Surveys in Geophysics最新文献

Integral formulas represent a methodological basis for the determination of gravitational fields generated by planetary bodies. In particular, spherical integral transformations are preferred for their symmetrical properties with the integration domain being the entire surface of the sphere. However, global coverage of boundary values is rarely guaranteed. In practical calculations, we therefore split the spherical surface into a near zone and a far zone, for convenience, by a spherical cap. While the gravitational effect in the near zone can be evaluated by numerical integration over available boundary values, the contribution of the far zone has to be precisely quantified by other means. Far-zone effects for the isotropic integral transformations and those depending on the direct azimuth have adequately been discussed. On the other hand, this subject has only marginally been addressed for the spherical integral formulas that are, except for other variables, also functions of the backward azimuth. In this article, we significantly advance the existing geodetic methodology by deriving the far-zone effects for the two classes of spherical integral transformations: (1) the analytical solutions of the horizontal, horizontal–horizontal, and horizontal–horizontal–horizontal BVPs including their generalisations with arbitrary-order vertical derivative of respective boundary conditions and (2) spatial (vertical, horizontal, or mixed) derivatives of these generalised analytical solutions up to the third order. The integral and spectral forms of the far-zone effects are implemented in MATLAB software package, and their consistency is tested in closed-loop simulations. The presented methodology can be employed in upward/downward continuation of potential field observables or for a quantification of error propagation through spherical integral transformations.

Electromagnetic (EM) imaging aims to produce large-scale, high-resolution soil conductivity maps that provide essential information for Earth subsurface exploration. To rigorously generate EM subsurface models, one must address both the forward problem and the inverse problem. From these subsurface resistivity maps, also referred to as volumes of resistivity distribution, it is possible to extract useful information (lithology, temperature, porosity, permeability, among others) to improve our knowledge about geo-resources on which modern society depends (e.g., energy, groundwater, and raw materials, among others). However, this ability to detect electrical resistivity contrasts also makes EM imaging techniques sensitive to metallic structures whose EM footprint often exceeds their diminutive stature compared to surrounding materials. Depending on target applications, this behavior can be advantageous or disadvantageous. In this work, we review EM modeling and inverse solutions in the presence of metallic structures, emphasizing how these structures affect EM data acquisition and interpretation. By addressing the challenges posed by metallic structures, our aim is to enhance the accuracy and reliability of subsurface EM characterization, ultimately leading to improved management of geo-resources and environmental monitoring. Here, we consider the latter through the lens of a triple helix approach: physics behind metallic structures in EM modeling and imaging, development of computational tools (conventional strategies and artificial intelligence schemes), and configurations and applications. The literature review shows that, despite recent scientific advancements, EM imaging techniques are still being developed, as are software-based data processing and interpretation tools. Such progress must address geological complexities and metallic casing measurements integrity in increasing detail setups. We hope this review will provide inspiration for researchers to study the fascinating EM problem, as well as establishing a robust technological ecosystem to those interested in studying EM fields affected by metallic artifacts.

The adjoint method is a popular method used for seismic (full-waveform) inversion today. The method is considered to give more realistic and detailed images of the interior of the Earth by the use of more realistic physics. It relies on the definition of an adjoint wavefield (hence its name) that is the time-reversed synthetics that satisfy the original equations of motion. The physical justification of the nature of the adjoint wavefield is, however, commonly done by brute force with ad hoc assumptions and/or relying on the existence of Green’s functions, the representation theorem and/or the Born approximation. Using variational principles only, and without these mentioned assumptions and/or additional mathematical tools, we show that the time-reversed adjoint wavefield should be defined as a premise that leads to the correct adjoint equations. This allows us to clarify mathematical inconsistencies found in previous seminal works when dealing with viscoelastic attenuation and/or odd-order derivative terms in the equation of motion. We then discuss some methodologies for the numerical implementation of the method in the time domain and to present a variational formulation for the construction of different misfit functions. We here define a new misfit travel-time function that allows us to find consensus for the longstanding debate on the zero sensitivity along the ray path that cross-correlation travel-time measurements show. In fact, we prove that the zero sensitivity along the ray path appears as a consequence of the assumption on the similarity between data and synthetics required to perform cross-correlation travel-time measurements. When no assumption between data and synthetics is preconceived, travel-time Fréchet kernels show an extremum along the ray path as one intuitively would expect.

