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## 3-D velocity images beneath the Chinese continent and adjacent regions

Citations: | 1 - 0 self |

### Citations

557 |
Geophysical Data Analysis: Discrete Inverse Theory
- Menke
- 1984
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Citation Context ...an serve as thesquantitative description of the resolving length.sIn the present study models with discrete parameters aresused, therefore the above analysis of Backus & Gilbertsneeds to be modified (=-=Menke 1984-=-). From the generalizedslinear inversion theory, similar to (33), we haves2 = R(%,sR(') = V'VT,swhere R(') is the resolution matrix, V, is a sub-matrixscomposed of the first I columns of matrix V, whi... |

475 |
Introduction to Matrix Computations
- Stewart
- 1973
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Citation Context ...entialsorthogonal triangularization. Suppose that (R,-', djPl) hassbeen obtained after the (i - 1)th step. In the ith step wesintroduce an enlarged matrixsUsing an elementary orthogonal transform Q, (=-=Stewart 1973-=-;sGolub & van Loan 1983) so thatsl o ,s] = Osas a result after the qth step we getsR d }ns(a, dq,'(o e)}l. (24)sIt can be shown that we can find an elementarysorthogonal transform matrix Q which satis... |

319 |
Preliminary reference Earth model, Phys. Earth planet
- Dziewonski, Anderson
- 1981
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Citation Context ...pth of 800 km beneathsthe Chinese continent are in a range of 11.07 tos11.28 km s-'. This means that the velocity at this depth isscloser to Dziewonski & Anderson's Preliminary ReferencesEarth Model (=-=Dziewonski & Anderson 1981-=-) than to thestraveltime model of Herrin et al. (1968). From Fig. 12 wescan see that negative perturbations prevail at l l00kmsunder the mainland China relative to the reference velocitysof 11.605 km ... |

287 |
Singular value decomposition and least squares solutions
- Golub, Reinsch
- 1970
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Citation Context ...on system assCz = b, (19)swhere C is an m X n matrix and b is a known rn-dimensionalsvector. The generalized inverse solution of (19) is usuallysobtained by means of the singular value decompositions(=-=Golub & Reinsch 1971-=-)swhere C' is the generalized inverse matrix of C. But thescommon difficulty in seismic tomography is the very largesRAM requirement and very high computing cost.sTherefore, in designing the algorithm... |

126 |
The Resolving Power of Gross Earth Data
- Backus, Gilbert
- 1968
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Citation Context ...on.sResolution analysis of the solutionsTo describe the uncertainties of the solution, the resolutionstheory developed by Backus & Gilbert for continuous earthsmodels (Backus & Gilbert 1%7; Backus 8~ =-=Gilbert 1968-=-) arescommonly used at present. The basic idea is that with ansaveraging kernel A(r, ra) which satisfiesswe takes(33)sas the approximate value of solution z(r,) at r,, where Q issthe region under stud... |

104 | Determination of the three dimensional seismic structure of the lithosphere, - Aki, Christofferson, et al. - 1977 |

93 | Numerical Applications of a Formalism for Geophysical Inverse Problems.” - Backus, Gilbert - 1967 |

89 |
Interpretation of inaccurate, insufficient, and inconsistent
- Jackson
- 1972
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Citation Context ... cover thesestwo aspects.sError analysis of the solutionsThe errors of the solution are simply described by thesvariances of the solution. From the generalized linearsinversion theory (Franklin 1970; =-=Jackson 1972-=-; Wigginss1972), the diagonal element of the covariance matrix of thessolution is the variance of the corresponding component ofsthe solution.sResolution analysis of the solutionsTo describe the uncer... |

73 | The general linear inverse problem: implication of surface waves and free oscillations for earth structure, Rev. Geophys. Space Phys - Wiggins - 1972 |

59 | Determination of three-dimensional velocity anomaly under a seismic array using first P arrival times from local earthquakes, I. A homogeneous initial model, - Aki, Lee - 1976 |

