНЫХ ГЕОДЕЗИЧЕСКИХ ИЗМЕРЕНИЙ
Даны основные характеристики существующих в настоящее время космических
навигационных систем, включая подробное описание спутниковых систем GPS
и ГЛОНАСС, а также находящейся в разработке системы GALILEO. Приводится
описание основных методов измерений и определения положения пунктов
спутниковыми методами.
В качестве опорных пунктов с известными координатами используются
навигационные спутники, а в качестве устройства для измерения координат
– антенна с электронным вычислительным блоком, так называемый приемник –
эта часть называется «Сектор потребителя». При этом вычисляются
расстояния от объекта на поверхности Земли или в воздухе до видимых
спутников.
Для решения большинства геодезических задач основная роль отводится
относительным режимам (дифференциальным), так как они существенно
отличаются по точности определения приращений координат. Точность
методов СРНС (спутниковая радионавигационная система) зависит от
расстояния между приемником и опорной станцией, от числа спутников на
орбите, от расположения спутников относительно приемников, от типа и
точностных возможностей приемника и от типа местности, а также от
времени наблюдений. СРНС обеспечивает исключительные возможности для
создания геодезических сетей различного назначения, что представляется
более экономичным и быстрым. СРНС работает практически в любых погодных
условиях и не требует взаимной видимости между приемниками.
Использование СРНС является относительно дешевой технологией, и ее
использование не требует высококвалифицированных специалистов в полевых
условиях. Основной недостаток применения СРНС заключается в том, что в
период ее работы на небе должно находиться, по меньшей мере, четыре
спутника и должно обеспечиваться отсутствие помех, создаваемых,
например, высотными препятствиями и обильной лесной растительностью
территории.
Фазовые методы измерений являются основными при решении разнообразных
геодезических задач с помощью спутниковых систем, предусматривающих
обеспечение высокой точности измерений.
Основное внимание в данной главе уделено подходам к решениям,
ориентированным на минимизацию влияния основных источников ошибок
спутниковых измерений.
При изучении проблемы, касающейся учета влияния ионосферы на результаты
спутниковых измерений, безоговорочного предпочтения заслуживают
двухчастотные методы, основные особенности которых достаточно подробно
изложены в опубликованных работах.
Изложенные предпосылки принимались во внимание как при проведении
соответствующих измерений, так и при организации производственного
мониторинга в районе плотины «Саналона», Мексика. К особенностям
организации спутниковых наблюдений следует отнести такие факторы, как
оптимальная длительность сеанса наблюдений, выбор приемников с
соответствующими техническими характеристиками, интервал времени, в
течение которого производят измерения с оптимальными значениями
геометрического фактора.
ГЛАВА 3. ОСНОВНЫЕ РЕКОМЕНДАЦИИ ПО НАБЛЮДЕНИЯМ ЗА ОСАДКАМИ И ДЕФОРМАЦИЯМИ
КРУПНЫХ ИНЖЕНЕРНЫХ СООРУЖЕНИЙ
В главе даются основные рекомендации по наблюдениям за осадками и
деформациями крупных сооружений, периодичности и точности измерений. При
внедрении спутниковых технологий в топографо-геодезическое производство
резко изменились организационные и технологические принципы проведения
полевых и камеральных работ, что дает основание говорить о революционных
изменениях в области геодезических измерений. В настоящее время
спутниковые методы измерений находят все более и более широкое
применение для изучения и мониторинга деформаций крупных инженерных
сооружений. При этом необходимо учитывать, что нормальная высота пунктов
определятся менее точно, кроме того, точность определения изменений
координат пунктов зависит от широты объекта.
На опыте работ показано, что при благоприятном расположении спутников и
при исключении многолучевого распространения сигнала возможно достижение
высокой точности вплоть до нескольких миллиметров. Рассматривается
алгоритм применения топоцентрических прямоугольных координат для
изучения деформаций гидротехнических сооружений. Осадки и горизонтальные
смещения наблюдаемых точек на сооружении определяют как разность их
координат, полученных в различные моменты времени в единой системе
координат. При анализе смещений пунктов в плане и по высоте
целесообразно использовать топоцентрическую прямоугольную систему
координат.
В криволинейной системе координат положение точки P характеризуется
широтой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,
долготой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 и
геодезической высотой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.
Соотношения между геоцентрическими декартовыми координатами и
эллипсоидальными криволинейными координатами имеют вид: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, (1)
где N – радиус кривизны нормального сечения эллипсоида в плоскости
первого вертикала, который равен
picscalex100010009000003a001000004001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c022005400c1200000026060f001a00ffffffff000010000000c0ffffff
aaffffff000c0000ca0400000b00000026060f000c004d61746854797065000030010800
0000fa0200000100000000000000040000002d01000005000000140210042c0305000000
1302ef036f0308000000fa0200000200000000000000040000002d010100050000001402
f0036f03050000001302da04d303040000002d010000050000001402da04d30305000000
130285023804050000001402850238040500000013028502e00b05000000140250020c03
0500000013025002000c1c000000fb0240fe000000000000900101000000040200105469
6d6573204e657720526f6d616e00d89ff377e19ff3772020f577310a66dc040000002d01
020008000000320a5204b60a01000000427908000000320a520414060100000065790800
0000320aad01160701000000617908000000320ac0024e00010000004e791c000000fb02
00ff0000000000009001000000000402001054696d6573204e657720526f6d616e00d89f
f377e19ff3772020f577310a66dc040000002d01030004000000f001020008000000320a
8903e10901000000327908000000320a8903f2060100000032791c000000fb0240fe0000
000000009001000000000402001054696d6573204e657720526f6d616e00d89ff377e19f
f3772020f577310a66dc040000002d01020004000000f001030009000000320a5204ab07
0300000073696e6508000000320a520423040100000031691c000000fb0240fe00000000
00009001000000020002001053796d626f6c0000b30e0af20cfa1200d89ff377e19ff377
2020f577310a66dc040000002d01030004000000f001020008000000320a5204ff040100
00002d6908000000320ac002da01010000003d690a00000026060f000a00ffffffff0100
000000001c000000fb021000070000000000bc02000000cc0102022253797374656d00dc
310a66dc00000a0021008a01000000000200000028fc1200040000002d01020004000000
f0010300030000000000, (2)
Где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 –
большая полуось эллипсоида,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- первый эксцентриситет; (3)
Н – геодезическая высота.
Введем обозначение: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,
(4)
геодезическая высота вычисляется по формуле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. (5)
Для того чтобы вычислить геодезическую высоту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,
необходимо знать широту
picscalex1030100090000039d00000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02c001a0011200000026060f001a00ffffffff000010000000c0ffffff
d7ffffff60010000970100000b00000026060f000c004d61746854797065000020001c00
0000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e0078a4f37781a4f3772030f577240d6693040000002d01000008000000320a80014700
0100000042790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d0000240d669300000a0021008a010000
0000ffffffffbcf31200040000002d01010004000000f0010000030000000000. Для
вычисления широты удобно воспользоваться формулой Боуринга: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, (6)
где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.
