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Estimation of elastic constants in homogeneous transversely isotropic
Using traveltimes to estimate elastic constants
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1-D isotropic 2-D inversion algorithm anisotropic inversion anisotropic media anisotropic ray tracing anisotropy and heterogeneity aperture artiﬁcial assume assumption axes axis of symmetry CG-iterations chapter corresponding cross-well geometries data space direction double elliptic approximation eigenvectors elliptical parameters elliptical velocities elliptically anisotropic models equation 3.8 estimated elastic constants estimation of elastic ﬁeld data examples ﬁnd ﬁne layering ﬁrst ﬁt ﬁve group velocity heterogeneous media homogeneous models horizontal component images impulse response interface inverse problem iterations linear measurements medium model is 2-D model space NMO velocities null space obtained P-wave traveltimes phase angle procedure ray angles ray paths rays that travel recording geometry SH-wave shear waves shown in Figure singular value decomposition singular vectors slowness surfaces smallest singular values solution solve sonic log sources and receivers synthetic transformed transmitted phase transversely isotropic V-wave elliptical V,NMQ velocities estimated velocity anisotropy vertical component wave type