4 |
Estimation of surface focus P travel times
- Herrin, Tucker, et al.
- 1968
(Show Context)
Citation Context ...rage traveltime residual usually not exceedings2.5 s. For the velocities above 110 km we used other studiessof the crust and upper mantle in China. For velocities belows110 km we used Herrin's model (=-=Herrin et al. 1968-=-). Third,sbesides the requirement of enough rays in each layer, thesgrid size in the vertical direction is restricted mainly by thescomputer ability. The depth of the Moho takes a value insbetween the... |

2 | Simultaneous inversion of earthquake hypocenters and velocity structure (1)-Theory and method - Futian - 1984 |

2 |
On the tomographic inverse method used in velocity image reconstruction
- Futian, Qiang, et al.
- 1989
(Show Context)
Citation Context ...resolutionsmatrix depicts the resolvability of the correspondingselement. In 3-D problems the interpretation is morescomplicated. In this case we recommend the followingsconvenient visual method (Liu =-=Futian et al. 1989-=-). First, R(')sis normalized by rows or columns, i.e.,s(37)swhere 1lRE)Il is the norm of the crth column vector in R(').sAfter that we fix the coordinate of r according to the naturalsorder, and let B... |

1 | An improved algorithm for computing the singular value decomposition - Cham - 1982 |

1 | Crustal thickness and densities in the upper mantle beneath China-the result of three dimensional gravity inversion - Rui - 1985 |

1 | Inversion of travel time data for laterally heterogeneous velocity structure-Linearization approach - Firbas - 1981 |

1 | Well-posed stochastic extensions of ill-posed linear problems - unknown authors - 1970 |

1 | Jiang Chungfa, Zhang Zhengkun & Qin deyu - Jiqing, Jishun - 1980 |

1 |
Three-dimensional seismic ray tracing, 1
- Julian, Gubbins
- 1977
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Citation Context ...- TT' = ILij 6(:) dF + VqiTj6q' + E , ~swhere Tzbs is the observed traveltime, TY' is the traveltimescalculated by ray tracing in a reference velocity structure vos(PSenEik 1972; Cervenf et al. 1977; =-=Julian & Gubbins 1977-=-)sand corrected for station altitudes, E~~ is an error termsincluding the clock and reading errors and qf ( 1 =s1, 2, 3, 4)sis the depth, latitude, longitude, and origin time of the ithsearthquake res... |

1 | Earthquake relocation in laterally varying - Qiang, Futian - 1990 |

1 | Qiang & Hu Xiaoxing - Futian, Li - 1982 |

1 | Seismic tomography of North China, Earthquake Res - Futian, Kexin, et al. - 1987 |

1 | Qiang & Hu Ge - Jianhua, Futian, et al. - 1989 |

1 | Summary of Lithospheric Dynamics - Xingyuan - 1987 |

1 | Linearized inversion of (teteseismic) data - Nolet - 1981 |

1 |
Kinematics of refrectal and reflected waves in inhomogeneous media with non-planar interfaces, Studia Geoph
- PSenEik
- 1972
(Show Context)
Citation Context ... (Firbass1981):s6T.- 11 = Tob" I ts- TT' = ILij 6(:) dF + VqiTj6q' + E , ~swhere Tzbs is the observed traveltime, TY' is the traveltimescalculated by ray tracing in a reference velocity structure vos(=-=PSenEik 1972-=-; Cervenf et al. 1977; Julian & Gubbins 1977)sand corrected for station altitudes, E~~ is an error termsincluding the clock and reading errors and qf ( 1 =s1, 2, 3, 4)sis the depth, latitude, longitud... |

1 | Zhihong, Yin Xluhua, Liu Zhanpo & Zhang Yuwei - Menghua, Qiming, et al. - 1981 |

1 | Zhanpo & Zhang Yumei - Xiuhua, Zhihong, et al. - 1980 |

1 | Determination of the threedimensional seismic structure of the lithosphere using the seismic data - Tianfei, Futian - 1982 |