Modeling And Dispersion Curve Inversion Of Rayleigh Waves In Viscoelastic Media

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media compared with in elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion curve inversion of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world.We apply a pseudospectral method to calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic homogeneous half-space comparing the phase velocities of Rayleigh wave between the theoretical values and dispersive image generated by high-resolution linear Radon transform.We introduce Muller method to calculate the dispersion curves of Rayleigh waves in viscoelastic layered media, and verify the correctness of the numerical results for a viscoelastic homogeneous half-space. Combining Muller method with wave field simulation, we design three kinds of layered models, i.e., regular layered model, low-velocity-layer model and high-velocity-layer model, to analyze their characteristics of dispersion curves. Furthermore, it is essential to analyze the sensitivity of Rayleigh-wave phase velocity and attenuation coefficient to S-wave velocity and quality factor in each layer. We apply an improved genetic algorithm to simultaneously invert Rayleigh-wave dispersion and attenuation curves, based on dispersion forward modeling and sensitivity analysis in viscoelastic layered media. We prove the inversion algorithm by testing three kinds of layered models and a real-world example.Results demonstrate that, 1) The pseudospectral method possesses very high accuracy and resolution with a maximum relative error 1% in amplitude. The modeling record shows relatively small amplitudes and relatively fast velocities, respectively due to amplitude attenuation and velocity dispersion in viscoelastic media.2) The phase velocities of Rayleigh waves in a viscoelastic homogeneous half-space are relatively higher than in an elastic one, which gives a constant velocity, and increases with frequencies due to the velocity dispersion of P and S waves. In addition, the attenuation coefficient of Rayleigh waves is approximately linear with frequecies, and is greater than P- and S-wave attenuation coefficients at a fixed frequecy.3) The higher modes of Rayleigh waves in viscoelastic layered media have higher cutoff frequencies than in the elastic case, and Rayleigh-wave attenuation curves have no clear bounds and intersect each other at higher frequencies which are affected by those of multilayered media with complexity.4) The attenuation coefficient is more sensitive to S-wave velocity than S-wave quality factor, and the phase velocity has much lower sensitivity to S-wave quality factor. The sensitivity of fundamental mode to S-wave velocity and quality factor of each layer change with frequencies, whose value achieves zero in some ranges of frequencies while is very high at particular points. In some special layers, such as low velocity layer, Rayleigh wavea possess higher and broader sensitivities to both S-wave velocity and S-wave quality factor. However, Rayleigh waves show extreme low sensitivities to both S-wave velocity and S-wave quality factor in layers that underneath low velocity layer.5) More attempts can provide a better chance of obtaining a truthful solution that is obtained by averaging results from completed trials. Inverted results show that the relative error for S-wave quality factor is greater than for S-wave velocity.