Two figure captions in this paper were in error, confusing compressibility and incompressibility (the figures themselves were correct). The proper figure captions are
FIGURE 2. Comparison of Berea sandstone data from Hart and Wang (2010) for Kud − Kfm (as functions of differential pressure, pd = p − pF) with predictions from Gassmann theory (Equation 1, using data for K𝑆 (from Equation 14; see also the unnumbered equation from B&K following Equation 17), or from VRH theory), and from B&K theory (Equation 19, using data for K𝑆 and for κM (from Equation 21)). The Fluid (water) incompressibility KF is taken as 2.3 GPa.
FIGURE 4. Comparison of Indiana limestone data from Hart and Wang (2010) for Kud − Kfm (as functions of differential pressure, pd = p − pF) with predictions from Gassmann theory (Equation 1, using data for KS (from Equation 14; see also the unnumbered equation from B&K following Equation 17), or from VRH theory), and from B&K theory (Equation 19, using data for K𝑆 and κM (from Equation 21)). The Fluid (water) incompressibility KF is taken as 2.3 GPa.
To address low detection accuracy and speed due to the multisolvability of the ground-penetrating radar signal, we proposed a novel centralized feature pyramid-YOLOv6l–based model to enhance detection precision and speed in road damage and pipeline detection. The centralized feature pyramid was used to obtain rich intra-layer features and improve the network performance. Our proposed model achieves higher accuracy compared with the existing detection models. We also built two new evaluating indexes, relative average precision and relative mean average precision, to fully evaluate the detection accuracy. To verify the applicability of our model, we conducted a road field detection experiment on a ground-penetrating radar dataset we collected and found that the proposed model had good performance in increasing detection precision, achieving the highest mean average precision compared with YOLOv7, YOLOv5 and YOLOx models, with relative mean average precision and frame rate per second at 16.38% and 30.5%, respectively. The detection information for the road damage and pipeline were used to conduct three-dimensional imaging. Our model is suitable for object detection in ground-penetrating radar images, thereby providing technical support for road damage and underground pipeline detection.
Reflectivity inversion is a key step in reservoir prediction. Conventional sparse-spike deconvolution assumes that the reflectivity (reflection coefficient series) is sparse and solves for the reflection coefficients by an L1-norm inversion process. Spectral inversion is an alternative to sparse-spike deconvolution, which is based on the odd–even decomposition algorithm and can accurately identify thin layers and reduce the wavelet tuning effect without using constraints from logging data, from horizon interpretations or from an initial model of the reflectivity. In seismic processing, an error exists in wavelet extraction because of complex geological structures, resulting in the low accuracy of deconvolution and inversion. Blind deconvolution is an effective method for solving the problem mentioned above, which comprises seismic wavelet and reflectivity sequence, assuming that the wavelets that affect some subsets of the seismic data are approximately the same. Therefore, we combined blind deconvolution with spectral inversion to propose blind spectral inversion. Given an initial wavelet, we can calculate the reflectivity based on spectral inversion and update the wavelet for the next iteration. During the update processing, we add the smoothness of the wavelet amplitude spectrum as a regularization term, thus reducing the wavelet oscillation in the time domain, increasing the similarity between inverted and initial wavelets, and improving the stability of the solution. The blind spectral inversion method inherits the wavelet robustness of blind deconvolution and high resolution of spectral inversion, which is suitable for reflectivity inversion. Applications to synthetic and field seismic datasets demonstrate that the blind spectral inversion method can accurately calculate the reflectivity even when there is an error in wavelet extraction.
Over the past decades, surface wave methods have been routinely employed to retrieve the physical characteristics of the first tens of meters of the subsurface, particularly the shear wave velocity profiles. Traditional methods rely on the application of the multichannel analysis of surface waves to invert the fundamental and higher modes of Rayleigh waves. However, the limitations affecting this approach, such as the 1D model assumption and the high degree of subjectivity when extracting the dispersion curve, motivate us to apply the elastic full-waveform inversion, which, despite its higher computational cost, enables leveraging the complete information embedded in the recorded seismograms. Standard approaches solve the full-waveform inversion using gradient-based algorithms minimizing an error function, commonly measuring the misfit between observed and predicted waveforms. However, these deterministic approaches lack proper uncertainty quantification and are susceptible to get trapped in some local minima of the error function. An alternative lies in a probabilistic framework, but, in this case, we need to deal with the huge computational effort characterizing the Bayesian approach when applied to non-linear problems associated with expensive forward modelling and large model spaces. In this work, we present a gradient-based Markov chain Monte Carlo full-waveform inversion where we accelerate the sampling of the posterior distribution by compressing data and model spaces through the discrete cosine transform. Additionally, a proposal is defined as a local, Gaussian approximation of the target density, constructed using the local Hessian and gradient information of the log posterior. We first validate our method through a synthetic test where the velocity model features lateral and vertical velocity variations. Then we invert a real dataset from the InterPACIFIC project. The obtained results prove the efficiency of our proposed algorithm, which demonstrates to be robust against cycle-skipping issues and able to provide reasonable uncertainty evaluations with an affordable computational cost.