Долгота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вычисляется по формуле: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.(7)
Для перехода от геоцентрических координат к топоцентрическим координатам
необходимо выбрать один пункт за исходный. При решении геодезических
задач между точками в пространстве используют систему топоцентрических
декартовых координат, начало координат находится в исходной точке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(picscalex98010009000003c900000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600200021200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffc0010000170200000b00000026060f000c004d61746854797065000060001c00
0000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e0078a4f37781a4f3772030f577ff0a6681040000002d01000008000000320a10025001
0100000069791c000000fb0240fe0000000000009001010000000402001054696d657320
4e657720526f6d616e0078a4f37781a4f3772030f577ff0a6681040000002d0101000400
0000f001000008000000320aa00147000100000042790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
0081ff0a668100000a0021008a010000000000000000e4e31200040000002d0100000400
0000f0010100030000000000,picscalex100010009000003c900000002001c000000000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,picscalex9801000900000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), расположенной обычно на земной поверхности. Ось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расположена на продолжении нормали к поверхности эллипсоида в точке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, ось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расположена в плоскости меридиана точки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 перпендикулярно к оси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 и
направлена в сторону оси вращения эллипсоида, ось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перпендикулярна к осям
picscalex1050100090000039d00000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02200240011200000026060f001a00ffffffff000010000000c0ffffff
d7ffffff00010000f70100000b00000026060f000c004d61746854797065000050001c00
0000fb0240fe0000000000009001000000020002001053796d626f6c0000e5050aebc8e1
120078a4f37781a4f3772030f577730766b8040000002d01000008000000320a80013200
0100000078790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d0000730766b800000a0021008a010000
0000ffffffffe4e31200040000002d01010004000000f0010000030000000000 и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 и
направлена в сторону увеличения долготы.
Связь между декартовыми топоцентрическими и декартовыми геоцентрическими
координатами устанавливается следующим образом: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. (8)
Чтобы найти обратные зависимости, решим эти уравнения относительно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,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 и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. В
результате решения получим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; (9)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; (10)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. (11)
При использовании спутниковой навигационной системы GPS координаты
земных объектов получаются в системе координат WGS-84. При выполнении
геодезических работ обычно используются местные системы координат. При
обработке результатов спутниковых измерений при наблюдениях за
деформациями инженерных сооружений возникает необходимость отделить
осадки наблюдаемых объектов от горизонтальных смещений, поэтому система
координат WGS-84 не полностью отвечает поставленным задачам. В связи с
этим в работе рассмотрен процесс определения средних квадратических
ошибок определения топоцентрических координат.
С этой целью установим зависимость между малыми изменениями декартовых
топоцентрических координат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,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 и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 и
геоцентрических координат начальной точки 1 и конечной точки 2.
Дифференцируем сначала равенство
picscalex100010009000003d202000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002e0221200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffa0220000170200000b00000026060f000c004d61746854797065000060001c00
0000fb02c7fd0901000000009001000000020002001053796d626f6c00000f0d0a6e00e9
1200d89ff377e19ff3772020f577650966b4040000002d01000008000000320a9f019803
0100000028791c000000fb02c7fd0901000000009001000000020002001053796d626f6c
000049080a2400e91200d89ff377e19ff3772020f577650966b4040000002d0101000400
0000f001000008000000320a9f01020d0100000029791c000000fb02c7fd090100000000
9001000000020002001053796d626f6c00000f0d0a6f00e91200d89ff377e19ff3772020
f577650966b4040000002d01000004000000f001010008000000320a9f01c51201000000
28791c000000fb02c7fd0901000000009001000000020002001053796d626f6c00004908
0a2500e91200d89ff377e19ff3772020f577650966b4040000002d01010004000000f001
000008000000320a9f016f1e0100000029791c000000fb0200ff00000000000090010000
00000402001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f5776509
66b4040000002d01000004000000f001010008000000320a100224220100000031790800
0000320afe01dc1d01000000317908000000320afe01821a01000000327908000000320a
12023e1801000000317908000000320a1202a61401000000327908000000320a1002f510
01000000317908000000320a12026f0c01000000317908000000320a12020d0901000000
317908000000320a59016a0701000000327908000000320a12022c050100000032790800
0000320a100205010200000031321c000000fb0240fe0000000000009001000000000402
001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577650966b40400
00002d01010004000000f001000009000000320aa001ed1e0300000073696e6509000000
320aa001001b0300000073696e6509000000320aa0012b1503000000636f736509000000
320aa001870d03000000636f736509000000320aa00178090300000073696e651c000000
fb0240fe0000000000009001000000a10402001054696d6573204e657720526f6d616e00
d89ff377e19ff3772020f577650966b4040000002d01000004000000f001010008000000
320aa001320001000000ee691c000000fb0240fe00000000000090010100000004020010
54696d6573204e657720526f6d616e00d89ff377e19ff3772020f577650966b404000000
2d01010004000000f001000008000000320aa001312101000000426908000000320aa001
241d010000004c6908000000320aa001921901000000596908000000320aa00186170100
00004c6908000000320aa001781301000000586908000000320aa0010210010000004269
08000000320aa0019c0b01000000426908000000320aa001fb07010000004e6908000000
320aa001a80601000000656908000000320aa0012f04010000005a691c000000fb0240fe
0000000000009001000000020002001053796d626f6c00000f0d0a72d0e91200d89ff377
e19ff3772020f577650966b4040000002d01000004000000f001010008000000320aa001
b718010000002b6908000000320aa001be11010000002d6908000000320aa001b8050100
00002b6908000000320aa0017102010000003d690a00000026060f000a00ffffffff0100
000000001c000000fb021000070000000000bc02000000cc0102022253797374656d00b4
650966b400000a0021008a010000000001000000eceb1200040000002d01010004000000
f0010000030000000000.
