In the context of machine learning for uncertainty quantification (UQ) of inverse problems: we propose to first transform input observations using the adjoint. We demonstrate with two imaging examples (photoacoustic imaging and CT) that firstly: the adjoint partially undoes the physics of the problem resulting in faster convergence of the learning phase and secondly: the final algorithm is now robust to changes in observations such as changing transducer subsampling in photoacoustic imaging and angles in CT. Our adjoint-based method gives point estimates faster than traditional baselines and with higher SSIM metrics, while also providing validated UQ.
Images obtained from seismic data are used by the oil and gas industry for geophysical exploration. Cutting-edge
methods for transforming the data into interpretable images are moving away from linear approximations and
high-frequency asymptotics towards Full Waveform Inversion (FWI), a nonlinear data-fitting procedure based
on full data modeling using the wave-equation. The size of the problem, the nonlinearity of the forward model,
and ill-posedness of the formulation all contribute to a pressing need for fast algorithms and novel regularization
techniques to speed up and improve inversion results.
In this paper, we design a modified Gauss-Newton algorithm to solve the PDE-constrained optimization problem
using ideas from stochastic optimization and compressive sensing. More specifically, we replace the Gauss-Newton
subproblems by randomly subsampled, ℓ1 regularized subproblems. This allows us us significantly reduce the
computational cost of calculating the updates and exploit the compressibility of wavefields in Curvelets.
We explain the relationships and connections between the new method and stochastic optimization and compressive
sensing (CS), and demonstrate the efficacy of the new method on a large-scale synthetic seismic example.
KEYWORDS: Data modeling, Reflectors, Wavelets, Signal to noise ratio, Associative arrays, Scattering, Chemical species, Denoising, Receivers, Reflectivity
Seismic imaging commits itself to locating singularities in the elastic properties of the Earth's subsurface. Using the high-frequency ray-Born approximation for scattering from non-intersecting smooth interfaces, seismic data can be represented by a generalized Radon transform mapping the singularities in the medium to seismic data. Even though seismic data are bandwidth limited, signatures of the singularities in the medium carry through this transform and its inverse and this mapping property presents us with the possibility to develop new imaging techniques that preserve and characterize the singularities from incomplete, bandwidth-limited and noisy data. In this paper we propose a non-adaptive Curvelet/Contourlet technique to image and preserve the singularities and a data-adaptive Matching Pursuit method to characterize these imaged singularities by Multi-fractional Splines. This first technique borrows from the ideas within the Wavelet-Vaguelette/Quasi-SVD approach. We use the almost diagonalization of the scattering operator to approximately compensate for (i) the coloring of the noise and hence facilitate estimation; (ii) the normal operator itself. Results of applying these techniques to seismic imaging are encouraging although many open fundamental questions remain.
Inversion algorithms for UXO discrimination using magnetometery
have recently been used to achieve very low False Alarm Rates,
with 100% recovery of detected ordnance. When there are many UXO
and/or when the UXO are at significantly different depths, manual
estimation of the initial position and scale for each item, is a
laborious and time-consuming process. In this paper, we utilize the multi-resolution properties of wavelets to automatically estimate both the position and scale of dipole peaks. The Automated Wavelet Detection (AWD) algorithm that we develop consists of four-stages: (i) maxima and minima in the data are followed across multiple scales as we zoom with a continuous wavelet transform; (ii) the decay of the amplitude of each peak with scale is used to estimate the depth to source; (iii) adjacent maxima and minima of comparable depth are joined together to form dipole anomalies; and (iv) the relative positions and amplitudes of the extrema, along with their depths, are used to estimate a dipole model. We demonstrate the application of the AWD algorithm to three datasets with different characteristics. In each case, the method rapidly located the majority of dipole anomalies and produced accurate estimates of dipole parameters.
Acoustic/elastic surface seismic and borehole oriented remote sensing methods generally derive their existence from the presence of singularities, regions of rapid variation, in the medium properties that carry the waves. Coherent reflections emanate at these singularities and the primary aim of this paper is: (1) to find a characterization for the singularity structure by means of scaling exponents and singularity spectra; (2) to better understand how the singularity structure is being mapped from space (the medium) to space-time (the wavefield); and (3) to initiate a theoretical discussion on the implications of the multiscale analysis findings in relation to wave theory. Applying multiscale analyses to well- and seismic reflection data shows two things. Firstly, the earth's subsurface behavior is much more intricate as assumed within the current piece- wise smooth medium representations. And, secondly, it reveals a direct relationship between the singularity structure of the medium, the well-log, and that of the wavefield, the reflection data. The medium's singularity structure shows that the singularities are not limited to jump discontinuities and that they lie dense. These important observations allude to the questions: (1) how to improve the understanding of the medium's scale dependence in relation to the amplitudes of waves, and (2) how to explain for the mapping of the singularity structure within the current wave theory.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.