HIGH RESOLUTION SEISMIC TOMOGRAPHY WITH THE GENERALIZED RADON TRANSFORM AND EARLY ARRIVAL WAVEFORM INVERSION (Ph.D. Dissertation)
Jianming Sheng, University of Utah
Traveltime tomography is an important imaging tool in oil and gas exploration, and earthquake seismology. However, the spatial resolution of traveltime tomograms are inherently restricted because of the finite-frequency effects in the data and the high-frequency approximation in ray-based tomography. In this dissertation, the generalized Radon transform (GRT) is used to derive the resolution limits for wavepath traveltime tomography, and a new imaging algorithm is developed based on the resolution formula. In addition, I develop and test a new imaging algorithm, early arrival waveform tomography (EWT) algorithm and show that it combines good convergence with high resolution capabilities.
GRT. The Rytov approximation that expresses phase residuals as an explicit function of the slowness perturbations, is also related to the GRT. Using Beylkin's formalism, the corresponding inverse GRT is obtained to give the slowness model as an explicit function of the phase residuals. A slowness resolution formula is obtained which explicitly gives the slowness perturbation function as a product of the frequency and the traveltime gradient obtained by ray tracing. I denote tomograms based on this new development GRT tomograms. Resolution limits are obtained for models estimated from several types of data: first-arrivals from a crosswell experiment, refraction data associated with diving-wave arrivals and earthquakes. A fat-ray traveltime tomography algorithm is derived that automatically limits the size of pixels based on diffraction theory. These new theoretical formulae provide powerful tools for realistically estimating slowness resolution in tomograms and imaging the earth's velocity distribution.
Early Arrival Waveform Tomography. Even GRT tomography has limits when multi-arrivals (e.g., diffraction events) interfere with one another at early times. In this case, I developed an alternative to waveform tomography which only predicts the early arrivals by finite-difference solutions to the wave equation. I denote this new method EWT. By fitting the early arrivals, EWT naturally takes into account more general wave propagation effects, such as diffractions and wavepath averaging. This means there is less conflict between the observed and predicted data, so a wider range of slowness wavenumbers can be estimated compared to traveltime tomography. EWT is not restricted by the high-frequency assumption of ray-based tomography and so a better slowness resolution is possible. Another benefit of EWT is that an early arrival misfit function contains fewer local minima than the entire trace misfit function in standard waveform tomography. Synthetic test results show that waveform tomograms are much more resolved than the traveltime tomogram, and that this algorithm has good convergence properties.
The successful EWT results with synthetic data motivated the application of this method to ChevronTexaco's 2-D Gulf of Mexico marine data and a near-surface refraction survey near Mapleton, Utah. For the marine data, the statics problem caused by the shallow gassy muds was attacked by using tomostatic waveform tomography to obtain a more accurate velocity model. Using the waveform tomogram, the stacked section and the migration images were significantly improved compared to using the NMO velocity.
The Mapleton data set is a challenge for EWT in several ways: seismic attenuation is quite serious; surface waves dominated the later arrivals; rugged topography produced significant near-surface scattering; and there were many faults and colluvial wedges near the surface. The attenuation factor Q was estimated from the data by determining the centroid frequencies of the first-arrivals as a function of offset. Source wavelets were estimated by stacking the early arrivals. Inverting the Mapleton data by EWT showed a velocity tomogram that was much more consistent with the trench log than the traveltime tomogram. The EWT tomogram was significantly more accountable than the traveltime tomogram.