The Examination And Application Of Mathematics In Microtremor Survey

The conventional microtremor survey is based on the single point of exploration, which includes collecting field data, estimating the phase velocity, investing the dispersion curve and obtaining the S–wave velocity structure. The most important part of the extraction of dispersion curves is to obtain the spatial autocorrelation function of the signal. This requires the instruments must be arranged in a circle which the exploration point is the center point. Due to the terrain, the observation array is not often strict arranged as a circle. In the case of large-scale exploration, and when making the two-dimensional velocity section, the inversion is quite time-consuming, laborious and its precision depends on the subjective interpretation, which makes the results differently from person to person.At first, this paper is desire to improve the calculation of spatial autocorrelation function as a way to find a new shape observation array that can be replaced the circle shape observation array when needed. Second, as the differences of purpose of observation we do not need the S-wave velocity values but only need the relative variation of velocity. This paper is desired to calculate the apparent S-wave velocity to replace the S-wave velocity inversion and to obtain the relative variation of the S-wave velocity. And then, using of the methods of data fitting, interpolation and micro computer program language, the apparent S-wave velocity section can be accomplished.This paper designs the calculation method of linear shape and L shape model experiments of two different observation array, after the contrast between the two shapes with circle shape, L shape array has certain practical value. Additionally, Through the application case of an actual downcast column analyses the method of apparent S-wave is proved to be reliable and effective. Depending on the apparent S-wave velocity depth chart can clearly showed abnormal areas such as downcast columns and the depth, horizon, boundary, and other important informations of them.