Переменными величинами являются координаты пунктов в геоцентрической
системе координат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,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,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 и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,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,
picscalex98010009000003c900000002001c00000000000500000009020000000005000
000020101000000050000000102ffffff00050000002e0118000000050000000b0200000
000050000000c02600240021200000026060f001a00ffffffff000010000000c0ffffffb
7ffffff00020000170200000b00000026060f000c004d61746854797065000060001c000
000fb02c0fe0000000000009001000000000402001054696d6573204e657720526f6d616
e0078a4f37781a4f3772030f5772d0b66be040000002d01000008000000320a100259010
100000032791c000000fb0240fe0000000000009001010000000402001054696d6573204
e657720526f6d616e0078a4f37781a4f3772030f5772d0b66be040000002d01010004000
000f001000008000000320aa0014000010000005a790a00000026060f000a00ffffffff0
100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d0
0be2d0b66be00000a0021008a010000000000000000bcf31200040000002d01000004000
000f0010100030000000000:
picscalex1000100090000033405000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02c00a40321200000026060f001a00ffffffff000010000000c0ffffff
b3ffffff00320000730a00000b00000026060f000c004d61746854797065000000021c00
0000fb0243fde300000000009001000000020002001053796d626f6c00007f0e0ac05cec
1200b8aef377c1aef3772040f577131466c0040000002d01000008000000320a67024804
010000005b791c000000fb0243fde300000000009001000000020002001053796d626f6c
00003e0e0a7b5cec1200b8aef377c1aef3772040f577131466c0040000002d0101000400
0000f001000008000000320a67020f2e010000005d7908000000fa020000100000000000
0000040000002d0100000500000014020a02852e0500000013020a02d2301c000000fb02
f3fde300000000009001000000020002001053796d626f6c00007f0e0ac134ec1200b8ae
f377c1aef3772040f577131466c0040000002d01020004000000f001010008000000320a
bf06770b010000005b791c000000fb02f3fde30000000000900100000002000200105379
6d626f6c00003e0e0a7c34ec1200b8aef377c1aef3772040f577131466c0040000002d01
010004000000f001020008000000320abf069a17010000005d7905000000140260062218
0500000013026006571a1c000000fb0280fe000000000000900100000000040200105469
6d6573204e657720526f6d616e00b8aef377c1aef3772040f577131466c0040000002d01
020004000000f001010008000000320a1f0a2c27010000002e7909000000320a1f0af620
03000000636f736509000000320a1f0a161a0300000073696e6509000000320a1f0aa116
0300000073696e6509000000320a1f0a790f0300000073696e6509000000320a1f0ad40b
03000000636f736509000000320ac006da2003000000636f736509000000320ac006471d
0300000073696e6509000000320ac0060f1403000000636f736509000000320ac006e30d
0300000073696e6508000000320a6a02852d01000000296909000000320a6a022e2a0300
000073696e6509000000320a6a02d22303000000636f736508000000320a6a0241210100
0000286f09000000320a6a02a21d03000000636f736509000000320a6a02231803000000
636f736508000000320a6a02261301000000296f09000000320a6a02b70f030000007369
6e6508000000320a6a02190901000000286909000000320a6a02aa050300000073696e65
1c000000fb0220ff0000000000009001000000000402001054696d6573204e657720526f
6d616e00b8aef377c1aef3772040f577131466c0040000002d01010004000000f0010200
08000000320a7f0a352601000000326908000000320a7f0a032401000000316908000000
320a7f0afb1e01000000326908000000320a7f0af31c01000000316908000000320a7f0a
661901000000316908000000320a7f0ab21401000000326908000000320a7f0a56120100
0000316908000000320a7f0ac90e01000000316908000000320a20072a26010000003169
08000000320a2007e72301000000316908000000320a2007242001000000316908000000
320a1406861c01000000326908000000320a2906b71901000000316908000000320a2007
041701000000316908000000320a2007481301000000326908000000320a2007a8100100
0000316908000000320a2007220d01000000326908000000320ad3013230010000003169
08000000320aca02f32c01000000316908000000320aca026d2901000000326908000000
320aca02c72601000000316908000000320aca020b2301000000326908000000320aca02
af2001000000316908000000320aa201ad1b01000000326908000000320aca02301b0100
0000316908000000320aca026d1701000000316908000000320abe01c715010000003269
08000000320aca02941201000000316908000000320aca02070f01000000316908000000
320abe01610d01000000326908000000320aca02a10a01000000326908000000320aca02
870801000000316908000000320aca02bb010200000031321c000000fb0280fe00000000
00009001010000000402001054696d6573204e657720526f6d616e00b8aef377c1aef377
2040f577131466c0040000002d01020004000000f001010008000000320a1f0a7d240200
0000645a08000000320a1f0a302301000000425a08000000320a1f0a6d1d020000006459
08000000320a1f0a201c01000000425908000000320a1f0aab18010000004c5908000000
320a1f0ad01202000000645808000000320a1f0a831101000000425808000000320a1f0a
0e0e010000004c5808000000320ac006612402000000644e08000000320ac00614230100
0000424e08000000320ac006511f01000000424e08000000320ac006c11b01000000654e
08000000320ac9053c1802000000644c08000000320ac0064916010000004c4c08000000
320ac0067a1201000000594c08000000320ac006ed0f010000004c4c08000000320ac006
000c01000000584c08000000320a73019f2e02000000644208000000320a6a02382c0100
00004c4208000000320a6a029f2801000000594208000000320a6a020c26010000004c42
08000000320a6a02e92101000000584208000000320a6a02dc1f01000000424208000000
320a6a025d1a01000000424208000000320a6a026416010000004e4208000000320a6a02
021501000000654208000000320a6a02c11101000000424208000000320a6a02fe0d0100
00004e4208000000320a6a029c0c01000000654208000000320a6a02a909010000005a42
08000000320a6a02b40701000000424208000000320a6a023a000100000064421c000000
fb0280fe0000000000009001000000020002001053796d626f6c00003e0e0a7e2ced1200
b8aef377c1aef3772040f577131466c0040000002d01010004000000f001020008000000
320a1f0ade1f010000002b4208000000320a1f0a9515010000002d4208000000320a1f0a
c20a010000002d4208000000320ac006fc26010000002d4208000000320ac006a91a0100
00002b4208000000320ac0067a11010000002d4208000000320ac006690a010000002b42
08000000320a6a022431010000002b4208000000320a6a029927010000002b4208000000
320a6a02901c010000002d4208000000320a6a02ea13010000002b4208000000320a6a02
840b010000002b4208000000320a6a029e04010000002d4208000000320a6a0224030100
00003d421c000000fb0280fe0000000000009001010000020402001053796d626f6c0000
7f0e0ac42ced1200b8aef377c1aef3772040f577131466c0040000002d01020004000000
f001010008000000320aeb07cd1801000000724208000000320a95033c2f010000007242
08000000320a6a02fa000100000078420a00000026060f000a00ffffffff010000000000
1c000000fb021000070000000000bc02000000cc0102022253797374656d00c0131466c0
00000a0021008a01000000000100000048ef1200040000002d01010004000000f0010200
030000000000 (12)
Для нахождения зависимости дифференциала широты от изменений декартовых
координат дифференцируем формулу Боуринга (6):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. (13)
В свою очередь
picscalex99010009000003a701000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02e004a00e1200000026060f001a00ffffffff000010000000c0ffffff
abffffff600e00008b0400000b00000026060f000c004d61746854797065000000010800
0000fa0200000100000000000000040000002d0100000500000014027002290205000000
13027002f40305000000140270023a060500000013027002de080500000014027002350a
05000000130270024e0c1c000000fb0240fe000000000000900101000000040200105469
6d6573204e657720526f6d616e00d89ff377e19ff3772020f5773f0e661a040000002d01
010008000000320ae002740c02000000645208000000320a38045c0a0100000052520800
0000320acc017c0a010000005a5208000000320a38040b0701000000525208000000320a
cc01530602000000645a08000000320a38048d0201000000525a08000000320acc014902
010000005a5a08000000320ae002390001000000645a1c000000fb0200ff000000000000
9001000000000402001054696d6573204e657720526f6d616e00d89ff377e19ff3772020
f5773f0e661a040000002d01020004000000f001010008000000320a6f038e0b01000000
325a08000000320a3c027a0b01000000315a08000000320a3c02310801000000315a0800
0000320a3c02470301000000315a1c000000fb0240fe0000000000009001000000020002
001053796d626f6c00006f0d0a33d0e91200d89ff377e19ff3772020f5773f0e661a0400
00002d01010004000000f001020008000000320ae0021309010000002d5a08000000320a
e0020905010000003d5a08000000320a11032c0401000000f75a08000000320a68042c04
01000000f85a08000000320af2012c0401000000f65a08000000320a1103430101000000
e75a08000000320a6804430101000000e85a08000000320af201430101000000e65a0a00
000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc020000
00cc0102022253797374656d001a3f0e661a00000a0021008a010000000002000000eceb
1200040000002d01020004000000f0010100030000000000. (14)
Величину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определим из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: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,
следовательно,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. (15)
Зависимость изменения широты пункта от изменений декартовых
геоцентрических координат окончательно представим в виде: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 (16)
где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.