We apply a machine learning approach to automatically infer two key attributes – the location of fault or shear zone structures and the thickness of the overburden – in an 18 km2 study area within and surrounding the Archean Fenelon gold deposit in Quebec, Canada. Our approach involves the inversion of carefully curated borehole lithological and structural observations truncated at 480 m below the surface, combined with magnetic and Light Detection and Ranging survey data. We take a computationally low-cost approach in which no underlying model for geological consistency is imposed. We investigated three contrasting approaches: (1) an inferred fault model, in which the borehole observations represent a direct evaluation of the presence of fault or shear zones; (2) an inferred overburden model, using borehole observations on the overburden-bedrock contact; (3) a model with three classes – overburden, faulted bedrock and unfaulted bedrock, which combines aspects of (1) and (2). In every case, we applied all 32 standard machine learning algorithms. We found that Bagged Trees, fine K-nearest neighbours and weighted K-nearest neighbour were the most successful, producing similar accuracy, sensitivity and specificity metrics. The Bagged Trees algorithm predicted fault locations with approximately 80% accuracy, 70% sensitivity and 73% specificity. Overburden thickness was predicted with 99% accuracy, 77% sensitivity and 93% specificity. Qualitatively, fault location predictions compared well to independently construct geological interpretations. Similar methods might be applicable in other areas with good borehole coverage, providing that criteria used in borehole logging are closely followed in devising classifications for the machine learning training set and might be usefully supplemented with a variety of geophysical survey data types.
By directly solving the full two-way wave equation, reverse time migration has superiority over other imaging algorithms in handling steeply dipping structures and other complicated geological models. Moreover, by incorporating the asymptotic inversion operator into reverse time migration imaging condition, the imaging algorithm is able to give a quantitative estimation of parameter perturbation in high-frequency approximation sense. However, because conventional asymptotic inversion only accounts for geometrical spreading, uneven illumination due to irregular acquisition geometry and inhomogeneous subsurface at each image point is neglected. The omit of illumination compensation significantly affects the imaging quality. Wave-equation-based illumination compensation methods have been extensively studied in the past. However, the traditional wave-equation-based illumination compensation methods usually require high computational cost and huge storage. In this paper, we propose an efficient wave-equation-based illumination compensation method. Under high-frequency approximation, we first define a Jacobian determinant to measure the regularity of subsurface illumination, and then illumination compensation operators are proposed based on the Jacobian. Through boundary integration, we further express the illumination compensation operators through extrapolated wavefields; the explicit computation of asymptotic Green's functions is thus avoided, and an efficient illumination compensation implementation for reverse time migration is achieved. Numerical results with both synthetic and field data validate the effectiveness and efficiency of the presented method.
Crystalline rocks in the subsurface are of interest for geothermal energy extraction, nuclear waste storage, and, when weathered or fractured, as aquifers. Compliant discontinuities such as microcracks, cracks and fractures may nucleate and propagate due to changes in pore pressure, stress and temperature. These discontinuities may provide flow pathways for fluids and, if fracturing extends to surrounding rocks, may allow escape of fluids to neighbouring formations. Monitoring such rocks using sonic logs, passive seismic, borehole seismic and surface seismic requires understanding of the propagation of elastic waves in the presence of such discontinuities. These may have an anisotropic orientation distribution as in situ stress may be anisotropic. As crystalline rock may display intrinsic anisotropy due to foliation and the preferential orientation of anisotropic minerals, quantification of the relative importance of intrinsic and microcrack-induced anisotropy is important. This may be achieved based on the stress sensitivity of elastic wave velocities. A method that allows both the orientation distribution of microcracks and the stress dependence of their normal and shear compliance to be estimated independently of the elastic anisotropy of the background rock is presented. Results are given for anisotropic samples of gneiss from Bukov in the Czech Republic and granite from Grimsel in Switzerland based on the ultrasonic velocity measurements of Aminzadeh et al. The microcrack orientation distribution is approximately transversely isotropic for both samples with a preferred orientation of microcrack normals perpendicular to foliation. This preferred alignment is stronger in the sample of gneiss than in the granite sample, and the normal and shear compliance of the microcracks decreases with increasing compressive stress. This occurs because the contact between opposing faces of the discontinuities grows with increasing compressive stress, and this results in a decrease in elastic anisotropy with increasing compressive stress. At low stress, the ratio of microcrack normal compliance to shear compliance is approximately 0.25 for the granite sample and 0.7 for the sample of gneiss. The normal compliance ZN for both samples decreases faster with increasing compressive stress than the shear compliance ZT, resulting in a decrease in ZN/ZT with increasing compressive stress.
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