Some aspects of the inversion problem of surface wave dispersion data.

Dispersion characteristics of seismic surface waves were analyzed with and without a homogeneously layered approximation of the earth. Special attention was paid to the relations of dispersion to S-wave velocity contrast and density distribution as well as the significance of these relations to the structural interpretation of dispersion measurements. An approach for inversion of dispersion data with continuous model parameterization and an integration algorithm for solving the corresponding forward problem were developed. The major merit of this approach is that it may reflect the true resolving power of surface wave data and reduces the chances of mis- or over-interpretation of inversion results as compared to those approaches based on various layered models. By extending the diagnostic analysis of the partial derivatives of phase and group velocities with respect to model parameters, a detailed investigation of the factors which determine the condition of the inverse problem was conducted. These factors mainly include the wave type, velocity type, excitation mode, and period range of dispersion measurements. The usefulness of the inversion approach formulated and the concepts drawn during this study are examined and illustrated by using one set of synthetic data and several sets of actual measurements reported previously in the literature. Specific conclusions from this study are: (1) Surface wave dispersion is sensitive to the change in the magnitude of S-wave velocity distribution, including the depth of a large velocity contrast and low velocity zones of significance, but are not sensitive to the gradient or shape of velocity contrasts. (2) Higher modes and the fundamental mode, group velocity and phase velocity contain almost the same information about the earth\u27s structure. However, the inclusion of higher mode or group velocity data in inversion may provide useful constraints on resulting models, even when they contain large random errors. (3) Surface wave dispersion is only sensitive to the shape not the absolute value of a density distribution, and this sensitivity is basically restricted to the fundamental mode. When the active parameter of inversion is assigned to S-wave velocity, the representation of density in models may have a small effect on the magnitude of S-wave velocity determinations but has almost no influence on the structural features obtainable. (4) Quantitative information about the condition of the inverse problem in terms of the distribution of the singular values of partial derivative matrix is very helpful to the considerations of stability and resolution for the inverse problem. (5) Although non-uniqueness in the inversion of dispersion data is well known, a preferred model is required to represent and interpret the data. It is desirable to avoid including features in that model which are merely consistent with but not actually required by the data