Представим формулу (16) более компактно, с этой целью введем
обозначения: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 (17)
С учетом (17) формулу (16) представим в виде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. (18)
Для нахождения изменения долготы дифференцируем формулу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: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. (19)
Зависимость изменения радиуса кривизна первого вертикала найдем из
picscalex97010009000003a001000004001c00000000000500000009020000000005000
000020101000000050000000102ffffff00050000002e0118000000050000000b0200000
000050000000c020005200c1200000026060f001a00ffffffff000010000000c0ffffffa
dffffffe00b0000ad0400000b00000026060f000c004d617468547970650000200108000
000fa0200001000000000000000040000002d010000050000001402fb03f202050000001
302da032d0308000000fa0200002000000000000000040000002d010100050000001402e
2032d030500000013029a048203040000002d0100000500000014029a048a03050000001
3028d02f6030500000014028d02f6030500000013028d02a10b0500000014025002ca020
500000013025002c10b1c000000fb0240fe0000000000009001010000000402001054696
d6573204e657720526f6d616e0078a4f37781a4f3772030f57780086639040000002d010
20008000000320a9304780a01000000427908000000320a9304af0501000000657908000
000320aaa01d50601000000617908000000320ac0024e00010000004e791c000000fb02c
0fe0000000000009001000000000402001054696d6573204e657720526f6d616e0078a4f
37781a4f3772030f57780086639040000002d01030004000000f001020008000000320ac
a038c0901000000327908000000320aca038a060100000032791c000000fb0240fe00000
00000009001000000000402001054696d6573204e657720526f6d616e0078a4f37781a4f
3772030f57780086639040000002d01020004000000f001030009000000320a93045a070
300000073696e6508000000320a9304e1030100000031691c000000fb0240fe000000000
0009001000000020002001053796d626f6c0000810b0ab340f1120078a4f37781a4f3772
030f57780086639040000002d01030004000000f001020008000000320a9304ac0401000
0002d6908000000320ac002b901010000003d690a00000026060f000a00ffffffff01000
00000001c000000fb021000070000000000bc02000000cc0102022253797374656d00398
008663900000a0021008a0100000000020000005cf31200040000002d01020004000000f
0010300030000000000,
следовательно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. (20)
Подставив значения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,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 и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 в уравнение (12), имеем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000000000, (21)
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;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;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.
Аналогично дифференцируем равенство (10):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. (22)
С учетом (19) представим (22) в следующем виде:
picscalex94010009000003cd03000003001c00000000000500000009020000000005000
000020101000000050000000102ffffff00050000002e0118000000050000000b0200000
000050000000c02400800371200000026060f001a00ffffffff000010000000c0ffffffc
0ffffffc0360000000800000b00000026060f000c004d617468547970650000e00108000
000fa0200001000000000000000040000002d010000050000001402bd026005050000001
302bd028d0d050000001402bd02bc0e050000001302bd02041a050000001402bd026d200
50000001302bd026327050000001402bd028a28050000001302bd029b321c000000fb024
0fe0000000000009001000000000402001054696d6573204e657720526f6d616e0078a4f
37781a4f3772030f57752076640040000002d01010008000000320a7107d412010000002
e7909000000320a7107720c03000000636f736509000000320a7107eb040300000073696
e6509000000320a1802d92d03000000636f736509000000320a18022c2a0300000073696
e6509000000320a1802b52203000000636f736509000000320a1802421503000000636f7
36509000000320a180295110300000073696e6509000000320a1802df0803000000636f7
3651c000000fb02c0fe0000000000009001000000000402001054696d6573204e6577205
26f6d616e0078a4f37781a4f3772030f57752076640040000002d01020004000000f0010
10008000000320ae107f91101000000326f08000000320ae107a40f01000000316f08000
000320ae1079c0a01000000326f08000000320ae107e60701000000316f08000000320a9
d03183501000000316f08000000320af604e12d01000000316f08000000320a8802df310
1000000316f08000000320a4f013b3001000000326f08000000320a8802272d010000003
16f08000000320a8802682901000000326f08000000320af604372401000000316f08000
000320a8802a72601000000316f08000000320a4f010d2501000000336f08000000320a8
802ea2101000000326f08000000320a9d03e21c01000000316f08000000320adf03ee140
1000000326f08000000320a2a05571401000000316f08000000320a88024819010000003
16f08000000320a4f01a41701000000326f08000000320a8802901401000000316f08000
000320a8802d11001000000326f08000000320a8802770f01000000316f08000000320ad
f03040a01000000326f08000000320a2a056d0901000000316f08000000320a8802d10c0
1000000316f08000000320a4f01370b01000000336f08000000320a88021408010000003
26f08000000320a88021b0601000000316f08000000320a9d0303020200000031321c000
000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d616
e0078a4f37781a4f3772030f57752076640040000002d01010004000000f001020008000
000320a7107391002000000645908000000320a7107e00e010000004c5908000000320a7
1077b0802000000645808000000320a71072207010000004c5808000000320a2d037b330
2000000645908000000320a8604c32c01000000585908000000320a18021b31010000004
c5908000000320a1802632c010000004c5908000000320a1802882801000000595908000
000320a8604192301000000585908000000320a1802e325010000004c5908000000320a1
802a92001000000585908000000320a2d03e41a02000000645808000000320aba0439130
1000000585808000000320a18028418010000004c5808000000320a1802cc13010000004
c5808000000320a1802f10f01000000595808000000320a1802ba0e01000000595808000
000320aba044f0801000000585808000000320a18020d0c010000004c5808000000320a1
802d30601000000585808000000320a18025e0501000000595808000000320a2d0339000
100000064581c000000fb0240fe0000000000009001000000020002001053796d626f6c0
000e7080a5e94de120078a4f37781a4f3772030f57752076640040000002d01020004000
000f001010008000000320a71076e0b010000002b5808000000320a7107f603010000002
d5808000000320a2d03d135010000002d5808000000320a9703b73201000000fa5808000
000320a0d05b73201000000fb5808000000320ae701b73201000000f95808000000320a9
703ad1e01000000ea5808000000320a0d05ad1e01000000eb5808000000320ae701ad1e0
1000000e95808000000320a2d038027010000002d5808000000320a2d03631f010000002
d5808000000320a2d039b1d010000002b5808000000320a8d03201a01000000fa5808000
000320a1705201a01000000fb5808000000320add01201a01000000f95808000000320a8
d03a30401000000ea5808000000320a1705a30401000000eb5808000000320add01a3040
1000000e95808000000320a2d03aa0d010000002b5808000000320a2d038703010000003
d5808000000320a2d0319010100000068580a00000026060f000a00ffffffff010000000
0001c000000fb021000070000000000bc02000000cc0102022253797374656d004052076
64000000a0021008a010000000001000000b0e01200040000002d01010004000000f0010
200030000000000
Введем обозначения и представим (22) в виде: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, (23)
где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,pic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,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,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.
