Acoustic Waveform Tomography: A Blind Test on A Synthetic Dataset

Acoustic waveform tomography is applied to a 2D synthetic dataset from Saudi Aramco to test if we will be able to obtain an accurate and highly resolved velocity tomogram. Source and receiver locations are not located along a flat surface so we assume a surface topography from the source and receiver locations. The initial velocity model was obtained using traveltime tomography and the source wavelet was estimated from the frequency spectra of the data. Two sets of lowfrequency data with peak frequencies of 2 Hz and 5 Hz were used in waveform inversion. Our waveform tomogram is not accurate compared to the true model. To investigate why waveform inversion failed, I generated synthetic traces using the true model, inverted them to get an accurate tomogram. Apparently some of the information about the model needs to be corrected so that the data file is reliable. After I obtain the correct acquisition information, I should get a more accurate inversion result. INTRODUCTION Waveform tomography inverts the full-waveform information in seismic data to get a high-resolution and highaccuracy velocity estimate of the subsurface geology. In practice, waveform tomography is a highly nonlinear inverse problem and very sensitive to the source wavelet, initial model and other factors. Some time-domain methods were proposed to reduce the nonlinearity of waveform tomography including early-arrival waveform tomography (Sheng et al., 2006) and multiscale waveform tomography (Bunks et al., 1995). Though waveform tomography has been developed for more than 20 years, it is still not a standard method for velocity estimation. Successful applications of waveform tomography are limited to a few examples. There are several factors that affects its success including an unknown source signature, choice of forward modeling (acoustic, elastic, or anisotropic wave equation), surface topography, correct selection of the number of model parameters, etc. Research is still needed to make waveform inversion a more robust and practical tool in exploration geophysics. In this work, I applied acoustic waveform inversion to a synthetic dataset generated by Saudi Aramco. The goal of this study is to test the sensitivity of our waveform inversion method to some factors mentioned earlier and to obtain an accurate velocity tomogram compared to the true model from Saudi Aramco. We have to deal with an unknown source wavelet, surface topography, and unknown forward modeling. The latter problem occurs when different forward modeling codes are used for synthetic trace generation and inversion. The waveform inversion results presented in this report were obtained using a rugged surface topography implied from the source and receiver locations. Later I discovered that the acquisition surface was flat. However, I do not have time to rerun the inversion using a flat surface. THEORY In this report, we consider wave propagation as described by the 2D acoustic wave equation, 1 κ(r) ∂p(r, t|rs) ∂t −∇ · [ 1 ρ(r) ∇p(r, t|rs) ] = s(r, t|rs), (1) where p(r, t|rs) is a pressure field at position r at time t from a source at rs; κ(r) and ρ(r) are the bulk modulus and density, respectively; and s(r, t|rs) is the source function. The forward solution, p(r, t; rs), of the twoway wave equation 1 is computed by a staggered-grid, explicit finite-difference method with 4-order accuracy in space and 2-order accuracy in time (Levander, 1988). The free-surface boundary condition is applied to the top boundary of the model, and the perfectly matched layer (PML) boundary conditions (Berenger, 1994; Chew and Liu, 1996; Zeng et al., 2001; Festa and Nielson, 2003) are 193 194 Boonyasiriwat utilized at the other boundaries. In terms of the Green’s function G(r, t|r, 0), one can write the solution p(r, t|rs) of equation 1 as