Abstract
The paper presents results of the mathematical synthesis of the method of passive location of a seismic wave source. The method employs measurements of regular attenuation of seismic oscillation amplitudes. If it is impossible to determine the location of a seismic event by means of direct measurements, indirect measurements are needed. A priori information for the mathematical synthesis was obtained from functional equations showing inverse proportions of measured amplitudes, arbitrary effective attenuation coefficients and corresponding coordinates. An original method was applied to process the data. The method providing for passive location of seismic waves sources has been developed; it is called the radial basic method. In the one-dimensional case, a distance is determined on the basis of seismic oscillation amplitudes measured by two seismographs that are located at a known base distance coinciding with the direction to the source of seismic waves. The distance is calculated from the receiver that is nearest to the source. If the base distance and the direct line between the seismograph and the seismic wave source do not coincide, a projection of the distance between the receivers to the given straight line is taken into account. Three seismographs were placed at mutually perpendicular base distances in a plane (i.e. the two-dimensional space). This allowed us to obtain an analytical equation for determining the direction to the seismic wave source using measured amplitudes. The value of the angle is taken into account when calculating the distance. For the seismic wave source located in the three-dimensional space, transition equations for combined coordinate systems (i.e. the Descartes (Cartesian)), at the axes of which the seismographs were placed, and the spherical coordinate systems were applied, and analytical equations were obtained for determination of coordinates, such as distance/polar radius, elevation angle/latitude, and bearing angle/longitude. To analyze the application of the radial basic method of passive location, an absolute error resulting from indirect measurement was calculated. This method is a special case of determining the statistical characteristics of the sought function (coordinates) out of random values, which are the measured amplitudes of seismic oscillations. In the obtained analytical expressions for determination of the mean square deviation of the distance and direction to the seismic wave source, noise from seismographs is taken into account, as well as external noise manifested as microseisms and other interfering seismic waves. For the three-dimensional space, equations are derived for calculation of RMS distance, elevation and bearing angles. In cases where distances to seismic wave sources, directions, coefficients that factor properties of the medium, and base distances are known, the radial basic method allows us to determine effective coefficients of seismic wave attenuation and capacities of seismic wave sources.
Highlights
Three seismographs were placed at mutually perpendicular base distances in a plane
A priori in formation for the mathematical synthesis was obtained from functional equations showing inverse proportions of measured amplitudes, arbitrary effective attenuation coefficients and corresponding coordinates
In the onedimensional case, a distance is determined on the basis of seismic oscillation amplitudes measured by two seismographs that are located at a known base distance coinciding with the direction to the source of seis mic waves
Summary
Определение координат очагов землетрясений, взрывов различного рода и других механических воз действий в водных акваториях и горных породах пред ставляется актуальной задачей. Для определе ния координат источников сейсмических волн тради ционно применяется фазовый метод. Для определения местоположения источников сейс мических волн также используется амплитудный ме тод пассивной локации. В работе [Gelmor, 1954] нахождение координат источников микросейсм осу ществлялось по отношению амплитуд трех пространственно разнесенных станций. Амплитудный метод применен в работе [Cher nykh, Tabulevich, 2004] для определения местоположе ния виброисточников (без учета влияния помех). Получение информации об объектах и явлениях, недоступных для непосредственного измерения, в ча стности в геофизике, приводит к необходимости кос венных измерений. Для обработки результатов кос венных измерений существенную роль играет априор ная информация об исследуемых зависимостях. Geodynamics & Tectonophysics 2012 Volume 3 Issue 4 Pages 409–416 смических волн, предлагается использовать метод [Sy ten’ky, 1992 ] пассивной локации, основанный на зако номерном затухании амплитуды сейсмических коле баний
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