Дифференцируя уравнение (11), получим: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 (24)
Для определения величины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 дифференцируем уравнение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,
следовательно,
picscalex1000100090000035f03000003001c000000000005000000090200000000050
00000020101000000050000000102ffffff00050000002e0118000000050000000b02000
00000050000000c026005602e1200000026060f001a00ffffffff000010000000c0fffff
fa1ffffff202e0000010500000b00000026060f000c004d6174685479706500003001080
00000fa0200000100000000000000040000002d01000005000000140290026d040500000
013029002d4090500000014029002f60d05000000130290025d1305000000140290021c1
70500000013029002171c0500000014029002441c0500000013029002db1e1c000000fb0
243fd0901000000009001000000020002001053796d626f6c000036100a0fc4e81200d89
ff377e19ff3772020f5777114660d040000002d01010008000000320aa30445200100000
028791c000000fb0243fd0901000000009001000000020002001053796d626f6c0000691
30a9fc4e81200d89ff377e19ff3772020f5777114660d040000002d01020004000000f00
1010008000000320aa304c02801000000297905000000140290023220050000001302900
2dd2a0500000014029002852b05000000130290021c2e1c000000fb0240fe00000000000
09001000000020002001053796d626f6c000036100a1034ea1200d89ff377e19ff377202
0f5777114660d040000002d01010004000000f001020008000000320a5804562c0100000
0727908000000320a0003fd2a01000000d77908000000320aaa046b21010000002d79080
00000320a0003101f010000002d7908000000320a5804151d01000000727908000000320
a0003f215010000002b7908000000320a0003cc0c010000002b7908000000320a00033c0
3010000003d791c000000fb0200ff0000000000009001000000000402001054696d65732
04e657720526f6d616e00d89ff377e19ff3772020f5777114660d040000002d010200040
00000f001010008000000320a5c026f2d01000000317908000000320a89031d2a0100000
0327908000000320a8903bb29010000002f7908000000320a89033129010000003379080
00000320a1a05102801000000317908000000320ae1034b2601000000327908000000320
ae1035d2301000000327908000000320a5c02902801000000317908000000320a2301c02
301000000327908000000320a5c022e1e01000000317908000000320ac804651b0100000
0317908000000320a8f03a01901000000327908000000320a5c02591a010000003179080
00000320a7003301501000000317908000000320ac804b01201000000317908000000320
a5c02b81001000000317908000000320a70030a0c01000000317908000000320ac804270
901000000317908000000320a5c02800701000000317908000000320a70036b020100000
031791c000000fb0240fe0000000000009001000000000402001054696d6573204e65772
0526f6d616e00d89ff377e19ff3772020f5777114660d040000002d01010004000000f00
1020009000000320aaa0415240300000073696e6508000000320aaa048e2001000000316
908000000320aec01ab2601000000326909000000320aec0178240300000073696e65090
00000320a5804321703000000636f736509000000320aec0127170300000073696e65090
00000320a5804460f03000000636f736509000000320a5804bd0503000000636f73651c0
00000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d6
16e00d89ff377e19ff3772020f5777114660d040000002d01020004000000f0010100080
00000320aec019e2b02000000644208000000320aaa041f2701000000424208000000320
aaa047f2201000000654208000000320aec019f2701000000424208000000320aec01e22
201000000654208000000320aec01ea2101000000614208000000320aec015d1c0200000
0644208000000320a5804741a01000000424208000000320aec01ed1a010000005242080
00000320aec01681901000000424208000000320a0003831302000000645908000000320
a5804bf1101000000425908000000320a58041d0e01000000525908000000320aec01eb0
f01000000595908000000320a0003fa0902000000645808000000320a580436080100000
0425808000000320a5804940401000000525808000000320aec015006010000005858080
00000320a000339000200000064480a00000026060f000a00ffffffff0100000000001c0
00000fb021000070000000000bc02000000cc0102022253797374656d000d7114660d000
00a0021008a01000000000100000050ec1200040000002d01010004000000f0010200030
000000000. (25)
Подставив значения (19), (20) и (25) в уравнение (24), получим
дифференциальную формулу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, (26)
где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picscalex950100090000030b06000003001c00000000000500000009020000000005000
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9000000320ae40147180300000073696e6508000000320ae401f71201000000296909000
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01054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577820c668c04000
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20008000000320a54025301010000007a6f1c000000fb0240fe000000000000900101000
0000402001054696d6573204e657720526f6d616e00d89ff377e19ff3772020f577820c6
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26f08000000320a18087b2c01000000426f08000000320a1808c62701000000656f08000
000320aa805ee2c01000000426f08000000320aa805422702000000616508000000320ac
006962301000000426508000000320ac006e11e01000000656508000000320a1808421a0
1000000586508000000320aa805001c010000004c6508000000320ac0068116010000004
26508000000320ac0065f1201000000426508000000320ac006300e01000000596508000
000320ac006840b010000004c6508000000320ac006a10701000000426508000000320ac
006100301000000586508000000320ae401d63301000000426508000000320ae4014a310
10000004c6508000000320ae4015a2d01000000596508000000320ae401ae2a010000004
c6508000000320ae4011d2601000000586508000000320ae401c02301000000426508000
000320ae401ad1e01000000426508000000320ae4018b1a01000000426508000000320ae
4016916010000004e6508000000320ae401d51401000000656508000000320ae4015e110
1000000426508000000320ae4013c0d010000004e6508000000320ae401a80b010000006
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000320ae40147000100000042650a00000026060f000a00ffffffff0100000000001c000
000fb021000070000000000bc02000000cc0102022253797374656d008c820c668c00000
a0021008a01000000000100000028fc1200040000002d01010004000000f001020003000
0000000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;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;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.
