The problem of estimating relative time (or depth) shifts between two seismic images is ubiquitous in seismic data processing. This problem is especially difficult where shifts are large and vary rapidly with time and space, and where images are contaminated with noise or for other reasons are not shifted versions of one another. A new solution to this problem requires only simple extensions of a classic dynamic time warping algorithm for speech recognition. A key component of that classic algorithm is a nonlinear accumulation of alignment errors. By applying the same nonlinear accumulator repeatedly in all directions along all sampled axes of a multidimensional image, I obtain a new and effective method for dynamic image warping (DIW). In tests where known shifts vary rapidly, this new method is more accurate than methods based on crosscorrelations of windowed images. DIW also aligns seismic reflectors well in examples where shifts are unknown, for images with differences not limited to time shifts.
Fault interpretation enhances our understanding of complex geologic structures and stratigraphy apparent in 3D seismic images. Common steps in this interpretation include image processing to highlight faults, the construction of fault surfaces, and estimation of fault throws. Although all three of these steps have been automated to some extent by others, fault interpretation today typically requires significant manual effort, suggesting that further improvements in automatic methods are feasible and worthwhile. I first used an efficient algorithm to compute images of fault likelihoods, strikes, and dips from a 3D seismic image. From these three fault images, I then automatically extracted fault surfaces as meshes of quadrilaterals that coincide with ridges of fault likelihood. A quadrilateral mesh is a simple data structure alongside which one can easily gather samples of the 3D seismic image. I automatically estimated fault throws by minimizing differences in values of samples gathered from opposite sides of a fault, while constraining the variation of throw within a fault surface. I tested the fidelity of estimated fault throws by using them to undo faulting. After unfaulting, reflectors in 3D seismic images were more continuous than those in the original 3D seismic image. In one example, this unfaulting test supported the observation that some extracted fault surfaces have unusual conical shapes.
In reflection seismology, full-waveform inversion (FWI) can generate high-wavenumber subsurface velocity models but often suffers from an objective function with local minima caused mainly by the absence of low frequencies in seismograms. These local minima cause cycle skipping when the low-wavenumber component in the initial velocity model for FWI is far from the true model. To avoid cycle skipping, we discovered a new wave-equation reflection traveltime inversion (WERTI) to update the low-wavenumber component of the velocity model, while using FWI to only update high-wavenumber details of the model. We implemented the low- and high-wavenumber inversions in an alternating way. In WERTI, we used dynamic image warping (DIW) to estimate the time shifts between recorded data and synthetic data. When compared with correlation-based techniques often used in traveltime estimation, DIW can avoid cycle skipping and estimate the time shifts accurately, even when shifts vary rapidly. Hence, by minimizing traveltime shifts estimated by dynamic warping, WERTI reduces errors in reflection traveltime inversion. Then, conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high-wavenumber details. The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.
Uniformly sampled images are often used to interpolate other data acquired more sparsely with an entirely different mode of measurement. For example, downhole tools enable geophysical properties to be measured with high precision near boreholes that are scattered spatially, and less precise seismic images acquired at the earth's surface are used to interpolate those properties at locations far away from the boreholes. Image-guided interpolation is designed specifically to enhance this process. Most existing methods for interpolation require distances from points where data will be interpolated to nearby points where data are known. Image-guided interpolation requires non-Euclidean distances in metric tensor fields that represent the coherence, orientations and shapes of features in images. This requirement leads to a new method for interpolating scattered data that I call blended neighbor interpolation. For simple Euclidean distances, blended neighbor interpolation resembles the classic natural neighbor interpolation.
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