Conditioning bounds for traveltime tomography in layered media

This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that traveltimes of reflected rays do not contain enough information to recover the medium in a well-posed manner, regardless of the discretization. The counterpart of the Abel transform in the case of reflected rays is a Fredholm kernel of the first kind which is shown to have singular values that decay at least root-exponentially. Kinematically equivalent media are characterized in terms of a sequence of matching moments. This severe conditioning issue comes on top of the well-known rearrangement ambiguity due to low velocity zones. Numerical experiments in an ideal scenario show that a waveform-based model inversion code fits data accurately while converging to the wrong wave speed profile

Full waveform inversion with extrapolated low frequency data

The availability of low frequency data is an important factor in the success of full waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data below 2 or 3 Hz from the field is a challenging and expensive task. In this paper we explore the possibility of synthesizing the low frequencies computationally from high-frequency data, and use the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal processing problem, bandwidth extension is a very nonlinear and delicate operation. It requires a high-level interpretation of bandlimited seismic records into individual events, each of which is extrapolable to a lower (or higher) frequency band from the non-dispersive nature of the wave propagation model. We propose to use the phase tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. To demonstrate the reliability of bandwidth extension in the context of FWI, we first use the low frequencies in the extrapolated band as data substitute, in order to create the low-wavenumber background velocity model, and then switch to recorded data in the available band for the rest of the iterations. The resulting method, EFWI for short, demonstrates surprising robustness to the inaccuracies in the extrapolated low frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, we demonstrate that FWI based on an extrapolated [1, 5] Hz band, itself generated from data available in the [5, 15] Hz band, can produce reasonable estimations of the low wavenumber velocity models

Traveltime and conversion-point computations and parameter estimation in layered, anisotropic media by tau-p transform

Anisotropy influences many aspects of seismic wave propagation and, therefore, has implications for conventional processing schemes. It also holds information about the nature of the medium. To estimate anisotropy, we need both forward modeling and inversion tools. Forward modeling in anisotropic media is generally done by ray tracing. We present a new and fast method using the tau-p transform to calculate exact reflection-moveout curves in stratified, laterally homogeneous, anisotropic media for all pure-mode and converted phases which requires no conventional ray tracing. Moreover, we obtain the common conversion points for both P-SV and P-SH converted waves. Results are exact for arbitrary strength of anisotropy in both HTI and VTI media (transverse isotropy with a horizontal or vertical symmetry axis, respectively). Since inversion for anisotropic parameters is a highly nonunique problem, we also develop expressions describing the phase velocities that require only a reduced number of parameters for both types of anisotropy. Nevertheless, resulting predictions for traveltimes and conversion points are generally more accurate than those obtained using the conventional Taylor-series expansions. In addition, the reduced-parameter expressions are also able to handle kinks or cusps in the SV traveltime curves for either VTI or HTI symmetry

Seismic data analysis of an onshore-offshore transition zone at Ramså Basin, Norway – a modelling study

Postponed access: the file will be accessible after 2023-10-03Master's Thesis in Earth ScienceGEOV399MAMN-GEO

Anisotropic Waveform Tomography: Application to Crosshole data for Transversely Isotropic Media

Anisotropic Traveltime Tomography and Full Waveform Inversion were applied first to synthetic and then to real data following the development of a transversely isotropic model for handling anisotropy. Best-fitting models of seismic velocity and Thomsen\u27s anisotropy parameters were initially obtained from traveltime tomography, and then used as the starting models for Full Waveform Inversion. The use of a Laplace transform approach effectively damps late arriving S-wave artifacts that introduce errors into the modelling process. The results of the synthetic study highlights the tradeoffs in resolution between the two parameter classes, but verify anisotropic traveltime tomography as a valid method for generating starting models for Full Waveform Inversion. The joint technique was then applied to field gathers from Western Canada and compared to a similar analyses that used a simpler anisotropy model. The transversely isotropic approach yielded a Full Waveform Inversion model with superior resolution that better predicted the true data