Inversion Of Multimode Rayleigh-wave Dispersion Curves

Estimating near-surface S-wave velocities (Vs) from Rayleigh-wave phase velocities is aneffective and reliable geophysical method, which is widely used in geotechnical application andgeological investigation. The root-search scheme is improved for calculating multimodeRayleigh-wave dispersion curves, and the computer time of forward modeling is reduced. Threekinds of layered models, i.e., regular layered model, low-velocity-layer model andhigh-velocity-layer model, are desinged to analyze their characteristic of multimode dispersioncurves. Furthermore, it is essential to analyze the sensitivity of Rayleigh-wave phase velocities toS-wave velocity and thickness of different layer. A strategy of inversion is proposed as following, 1) selecting the multimode dispersive data, 2) paramaterizing models, 3) using an improvedgenetic algarithm in inversion, 4) calculating mean model and standar deviation of inversionresults. Finally, a relationship between results and relative factors is constructed to analyze thestability or the problem of inversion of dispersion curves.Sensitivity analysis of dispersion curves indicate that the sensitivity of one mode to theparameters of different layer change with frequencies. Its value is of zero in some ranges offrequency while is very high at particular points. Different modes possess different sensitivities tothe same parameter, normally, higher modes have higher sensitivities. Some special layers, suchas low velocity layer or high velocity layer, would strongly "trap" or "prevent" Rayleigh-wavetraveling along it, hence, it will influence the changes of Rayleigh-wave phase velocities againstto frequency, at presence of high sensitivity or low one. Rayleigh-wave, however, possessextreme low sensitivity to S-wave velocity of layers that underneath low velocity layer.Inverted results of three kinds of models show that,1) In all the models the bedrock (half-space) depth and velocity are identified with goodprecision. This represents an important achievement because it demonstrates an identificationability that cannot usually be equalled by common linear inversion procedures.2) The retrieved velocity and thickness are easily affected by the sensitivity of dispersivedata and the tentative of modeling parameterization, a) High sensitive data can reduce error andsuppress the uncertainty but the effects of low sensitive data are invisible, b) The syntheticnumber of layers in inversion influences the identification of bedrock depth and velocity little, c)Layers' thicknesses and velocities can be inverted synchronously by multimode dispersion dataonce the number of layers is known, with better presision than the fundamental mode. d) If theamount of layers is out of control, the thickness and velocity are obtained with high uncertainty; the procedure will be very instable. The results are yielded with an uncertainty of 15-20ï¼…forvelocity and of 30-40ï¼…for thickness even though the higher modes data were added in inversion.Consequently, the trad-off between fixed thickness of layer and fixed amount of layers should bemade in inversion.3) With the multimode data the velocity of low-velocity-layer is well estimated. Thevelocities, however, of other layers underneath it are retrieved with high uncertainties.4) Reliability and accuracy of inverted result of high-velocity-layer can be enhenced fromcapable higher mode data, which is only sensitive to this layer.5) There is an obvious correlation between the unertainties and the sensitivities of ultilizeddata to the inverted destination layers. Only the data of high sensitive to a certain layer haveability to improve the accuracy and stability of inversion.Improvents in the understanding of inveriting multimode Rayleigh-wave dispersion curvesare beneficial to the interpretation of S-wave velocity profile.