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

Increasing Reflection Coherency Through Improved Statics Corrections: An Iterative Tomographic Approach

Computation and application of statics corrections have always been problematic on CMP reflection data, especially in highly weathered and structurally altered environments. Tomographic estimation of the velocity field within the weathered layer is a severely underdetermined problem, only to be exacerbated by the lack of a priori information of most survey sites. Statistically driven static techniques are sometimes considered implausible for specific subsurface conditions where compensating for severe static problems is necessary. Using turning-ray tomography to make static corrections (tomostatics) and iteratively developing the best tomographic model based on site-specific reflection arrivals will ultimately optimize the static correction for each source and receiver station. Cross-correlation statics routines that monitored changes in specific near-surface reflections during iterative application of tomostatics guided the selection of the best initial model. Combining statistical techniques with geologically based models of the subsurface increased the overall reflection coherency and accuracy of the final stacked section

Imaging of structure at and near the core mantle boundary using a generalized radon transform

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2007.Includes bibliographical references (p. [163]-175).In this thesis, concepts from inverse scattering and modem statistics are combined into a powerful tool for imaging interfaces in Earth's deep interior. Specially, a generalized Radon transform (GRT) approach is developed to image heterogeneity at and near interfaces in Earth's lowermost mantle with broadband, three-component seismograms from Global Seismograph Networks (GSN). With this GRT method I transformed ~100,000 transverse-component ScS waveforms into image gathers of a core mantle boundary (CMB) patch beneath Central America and juxtaposition of stacks of these gathers produces a 2-D image profile. To enhance this image profile, I collaborated with statisticians and used mixed-effects statistical modeling to produce the best estimates of reflectivity along with their uncertainty. I demonstrate that the method outlined above works well and - thus - paves the way to large-scale seismic exploration of the lowermost mantle. With the new technology I mapped the structure at and near the CMB beneath Central and North America. Several interfaces are detected, and some of them are consistent with expectations from phase transformations in Magnesiiim perovskite. If we know which interface is associated with a particular phase transformation, and if we know the thermodynamic (P-T) relations of the stability fields of the phases, then we can estimate temperature from the pressure as inferred from the depth at which the transition occurs in the seismic sections. Here we associate a seismically observed wavespeed increase with the perovskite to post-perovskite transition and a wavespeed decrease with the back transformation to perovskite.(cont.) Using P-T data from experimental and theoretical mineral physics we can then estimate the lateral temperature variations and radial (thermal) gradients near the CMB. In addition, the temperature of the CMB and global heat loss are estimated. To improve D" imaging even further, I have constructed a generalized Radon transform approach, compensating for the liquid outer-core, which can be used to transform seismic signals passing trough the outer-core, such as SKKS and its precursors and coda. I apply this method to the same region as used in ScS studies. The image gathers computed from SKKS are in excellent agreement with the results (for the same image points) obtained from ScS. With this development we now have a tool for detailed D" imaging - on sub-global scale - with joint interpretation (by means of the GRT and mixed-method statistics) of the broadband ScS and SKKS wavefields.by Ping Wang.Ph.D

Three-dimensional anisotropic full-waveform inversion

Full-waveform inversion (FWI) is a powerful nonlinear tool for quantitative estimation of high-resolution high-fidelity models of subsurface seismic parameters, typically P-wave velocity. A solution is obtained via a series of iterative local linearised updates to a start model, requiring this model to lie within the basin of attraction of the solution space’s global minimum. The consideration of seismic anisotropy during FWI is vital, as it holds influence over both the kinematics and dynamics of seismic waveforms. If not appropriately taken into account, then inadequacies in the anisotropy model are likely to manifest as significant error in the recovered velocity model. Conventionally, anisotropic FWI either employs an a priori anisotropy model, held fixed during FWI, or uses a local inversion scheme to recover anisotropy as part of FWI; both of these methods can be problematic. Constructing an anisotropy model prior to FWI often involves intensive (and hence expensive) iterative procedures. On the other hand, introducing multiple parameters to FWI itself increases the complexity of what is already an underdetermined problem. As an alternative I propose here a novel approach referred to as combined FWI. This uses a global inversion for long-wavelength acoustic anisotropy, involving no start model, while simultaneously updating P-wave velocity using mono-parameter local FWI. Combined FWI is then followed by multi-parameter local FWI to recover the detailed final model. To validate the combined FWI scheme, I evaluate its performance with several 2D synthetic datasets, and apply it to a full 3D field dataset. The synthetic results establish the combined FWI, as part of a two-stage workflow, as more accurate than an equivalent conventional workflow. The solution obtained from the field data reconciles well with in situ borehole measurements. Although combined FWI includes a global inversion, I demonstrate that it is nonetheless affordable and commercially practical for 3D field data.Open Acces

Applied Measurement Systems

Measurement is a multidisciplinary experimental science. Measurement systems synergistically blend science, engineering and statistical methods to provide fundamental data for research, design and development, control of processes and operations, and facilitate safe and economic performance of systems. In recent years, measuring techniques have expanded rapidly and gained maturity, through extensive research activities and hardware advancements. With individual chapters authored by eminent professionals in their respective topics, Applied Measurement Systems attempts to provide a comprehensive presentation and in-depth guidance on some of the key applied and advanced topics in measurements for scientists, engineers and educators