Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves

Abstract

Ultrasonic measurements of acoustic wavefields scattered by single spheres placed in a homogenous background medium ͑water͒ are presented. The dimensions of the spheres are comparable to the wavelength and the wavelength and represent both positive ͑rubber͒ and negative ͑teflon͒ velocity anomalies with respect to the background medium. The sensitivity of the recorded wavefield to scattering in terms of traveltime delay and amplitude variation is investigated. The results validate a linear ͑first-order͒ diffraction theory for wavefields propagating in heterogeneous media with anomaly contrasts on the order of ±15%. The diffraction theory is compared further with the exact results known from literature for scattering from an elastic sphere, formulated in terms of Legendre polynomials. To investigate the 2D case, the firstorder scattering theory is tested against 2D elastic finite-difference calculations. As the presented theory involves a volume integral, it is applicable to any geometric shape, and the scattering object does not need to be spherical or any other specific symmetrical shape. Furthermore, it can be implemented easily in seismic data inversion schemes, which is illustrated with examples from seismic crosswell tomography and a reflection experiment.

The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

“…To do this, we create a relationship between these two parameters. Using the scattering theory, the scattered wave U can be obtained as ͑e.g., Woodward, 1992;Jocker et al, 2006͒ U D ͑r I ;r S ,͒ ‫ס‬ 2S͑͒ ͵ V k 0 2 m͑rЈ͒G D ͑rЈ;r S ,͒G͑rЈ;r I ,͒dVЈ, ͑6͒ are frequency-domain sensitivity or Fréchet kernels for source and receiver sides. Equations 8-12 give the relationship between the velocity perturbation and the phase delay in the depth image.…”

“…When a band-limited seismic wave propagates through a complex region, often the rays poorly approximate the actual wavepaths ͑Woodward, 1992; Biondi, 2006͒. The sensitivity of finite-frequency signals to the velocity model has been investigated by researchers working in earthquake seismology ͑Dahlen et al, Huang et al, 2000;Zhao et al, 2000;Dahlen, 2005;Chen et al, 2007͒, ocean acoustics ͑Skarsoulis and Cornuelle, 2004͒, and applied seismology ͑Luo and Schuster, 1991Woodward, 1992;Vasco et al, 1995;Sava and Biondi, 2004;Spetzler and Snieder, 2004;Jocker et al, 2006;Buursink and Routh, 2007;Fliedner et al, 2007͒. Finite-frequency sensitivity kernels have been used to solve many tomography problems with great success.…”

A wave‐equation migration velocity analysis approach based on the finite‐frequency sensitivity kernel

“…Currently, this has been dominated by the ray tracing based tomography method which assumes an infinitely high frequency. The sensitivity of finite-frequency signals to velocity model has been recently investigated by researchers working in different fields (Woodward, 1992;Vasco et al, 1995;Dahlen et al, 2000;Zhao, et al, 2000;Skarsoulis and Cornuelle, 2004;Spetzler and Snieder, 2004;Sava and Biondi, 2004;Jocker, et al, 2006;and Buursink and Routh, 2007;Fliedner et al, 2007). Finite-frequency sensitivity kernels have been calculated and used for solving many tomography problems with great success.…”

Seismic diffraction tomography technique using very fast simulated annealing method for delineating small subsurface features

“…But both the reflection and refraction ray tomography methods are unable to delineate small scale subsurface inhomogeneities whose size is comparable to or less than the wavelength of incident seismic wave. Such subsurface inhomogeneities of smaller dimension can aptly be delineated by recently developed diffraction tomography method (Devaney, 1981(Devaney, , 1982(Devaney, , 1984Wu and Toksöz, 1987;Pratt and Worthington, 1989;Thompson et al, 1994;Liu et al, 1997;Pratt et al, 1998;Pratt, 1999;Pratt and Shipp, 1999;Campman et al, 2005;Jocker et al, 2006). Both the seismic reflection and diffraction data are nonlinearly related to the Earth's model parameters.…”