Sensitivity kernels for seismic Fresnel volume tomography

Fresnel volume tomography FVT offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are 1 / 8, 2/ 8, 3/ 8 and 4 / 8 periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

[1]  C. Shin,et al.  An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator , 1996 .

[2]  Guust Nolet,et al.  Computing traveltime and amplitude sensitivity kernels in finite-frequency tomography , 2007, J. Comput. Phys..

[3]  T. Matsuoka,et al.  Seismic traveltime tomography using Fresnel volume approach , 1999 .

[4]  Don W. Vasco,et al.  Tomographic inversions for mantle P wave velocity structure based on the minimization of l 2 and l 1 norms of International Seismological Centre Travel Time Residuals , 1993 .

[6]  A. Morelli.  Inverse Problem Theory , 2010 .

[7]  K. Yomogida.  Fresnel zone inversion for lateral heterogeneities in the earth , 1992 .

[8]  Guust Nolet,et al.  Three-dimensional waveform sensitivity kernels , 1998 .

[9]  K. Wolf,et al.  Application of a linear finite-frequency theory to time-lapse crosswell tomography in ultrasonic and numerical experiments , 2007 .

[10]  Guust Nolet,et al.  Fréchet kernels for finite-frequency traveltimes—I. Theory , 2000 .

[11]  Marta Woodward,et al.  Wave-equation tomography , 1992 .

[12]  Reinaldo J. Michelena,et al.  Tomographic traveltime inversion using natural pixels , 1991 .

[13]  A. Devaney.  Geophysical Diffraction Tomography , 1984, IEEE Transactions on Geoscience and Remote Sensing.

[14]  T. Jordan,et al.  Structural sensitivities of finite-frequency seismic waves: a full-wave approach , 2006 .

[15]  Jr. John W. Stockwell.  Free software in education; a case study of CWP/SU; Seismic Un*x , 1997 .

[16]  Li Zhao,et al.  Finite‐frequency sensitivity kernels for head waves , 2006 .

[17]  Gilles Lambaré,et al.  Velocity macro‐model estimation from seismic reflection data by stereotomography , 1998 .

[18]  Thomas H. Jordan,et al.  Three‐dimensional Fréchet differential kernels for seismicdelay times , 2000 .

[19]  Roel Snieder,et al.  Wavefield smoothing and the effect of rough velocity perturbations on arrival times and amplitudes , 1996 .

[20]  Guust Nolet,et al.  Wavefront healing: a banana–doughnut perspective , 2001 .

[21]  Guust Nolet,et al.  Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana–doughnut paradox , 1999 .

[22]  R. Pratt,et al.  Combining wave-equation imaging with traveltime tomography to form high-resolution images from crosshole data , 1991 .

[23]  R. Snieder,et al.  The effect of small-scale heterogeneity on the arrival time of waves , 2001 .

[24]  Adam M. Dziewonski,et al.  Mapping the lower mantle: Determination of lateral heterogeneity in P velocity up to degree and order 6 , 1984 .

[25]  R. Snieder,et al.  The Fresnel volume and transmitted waves , 2004 .

[26]  Z. Xue,et al.  Case story: time-lapse seismic crosswell monitoring of CO2 injected in an onshore sandstone aquifer , 2008 .

[27]  Sensitivity Kernels And Fresnel Volumes For Transmitted Waves , 2008 .

[28]  G. Nolet,et al.  Seismic wave propagation and seismic tomography , 1987 .

[29]  K. Aki,et al.  Quantitative Seismology, 2nd Ed. , 2002 .

[30]  A. J. Devaney,et al.  Geophysical Diffraction Tomography , 1984 .

[31]  E. L. Majer,et al.  Wavepath traveltime tomography , 1993 .

[32]  D. Smeulders,et al.  Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves , 2006 .

[33]  Gerard T. Schuster,et al.  Wavepath eikonal traveltime inversion: Theory , 1993 .

[34]  L. E. Larsen,et al.  Limitations of Imaging with First-Order Diffraction Tomography , 1984 .

[35]  M. Toksöz,et al.  Diffraction tomography and multisource holography applied to seismic imaging , 1987 .

[36]  F. A. Dahlen,et al.  Finite-frequency sensitivity kernels for boundary topography perturbations , 2004 .

[37]  Vlastislav Cerveny,et al.  Fresnel volume ray tracing , 1992 .