Inversion Method Based On Elastic Wave Equation And Its Application In Geotechnical Engineering

With the geotechnical engineering become large-scale and complex,geotechnical detecting problems become more and more complex.In recent years,the detection methods of elastic wave propagation characteristics are highly concerned to detect hidden engineering.And the structure of the object can be detected as layered media.For example,The detection structure is generally composed of concrete bottom plate,sand filling layer and gravel cushion in detection of sand filling in foundation of immersed tunnel;the detection structure generally consists of track plate,CA mortar layer,Plate and subgrade in detection of structural disease under high-speed railwa.Therefore,this paper presents a layered medium inversion method based on the analytic solution of the elastic wave equation.First,the analytic solution of the elastic wave equation in the layered medium is obtained by theoretical derivation.Based on this method,quasi-linear method and regularization optimization method are used to obtain known parameters of the multilayer media.The method based on the elastic wave detection method solves the problems such as long calculation time,low computational efficiency and inaccurate inversion parameters.The analytical solution of the elastic wave equation in layered media is based on the basic equations of elastic dynamics,and obtains simplified the Lame equation.The formula of longitudinal wave and transverse wave reflection / transmission coefficient in frequency-slowness domain is obtained by the slowness integration method.The concept of "thick layer" and "thin layer" in seismology is introduced to solve the elastic wave equation to obtain the analytic solution of elastic wave propagation in thick layer and thin layer.Three layered medium model is established to analyze the theoretical solution,which are compared with the two-dimensional finite element under the same case.The correctness of the analytical solution is confirmed by comparing the waveform response,the travel time calculation and the response energy.Based on the "inversion" of the geophysical specialty,use of the waveform to respond to energy parameters,a proximate linear method is used to establish a linear system of equations for iterative calculation.In order to solve the ill-posedness of inverse calculation and the fast convergence of inversion results,obtaining the prior information of the model,optimization of the inversion parameters and regularization algorithm are introduced.The sensitivity of the parameters in the three-layer medium is analyzed.It is considered that the shear wave velocity of the target layer is the most sensitive,and the calculation time is fast.On the basis of this,the problem of interlayer non-uniformity is calculated by inversion.The underlying structure is assumed to be the inversion of layered medium,and the inversion result of each measuring point obtains the accurate interlayer transverse heterogeneous structure.In order to solve the problem of multi-layer and multi-parameter inversion,multi-parameter inversion is achieved by increasing the number of received waveform,and the precise inversion results can be obtained with the same number of received waveforms and inversion parameters.For the detection of interlayer defects,the detection layer is divided into multi-layered media.The more the number of layers is,the smaller the offset is,the more accurate the detection result is.Finally,the inversion method based on the elastic wave equation in layered medium is applied to the test of sand filling effect in Honggu tunnel of Nanchang.Firstly,the field data acquisition method andacquisition parameters are determined according to the construction technology of immersed tunnel immersed sand and the on-site detection conditions and requirements.According to the particularity of immersion tunnel sand filling test,the method and the step of data normalization are determined.The inversion calculation model is simplified as a three-layer model with high inversion efficiency,and the shear wave velocity of the sand layer is obtained in the fast time.The shear wave velocities of the whole model are obtained by inversion of the calculated shear wave velocities and compared with the relative density distribution maps obtained from the in field test.a curve between the shear wave velocities and the relative density is obtained of the curve to guide the entire sand filling process.