Theoretically, Fresnel volume ray theory is more suitable for handling real seismic propagation problems because the traveltime depends not only on the velocity distribution along a traditional geometric ray but also on the velocity distribution within a vicinal region (referred to as first Fresnel volume, abbreviated as FFV) which embraces the geometric ray. In this study, we used an exact solution to calculate multi-phase FFV rays for both 2-D and 3-D cases and introduced a normalized coefficient to account for different contributions inside the FFV ray on the traveltimes. Furthermore, we draw a new formula to calculate the partial traveltime derivatives with respective to the velocity variations and depth changes of the reflectors and finally present a simultaneous inversion method for updating both velocity field and reflector geometry by using these multi-phase FFV rays for both in 2-D and 3-D cases. Using synthetic data examples, we compare the reconstructions of the velocity field and the reflector geometry using the FFV ray tomographic methods and the traditional ray tomography approaches. The simulated inversion results for both 2-D and 3-D cases show that the FFV ray tomographic method is advantageous over the traditional ray tomography method, especially when the ray density is relatively low. The other advantage for the FFV ray tomography method is that it can capture the coarse velocity structure and reflector geometry by starting with a low-frequency data set and then map the fine velocity structure and the detailed reflector geometry by using a high-frequency data set.
First Fresnel volume Multi-phase FFV ray tracing Simultaneous traveltime inversion Seismic ray tomography 2-D/3-D cases
This is a preview of subscription content, log in to check access.
This research work was partially supported by the Doctoral Programming Research Fund of Higher Education, Chinese Ministry of Education (Project No: 20110205110010).
Bai CY, Greenhalgh SA (2005) 3-D non-linear travel time tomography: imaging high contrast velocity anomalies. Pure Appl Geophys 162:2029–2049CrossRefGoogle Scholar
Bai CY, Huang GJ, Zhao R (2010) 2D/3D irregular shortest-path ray tracing for multiple arrivals and its applications. Geophys J Int 183:1596–1612CrossRefGoogle Scholar
Bai CY, Li XL, Tang XP (2011) Seismic wavefront evolution of multiply reflected, transmitted and converted phases in 2D/3D triangular cell model. J Seismol 15:637–652CrossRefGoogle Scholar
Bai CY, Li XL, Wang QL, Peng JB (2012) Multiple arrival tracking within irregular triangular or tetrahedron cell model. J Geophys Eng 9:29–38CrossRefGoogle Scholar
Bai CY, Wang X, Wang CX (2013) Comparison wavefield simulation between the first- and the second-order separated wave equations through a high-order staggered-grid finite difference method. Earthq Sci 26(2):83–98CrossRefGoogle Scholar
Bai CY, Li XW, Huang GJ, Greenhalgh S (2014a) Simultaneous inversion for velocity and reflector geometry using multi-phase Fresnel volume rays. Pure Appl Geophys 171:1089–1105CrossRefGoogle Scholar
Bai CY, Huang GJ, Li XW, Greenhalgh S (2014b) 3D simultaneous traveltime inversion for velocity structure, hypocenter locations and reflector geometry using multiple classes of arrivals. Pure Appl Geophys. doi:10.1007/s00024-014-0945-1Google Scholar
Huang GJ, Bai CY, Zhu DL, Greenhalgh S (2012) 2D/3D seismic simultaneous inversion for velocity model and interface geometry using multiple classes of arrivals. Bull Seismol Soc Am 102:790–801CrossRefGoogle Scholar
Husen S, Kissling E (2001) Local earthquake tomography between rays and waves: fat ray tomography. Phys Earth Planet Inter 123:129–149Google Scholar
Kennett BLN, Sambridge M (1998) Inversion for multiple parameter classes. Geophys J Int 135:304–306CrossRefGoogle Scholar
Pratt RG, Goulty NR (1991) Combining wave-equation imaging with traveltime tomography to form high-resolution images from crosshole data. Geophysics 56:208–224CrossRefGoogle Scholar
Sheng J, Leed A, Buddensiek M, Schuster GT (2006) Early arrival waveform tomography on near-surface refraction data. Geophysics 71:47–57CrossRefGoogle Scholar
Thurber C, Eberhart-Phillips D (1999) Local earthquake tomography with flexible gridding. Comput Geosci 25:809–818CrossRefGoogle Scholar
Vasco DW, Peterson JE, Majer EL (1995) Beyond ray tomography: wave paths and Fresnel volumes. Geophysics 60:1790–1804CrossRefGoogle Scholar
Wielandt E., 1987. On the validity of the ray approximation for interpreting delay time. In: Seismic tomography, edited by Nolet G., Redel Publishing CompanyGoogle Scholar
Zhou B, Greenhalgh SA, Sinadinovski C (1992) Iterative algorithm for the damped minimum norm, least-squares and constrained problem in seismic tomography. Explor Geophys 23:497–505CrossRefGoogle Scholar