Abstract
SUMMARY Viscoelastic inversion is developed for a realistic, simple, causal hereditary model with a power-law attenuation. In this class of models the energy travels with a delay behind the wave front because the effective speed of the seismic signal is lower than the infinite-frequency limit of the propagation speed which determines the wave front propagation. In inversion this discrepancy affects the correct positioning of scatterers and interfaces. Our inversion method is an extension of Ribodetti’s imaging method. Using a power-law model, propagation- and attenuation-related parameters are uncoupled for the acquisition geometries used in laboratory and in field seismic experiments. The method is applied to ultrasonic laboratory data where we have complete control of the acquisition parameters and the physical properties of the medium to be recovered are well known. An application to ultrasonic data for a wavefield scattered from a hollow PVC sample and a lava sample immersed in a water tank demonstrates that the proposed inversion method allows reliable parameter estimation in the power-law class of viscoacoustic models.
Highlights
Realistic inversion of seismic wave data requires a model which is mathematically rigorous, physically acceptable and sufficiently flexible
Whenever the wave propagation occurs in one material it is convenient to hold α at a constant value while applying the inversion procedure; the value of α is determined a posteriori by optimizing the discrepancy between the recorded data and the synthetic data obtained from the parameters of the medium determined by inversion
7 CONCLUSIONS We have demonstrated that the viscoelastic inversion developed by Ribodetti et al (2000) yields fairly sharp and reliable parameter estimates in the power-law model class
Summary
Realistic inversion of seismic wave data requires a model which is mathematically rigorous, physically acceptable and sufficiently flexible. Power-law models can be associated with a subset of the class of viscoelastic equations of motion with singular memory, studied in a related paper (Hanyga & Seredynska 1999a). A scalar model of single-mode wave propagation with power-law attenuation can be represented by a frequency-domain expression:. For applications in seismic inversion the Green’s function for the background model should preferably be computable in the frequency domain This leaves the following possibilities for the background model: it is either an arbitrary power-law model (3) with the kernel K given by eq (5) and constant parameters, or a possibly heterogeneous model for which a ray-asymptotic Green’s function is available, defined by the time convolution kernels (7) with α = 1/2, 1/3, 2/3
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
