January 31
2017
2017
Mathematicians from Novosibirsk have developed a method for rapid determination of the tsunami cause
Specialists of the laboratory creation of methods of research and identification of mathematical models of Natural Sciences of the Novosibirsk State University and the Institute of Computational Mathematics and Mathematical Geophysics (ICM & MG) of Russian Academy of Sciences have developed a method that allows to identify the cause of the tsunami as soon as possible. According to the lab employee, instructor at the Department of Mathematics Faculty of Physics NSU Olga Krivorotko, the system will help the authorities and relevant agencies to predict the situation with the tsunami with more accuracy, without going deep into details of the mathematical models.
Olga Krivorotko notes that the tsunami usually occurs as a result of underwater earthquakes, details of which became known for a few minutes, as the speed of sound in the ground is ten times higher than the speed of sound in water. In most cases, the tsunami propagation predictions prove to be wrong:
According to information on the earthquake magnitude, the corners of the shift of the lithospheric plates and the approximate coordinates of the epicenter, the amplitude of the cause of arisen tsunami can be calculated with some error. In 80% of cases, these predictions are false, which entails enormous expenditure on the evacuation of the population and strategic facilities. False data on the tsunami cause is strongly reflected in the calculation of the height of the waves lapping on the shore: Each meter can be disastrous, as it had happened during the tsunami in Japan in 2011.
To clarify the source of the tsunami amplitude of mathematical modeling techniques is being applied. Employees of a joint laboratory of the Institute of Mathematics and Mathematical Geophysics (ICMMG) SB RAS and NSU use numerical methods for solving inverse and ill-posed problems.
—We select such parameters of the cause that can help us to see how a model wave of tsunami little deviates from the actual height of passing waves in the ocean.
The actual data can be obtained from satellite imagery, or is flooded stations. The measurements are processed by noise filters, then we create an algorithm of numerical solution of the problem of determining a source developed software system, and then the algorithm works through the test problems, - says Olga Krivorotko.
However, to prevent the events of the tsunami, emphasizes mathematician, you need to determine its source as soon as possible. In this direction, the Novosibirsk specialists have developed and tested an analytical method for determining the leading edge of the wave amplitude, which in calculative speed exceeds the finite difference methods in tenfold.
The basis of the method - a fundamental approach to the solution of the initial boundary value problem for the linear shallow water equations, the allocation of breaking part of the wave solutions and the properties of the delta function. Olga Krivorotko refers to an interesting fact: the results obtained by an analytical method, consistent with calculations of George Airy Biddel made in 1841 (G. Airy «Tides and waves»), which are, in turn, derived from the physical laws of conservation.
The developed algorithms are now actively being tested on historical data. The laboratory of mathematical problems of geophysics Institute of Computational Mathematics and Mathematical Geophysics SB RAS has a large base of the Tsunami that occurred from 1628 BC. e. and until 2012. The database contains a cause of tsunami characteristics, height map oncoming waves on the shore, and for some coasts - economic assessment of the possible destruction of the model wave. It is built into a software complex three-dimensional visualization of tsunami modeling, which was also created in the laboratory.
Purpose of the developed system - support and maintenance of the research of tsunami appearance and reasons that cause the earthquakes, as well as forecasting emergency situations. The complex includes a specialized database of tsunami causes, tools for processing and analyzing geodata software system for calculation of wave propagation and identify the source of origin. In addition, the system can predict the consequences and even to assess the material damage and damage to the strategically important objects.
Olga Krivorotko notes that using such a system, specialized units and the authorities will be able to monitor and predict a tsunami, without going into details of the mathematical models. However, scientists can use this product as a convenient platform for their research.
According to information on the earthquake magnitude, the corners of the shift of the lithospheric plates and the approximate coordinates of the epicenter, the amplitude of the cause of arisen tsunami can be calculated with some error. In 80% of cases, these predictions are false, which entails enormous expenditure on the evacuation of the population and strategic facilities. False data on the tsunami cause is strongly reflected in the calculation of the height of the waves lapping on the shore: Each meter can be disastrous, as it had happened during the tsunami in Japan in 2011.
To clarify the source of the tsunami amplitude of mathematical modeling techniques is being applied. Employees of a joint laboratory of the Institute of Mathematics and Mathematical Geophysics (ICMMG) SB RAS and NSU use numerical methods for solving inverse and ill-posed problems.
—We select such parameters of the cause that can help us to see how a model wave of tsunami little deviates from the actual height of passing waves in the ocean.
The actual data can be obtained from satellite imagery, or is flooded stations. The measurements are processed by noise filters, then we create an algorithm of numerical solution of the problem of determining a source developed software system, and then the algorithm works through the test problems, - says Olga Krivorotko.
However, to prevent the events of the tsunami, emphasizes mathematician, you need to determine its source as soon as possible. In this direction, the Novosibirsk specialists have developed and tested an analytical method for determining the leading edge of the wave amplitude, which in calculative speed exceeds the finite difference methods in tenfold.
The basis of the method - a fundamental approach to the solution of the initial boundary value problem for the linear shallow water equations, the allocation of breaking part of the wave solutions and the properties of the delta function. Olga Krivorotko refers to an interesting fact: the results obtained by an analytical method, consistent with calculations of George Airy Biddel made in 1841 (G. Airy «Tides and waves»), which are, in turn, derived from the physical laws of conservation.
The developed algorithms are now actively being tested on historical data. The laboratory of mathematical problems of geophysics Institute of Computational Mathematics and Mathematical Geophysics SB RAS has a large base of the Tsunami that occurred from 1628 BC. e. and until 2012. The database contains a cause of tsunami characteristics, height map oncoming waves on the shore, and for some coasts - economic assessment of the possible destruction of the model wave. It is built into a software complex three-dimensional visualization of tsunami modeling, which was also created in the laboratory.
Purpose of the developed system - support and maintenance of the research of tsunami appearance and reasons that cause the earthquakes, as well as forecasting emergency situations. The complex includes a specialized database of tsunami causes, tools for processing and analyzing geodata software system for calculation of wave propagation and identify the source of origin. In addition, the system can predict the consequences and even to assess the material damage and damage to the strategically important objects.
Olga Krivorotko notes that using such a system, specialized units and the authorities will be able to monitor and predict a tsunami, without going into details of the mathematical models. However, scientists can use this product as a convenient platform for their research.