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We present a detailed approach to implement a moment-tensor point source to compute displacements, particle velocities and accelerations using direct grid methods. Here, the wave modeling algorithm is based on pseudospectral methods to compute the partial derivatives. A comparison to the analytical solution in the 3D acoustic case verifies the discrete implementation of the source in the mesh. Then, the more general 3D elastic case is illustrated and simulations, with and without free surface, are performed that can be used as a reference solution for other grid methods. [ABSTRACT FROM PUBLISHER]

We estimate the quality factor ( Q) from seismic reflections by using a tomographic inversion algorithm based on the frequency-shift method. The algorithm is verified with a synthetic case and is applied to offshore data, acquired at western Svalbard, to detect the presence of bottom-simulating reflectors (BSR) and gas hydrates. An array of 20 ocean-bottom seismographs has been used. The combined use of traveltime and attenuation tomography provides a 3D velocity– Q cube, which can be used to map the spatial distribution of the gas-hydrate concentration and free-gas saturation. In general, high P-wave velocity and quality factor indicate the presence of solid hydrates and low P-wave velocity and quality factor correspond to free-gas bearing sediments. The Q-values vary between 200 and 25, with higher values (150–200) above the BSR and lower values below the BSR (25–40). These results seem to confirm that hydrates cement the grains, and attenuation decreases with increasing hydrate concentration. [ABSTRACT FROM AUTHOR]

We design a numerical algorithm for wave simulation in anelastic media in the presence of free surface, which can be used to model seismic waves at the Earth''s surface and ultrasonic waves in heterogeneous materials. The stress–strain relation is based on the Kelvin–Voigt mechanical model, which has the advantage of not requiring additional field variables. The model requires two anelastic parameters and twice the spatial derivatives of the lossless case. The high-frequency components of the wave field are more attenuated than the low-frequency components, with the attenuation factors being approximately proportional to the square of the frequency. The modeling simulates 3-D waves by using the Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. We stretch the mesh in the vertical direction to increase the minimum grid spacing and reduce the computational cost. Instabilities of the Chebyshev differential operator due to the implementation of the free-surface boundary conditions are solved with a characteristic approach, where the characteristic variables are evaluated at the source central frequency. The results of the modeling are verified by comparisons to the analytical solutions for Lamb''s problem and propagation in unbounded homogeneous media. Examples illustrating the propagation of Rayleigh and Love waves are presented. [Copyright &y& Elsevier]