Используя ранее полученные выражения (21), (23) и (26), получим
следующие дифференциальные формулы:
picscalex1000100090000030902000002001c000000000005000000090200000000050
00000020101000000050000000102ffffff00050000002e0118000000050000000b02000
00000050000000c02a00240251200000026060f001a00ffffffff000010000000c0fffff
fb7ffffff00250000570200000b00000026060f000c004d61746854797065000080001c0
00000fb0200ff0000000000009001000000000402001054696d6573204e657720526f6d6
16e00d89ff377e19ff3772020f5775410668a040000002d01000008000000320a1002892
401000000327908000000320a1002e51e01000000327908000000320a10024f190100000
0327908000000320a1002481301000000317908000000320a1002b20d010000003179080
00000320a10025a0801000000317908000000320a1002f4010200000031321c000000fb0
240fe0000000000009001010000000402001054696d6573204e657720526f6d616e00d89
ff377e19ff3772020f5775410668a040000002d01010004000000f001000008000000320
aa0018b2202000000645a08000000320aa001f72001000000465a08000000320aa001181
d02000000645908000000320aa001611b01000000455908000000320aa00120170200000
0645808000000320aa001461501000000445808000000320aa001661102000000645a080
00000320aa001940f01000000435a08000000320aa001010c02000000645908000000320
aa001580a01000000425908000000320aa001470602000000645808000000320aa001b40
401000000415808000000320aa00139000100000064581c000000fb0200ff00000000000
09001000000020002001053796d626f6c000090120ae30cfa1200d89ff377e19ff377202
0f5775410668a040000002d01000004000000f001010008000000320a1002ee210100000
0785808000000320a10027b1c01000000785808000000320a10028316010000007858080
00000320a1002c91001000000785808000000320a1002640b01000000785808000000320
a1002aa050100000078581c000000fb0240fe00000000000090010000000200020010537
96d626f6c00006e120aba0cfa1200d89ff377e19ff3772020f5775410668a040000002d0
1010004000000f001000008000000320aa001c21f010000002b5808000000320aa0012c1
a010000002b5808000000320aa0011114010000002b5808000000320aa0017b0e0100000
02b5808000000320aa0012309010000002b5808000000320aa0016103010000003d58080
00000320aa00119010100000078580a00000026060f000a00ffffffff0100000000001c0
00000fb021000070000000000bc02000000cc0102022253797374656d008a5410668a000
00a0021008a01000000000000000028fc1200040000002d01000004000000f0010100030
000000000;
picscalex100010009000003b901000002001c000000000005000000090200000000050
00000020101000000050000000102ffffff00050000002e0118000000050000000b02000
00000050000000c02a002801a1200000026060f001a00ffffffff000010000000c0fffff
fb7ffffff401a0000570200000b00000026060f000c004d61746854797065000080001c0
00000fb0200ff0000000000009001000000000402001054696d6573204e657720526f6d6
16e00d89ff377e19ff3772020f577f812668a040000002d01000008000000320a1002c11
901000000327908000000320a1002f41301000000327908000000320a1002fd0d0100000
0317908000000320a1002910801000000317908000000320a100217020200000031321c0
00000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d6
16e00d89ff377e19ff3772020f577f812668a040000002d01010004000000f0010000080
00000320aa001f41702000000645908000000320aa001061601000000445908000000320
aa001c51102000000645808000000320aa001df0f01000000435808000000320aa0014c0
c02000000645908000000320aa0018f0a01000000425908000000320aa0017e060200000
0645808000000320aa001d70401000000415808000000320aa00139000100000064581c0
00000fb0200ff0000000000009001000000020002001053796d626f6c000045140a7b0cf
a1200d89ff377e19ff3772020f577f812668a040000002d01000004000000f0010100080
00000320a1002431701000000685808000000320a1002141101000000685808000000320
a10029b0b01000000685808000000320a1002cd050100000068581c000000fb0240fe000
0000000009001000000020002001053796d626f6c000032140a9b0cfa1200d89ff377e19
ff3772020f577f812668a040000002d01010004000000f001000008000000320aa001d11
4010000002b5808000000320aa001c60e010000002b5808000000320aa0015a090100000
02b5808000000320aa0018403010000003d5808000000320aa00119010100000068580a0
0000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc02000
000cc0102022253797374656d008af812668a00000a0021008a01000000000000000028f
c1200040000002d01000004000000f0010100030000000000; (27)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.
Переходя к средним квадратическим ошибкам, окончательно получим: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picscalex1000100090000039502000002001c000000000005000000090200000000050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 (28)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.
Характерной особенностью этих формул является то, что в них
используются, кроме геодезических координат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,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,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 исходной точки, координаты пунктов 1 и 2 в
геоцентрической системе координат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,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,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 и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,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,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. Точность этих формул зависит только от
величины средних квадратических ошибок геоцентрических прямоугольных
координат пунктов 1 и 2. На основе этого анализа сделан вывод о
целесообразности использования топоцентрических прямоугольных координат
для изучения деформаций энергетических объектов в условиях Мексики.
ГЛАВА 4. РАЗРАБОТКА МЕТОДИКИ ОПРЕДЕЛЕНИЯ ОСАДОК И ДЕФОРМАЦИЙ
СПУТНИКОВЫМИ МЕТОДАМИ И МЕТОДОВ ОБРАБОТКИ
С целью экспериментальной проверки предлагаемой методики анализа
результатов спутниковых измерений за осадками и смещениями плотины
«Саналона» были проведены работы по созданию геодезической сети
спутниковыми методами в районе водохранилища.
Водохранилище находится на западном склоне Сьерра Мадре Оксиденталь
(западная горная цепь Мадре) в ее нижних отрогах. В данной местности
преобладают вулканические горные породы, главным образом интрузивные
базальты. Плотина Саналона (из грунтовых материалов) была построена на
реке Тамазула в 32 км западнее от города Кульякан штата Синалоа
(Мексика). Она представляет собой земляной вал, с левой стороны
находится дамба и на правом краю водослив в виде веера со свободным
гребнем. Слив плотины Саналона сделан в основном из гранита, который в
своей верхней части имеет участок с ярко выраженной альтерацией,
доходящей до глубин около 20,0 м.
Как уже отмечалось ранее, при решении данной проблемы установлена
целесообразность применения сетевого метода построений. По такому
принципу реализована, в частности, локальная сеть в зоне изучаемого
объекта. Для иллюстрации на рис. 1 приведена схема расположения опорных
и рабочих пунктов.
picscalex960100090000037800000002001c00000000000400000003010800050000000
b0200000000050000000c020e040907040000002e0118001c000000fb021000070000000
000bc02000000cc0102022253797374656d000409070000e2120000985c110004ee83398
068350c0c020000040000002d01000004000000020101001c000000fb02ceff000000000
0009001000000cc0440001254696d6573204e657720526f6d616e0000000000000000000
000000000000000040000002d010100050000000902000000020d000000320a2d0000000
10004000000000008070e04206a1600040000002d01000003000000000025
Рабочие пункты CASETA, B, A и TEMPLETE находятся на гребне плотины, а
опорные – вне зоны деформации в стабильных и прочных породах.
На плотине «Саналона» за исходные пункты приняты точки: CACTUS, LOMA и
CULEBRA, расположенные в нижнем бьефе за пределами зоны деформаций.
Основное требование, предъявляемое к опорным пунктам и к технологии их
закрепления на местности, сводится к обеспечению максимальной
стабильности их местоположения в течение времени.
В общем комплексе экспериментальных исследований, относящихся к
принципам построения локальных спутниковых геодезических сетей, должное
внимание было уделено также обоснованию выбора длительности сеанса
наблюдений, которая позволяет производить спутниковые определения на
требуемом уровне точности.
В результате анализа опубликованных работ, было решено при производстве
работ на плотине проводить сеансы наблюдений в течении одного часа.
Измерения на всех пунктах производились двухчастотными геодезическими
приемниками: 4 приемника «Z-200» фирмы ASTECH.
При условии соблюдения всех технических требований, погрешность взаимных
положений двух смежных пунктов этими типами приемников не должна
превышать 3-5 мм соответственно.
В таблице 1 приведены пространственные прямоугольные координаты X, Y, Z
и геодезические эллипсоидальные координаты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,picscalex100010009000003c900000002001c000000000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,picscalex1000100090000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 рабочих пунктов первого цикла наблюдений, полученные в результате
уравнивания базисных векторов с учетом их ковариационных матриц по
рекуррентному алгоритму с контролем и исключением грубых ошибок.
Средние квадратические ошибки пространственных прямоугольных координат
X, Y, Z рабочих пунктов из уравнивания даны в табл. 2
В таблице 3 приведены топоцентрические декартовые координаты рабочих
пунктов и их оценка точности, выполненная по формулам (28),
разработанным автором диссертационной работы.
Таблица 1
Рабочие пунктыX, м
Широта [С]Y, м
Долгота [З]Z, м
Высота,
мCASETA-1708627,31678-5535015,699232660596,8947424°48’55,95470″107°09’18
,5558″129,87617A-1707987,94741-5535267,220022660478,7931924°48’51,7647″1
07°08’54,1609″127,31152B-1708047,09865-5535251,727712660473,0477924°48’5
1,5592″107°08’56,3362″127,29411TEMP-1707602,55450-5535310,997172660636,9
994124°48’57,4106″107°08’40,5885″128,54945
Таблица 2
Рабочие
пунктыpicscalex100010009000003c900000002001c0000000000050000000902000000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,
ммpicscalex100010009000003c900000002001c00000000000500000009020000000005
000000020101000000050000000102ffffff00050000002e0118000000050000000b0200
000000050000000c02600280021200000026060f001a00ffffffff000010000000c0ffff
ffb7ffffff40020000170200000b00000026060f000c004d61746854797065000060001c
000000fb02c0fe0000000000009001010000000402001054696d6573204e657720526f6d
616e0078a4f37781a4f3772030f5776607663f040000002d01000008000000320a10025f
010100000059791c000000fb0240fe0000000000009001010000000402001054696d6573
204e657720526f6d616e0078a4f37781a4f3772030f5776607663f040000002d01010004
000000f001000008000000320aa0013900010000006d790a00000026060f000a00ffffff
ff0100000000001c000000fb021000070000000000bc02000000cc010202225379737465
6d003f6607663f00000a0021008a010000000000000000bcf31200040000002d01000004
000000f0010100030000000000,
ммpicscalex100010009000003c900000002001c00000000000500000009020000000005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,
ммCASETA3,68,13,3A3,47,43,4B2,96,83,7TEMPLETE3,38,34,2
Таблица 3
Рабочие
пунктыpicscalex970100090000039d00000002001c00000000000500000009020000000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,
мpicscalex100010009000003c900000002001c000000000005000000090200000000050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,
ммpicscalex1010100090000039d00000002001c00000000000500000009020000000005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,
мpicscalex101010009000003c900000002001c000000000005000000090200000000050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,
ммpicscalex1010100090000039d00000002001c00000000000500000009020000000005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,
мpicscalex97010009000003c900000002001c0000000000050000000902000000000500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,
ммCASETA677,401604,3-515,660114,148,803937,2A548,463244,4169,447434,746,
270316,5B542,140863,5108,358013,946,254785,4TEMP722,200864,1550,612945,3
47,469357,1
Из табл. 2 и 3, видно, что точность топоцентрических прямоугольных
координат после перехода от геоцентрических к топоцентрическим
прямоугольным координатам остается практически одной и тоже.
Основная цель проведенных в этой области экспериментов состояла в
практическом подтверждении эффективности действия изложенных выше
предпосылок, изыскании надежных критериев оценки применения
топоцентрических декартовых координат и конкретизации практической
реализации рекомендуемых методов.
В таблице 4 приведены топоцентрические декартовые координаты, полученные
по результатам наблюдений в период с января 2005 г. по июль 2006 г.
В табл. 5, 6, 7 и 8 приведены уклонения координат рабочих пунктов от
начального момента в каждом цикле измерений.
Таблица 4
Рабочие пунктыДата наблюденийТопоцентрические декартовые координаты
рабочих
пунктовpicscalex970100090000039d00000002001c0000000000050000000902000000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,
мpicscalex1010100090000039d00000002001c000000000005000000090200000000050
00000020101000000050000000102ffffff00050000002e0118000000050000000b02000
00000050000000c02c00160011200000026060f001a00ffffffff000010000000c0fffff
f3700000020010000f70100000b00000026060f000c004d61746854797065000050001c0
00000fb0240fe0000000000009001000000020002001053796d626f6c000060150aef0cf
a1200d89ff377e19ff3772020f5774b086608040000002d01000008000000320a2001320
00100000068790a00000026060f000a00ffffffff0100000000001c000000fb021000070
000000000bc02000000cc0102022253797374656d00004b08660800000a0021008a01000
00000ffffffff28fc1200040000002d01010004000000f0010000030000000000,
мpicscalex1010100090000039d00000002001c000000000005000000090200000000050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,
мCAST24-25.01.2005
18-19.07.2005
11-12.01.2006
02-03.07.2006677,40160
,40722
,41047
,40474-515,66011
,65871
,66721
,6630148,80393
,79822
,79617
,79432A24-25.01.2005
18-19.07.2005
11-12.01.2006
02-03.07.2006548,46324
,46075
,47016
,46383169,44743
,45062
,44621
,4516446,27031
,26715
,26426
,26241B24-25.01.2005
18-19.07.2005
11-12.01.2006
02-03.07.2006542,14086
,13518
,13987
,13629108,35801
,35019
,35211
,3565146,25478
,24935
,25116
,24675TEMP24-25.01.2005
18-19.07.2005
11-12.01.2006
02-03.07.2006722,20086
,20913
,20399
,20649550,61294
,61961
,61651
,6205347,46935
,46615
,46487
,46252
Таблица 5
Рабочий пункт CAST№
ЦикловИнтервал времени
(сутки)picscalex1000100090000031d01000002001c000000000005000000090200000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,
ммpicscalex1000100090000031d01000002001c00000000000500000009020000000005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,
ммpicscalex1000100090000031d01000002001c00000000000500000009020000000005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,
мм000001176+5+1-62354+8+7-83527+3+3-10
Таблица 6
Рабочий пункт A№
ЦикловИнтервал времени
(сутки)picscalex1000100090000031d01000002001c000000000005000000090200000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(в
мм)picscalex1000100090000031d01000002001c0000000000050000000902000000000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(в
мм)picscalex1000100090000031d01000002001c0000000000050000000902000000000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(в мм)000001176-3+4-32354-2-1-63527+1+5-8
Таблица 7
Рабочий пункт B№ цикловИнтервал времени
(сутки)picscalex1000100090000031d01000002001c000000000005000000090200000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 (в
мм)picscalex1000100090000031d01000002001c0000000000050000000902000000000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 (в
мм)picscalex1000100090000031d01000002001c0000000000050000000902000000000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 (в мм)000001176-6-8-62354-1-6-43527-5-2-8
Таблица 8
Рабочий пункт TEMP№
цикловИнтервал времени
(сутки)picscalex1000100090000031d01000002001c000000000005000000090200000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(в
мм)picscalex1000100090000031d01000002001c0000000000050000000902000000000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(в
мм)picscalex1000100090000031d01000002001c0000000000050000000902000000000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(в
мм)000001176+8+7-32354+3+3-43527+5+7-7picscalex1000100090000035100000000
001200000000000500000009020000000005000000020101000000050000000102ffffff
00050000002e0118000000050000000b0200000000050000000c02200220011200000026
060f001a00ffffffff000010000000c0ffffffa6ffffffe0000000c60100000b00000026
060f000c004d61746854797065000050000a00000026060f000a00ffffffff0100000000
00030000000000
Из рассмотрения этих графиков представляется возможным сделать выводы:
1. Средние квадратические погрешности определения смещений и осадок
рабочих пунктов составили соответственно по осям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,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,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, а предельные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,picscalex10001000900000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,picscalex1000100090000032901000002001c00000000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.
2. Измеренные смещения и осадки рабочих пунктов находятся в пределах до
10 мм по всем осям, что меньше предельной погрешности измерений этих
смещений и осадок всех наблюдаемых пунктов.
3. Из этого можно заключить, что деформации плотины, превосходящие
точность измерений, не обнаружены.
Сравнение превышений между пунктами показало, что их изменения за
последние 1,5 года находятся в пределах точности измерений (менее 5 мм).
Характерная особенность применения топоцентрических прямоугольных
координат при изучении осадок и горизонтальных смещений инженерных
сооружений состоит в том, что в отличие от остальных систем координат
преобразование осуществляется сравнительно просто; так как формулы
позволяют получить изменение координат рабочих пунктов относительно
исходной точки, условная поверхность отсчета высоты проходит через
исходную точку, исключается необходимость редуцирования результатов
измерений на референц-эллипсоид, а потом на плоскость, точность
вычисления координат после перехода от геоцентрических к
топоцентрическим прямоугольным координатам не снижает точности
геоцентрических координат после уравнивания.
Представленные в главе результаты опытно-производственных работ по
геодезической спутниковой сети подтверждают эффективность применения
спутниковых измерений на основе разработанной в диссертации методики и
указывают, что не происходить деформаций тела плотины, превосходящих
10-15 мм, т.е. точность предполагаемого метода.
ЗАКЛЮЧЕНИЕ
На основе исследований, проведенных в настоящей диссертационной работе,
представляется возможным сделать обобщенный вывод о том, что
представленный материал охватывает комплекс вопросов, относящихся к
разработке методов исследования деформационных процессов применительно к
крупным инженерным сооружениям. В основу разработанного метода положены
современные возможности определения осадок и смещений на основе
применения топоцентрических прямоугольных координат с применением
глобальных спутниковых навигационных систем. При этом в процессе
реализации упомянутого комплекса решены следующие задачи:
1. Разработана методика обработки результатов спутниковых измерений с
целью выявления деформаций крупных инженерных сооружений, используя
топоцентрическую систему координат.
2. Точностные исследования разработанной методики обработки результатов
спутниковых измерений показали, что средние квадратические ошибки
деформационных характеристик наблюдаемых объектов зависят только от
точности определения приращений координат и не зависят от точности
определения абсолютных координат и от точности знания аномалий высот в
районе выполненных работ.
3. Предложенный метод спутниковых измерений при мониторинге крупных
инженерных сооружений позволит существенно сократить время поиска
признаков деформаций в условиях Мексики.
4. Усовершенствован процесс проведения на геодезических сетях полевых
спутниковых измерений и процедур последующей обработки результатов
измерений с тем, чтобы на их основе получать надежные значения изучаемых
деформаций.
5. Выявлены математические зависимости изменения точности
топоцентрических декартовых координат при анализе деформаций крупных
инженерных сооружений.
6. Предположенный метод изучения деформаций не выявлен на изучаемом
объекте признаков смещений и осадок.
Новые принципы установления и дальнейшего развития системы
топоцентрических прямоугольных координат при изучении деформационных
процессов электроэнергетических объектов в Мексике на основе современных
спутниковых технологий обуславливают необходимость изменения структуры
геодезического обеспечения.
Результаты экспериментальных производственных работ, подтверждают
высокую эффективность применения GPS-методов при изучений деформаций
крупных инженерных сооружений.
Публикации по теме диссертации
1. Трехо Сото Мануэль. Применение топоцентрических прямоугольных
координат при изучении деформаций крупных инженерных сооружений
спутниковыми методами. Известия ВУЗов, Геодезия и аэрофотосъёмка, N 5,
2006, с. 53-60.
2. Трехо Сото Мануэль. Оценка точности топоцентрических прямоугольных
координат при изучении деформаций крупных инженерных сооружений
спутниковыми методами. Известия ВУЗов, Геодезия и аэрофотосъёмка, N 6,
2006, с. 75-86.
3. Трехо Сото Мануэль. Математический анализ спутниковых геодезических
сетей при изучении деформаций инженерных сооружений. Геодезия и
аэрофотосъёмка, N 1, 2007, с. 67-75.
4. Garcia Lopez Ramon, Moraila Valenzuela Carlos, Lopez Moreno Manuel,
Vazquez Becerra Esteban, Balderrama Corral Rigoberto, Plata Rocha
Wenseslao y Trejo Soto Manuel. Solucion del Campo de Gravedad Empleando
Datos Combinados de las misiones GRACE y CHAMP usando el principio de
Conservacion de la energia. Reunion Annual de la Union Geofisica
Mexicana. (29Oct-3Nov, 2006). http://www.ugm.org.mx.
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