Geophysical logging series are valuable geological data that record the physical and chemical information of borehole walls and in-situ formations, and are widely used by geologists for interpreting geological problems due to their continuity, high resolution, and ease of access. Recently, machine learning methods are gradually bringing data science and geoscience closer together, and Intelligent Recognition using Logging Data (IRLD) is increasingly becoming an important interpretation task. However, due to the specificity of geological information, relatively low data quality makes the direct application of machine learning models to IRLD often not optimal. And to the best of our knowledge, IRLDs are not highly generalizable and technical surveys are still lacking. Therefore, this paper presents a comprehensive review of IRLD. Specifically, after systematically reviewing geophysical well logging and machine learning techniques, the main applications and general processes for the cross-discipline task of IRLD are summarized. More importantly, the key challenges of IRLD in the four stages of data acquisition, feature engineering, model building, and practical application are discussed in this review. The potential risks of these challenges are visualized by using real logging data from a study area in the South China Sea and the example of a lithology identification task. For these challenges, we give the current state-of-the-art methods and feasible strategies in conjunction with published research. This comprehensive review is expected to provide insights for practitioners to construct more robust models and achieve more effective application results in IRLD.

The Earth exhibits an equatorial flattening specified by the ellipticity and the east longitude (or orientation) of the equatorial major axis, which is uniquely determined by the degree 2 and order 2 gravitational coefficients, C₂₂ and S₂₂. The 31-year SLR (satellite laser ranging) and 22-year GRACE/GRACE-FO (gravity recovery and climate experiment) data are analyzed to study the climate-related secular and 5.7 years to decadal variations in C₂₂ and S₂₂, in turn, the drift and decadal variation in the Earth’s equatorial ellipticity and orientation of the principal axis of the least moment of inertia. The effects of the surface floating mass changes (including atmosphere, ocean and surface water redistribution and the melting of the mountain and polar glaciers) and the interior fluid convective (Earth’s core flows) were evaluated. Results reveal that the equatorial ellipticity of the Earth is linearly increasing along with a remarkable decadal variation and the Earth’s equator is flattening by ~ 0.16 mm/yr.

Low-rank approximation has emerged as a promising technique for recovering five-dimensional (5D) seismic data, yet the quest for higher accuracy and stronger rank robustness remains a critical pursuit. We introduce a low-rank approximation method by leveraging the complete graph tensor network (CGTN) decomposition and the learnable transform (LT), referred to as the LRA-LTCGTN method, to simultaneously denoise and reconstruct 5D seismic data. In the LRA-LTCGTN framework, the LT is employed to project the frequency tensor of the original 5D data onto a small-scale latent space. Subsequently, the CGTN decomposition is executed on this latent space. We adopt the proximal alternating minimization algorithm to optimize each variable. Both 5D synthetic data and field data examples indicate that the LRA-LTCGTN method exhibits notable advantages and superior efficiency compared to the damped rank-reduction (DRR), parallel matrix factorization (PMF), and LRA-CGTN methods. Moreover, a sensitivity analysis underscores the remarkably stronger robustness of the LRA-LTCGTN method in terms of rank without any optimization procedure with respect to rank, compared to the LRA-CGTN method.

The quality factor Q is a dimensionless measure of the energy loss per cycle of a wave field, and a proper understanding of this factor is important in a variety of fields, from seismology, geophysical prospecting to electrical science. Here, the focus is on viscoelasticity. When interpreting experimental values, several factors must be taken into account, in particular the shape of the medium (rods, bars or unbounded media) and the fact that the measurements are made on stationary or propagating modes. From a theoretical point of view, the expressions of Q may differ due to different definitions, the spatial dimension and the inhomogeneity of the wave, i.e. the fact that the vectors of propagation (or wavenumber) and attenuation do not point in the same direction. We show the difference between temporal and spatial Q, the relationships between compressional and shear Q, the dependence on frequency, the case of poro-viscoelasticity and anisotropy, the effect of inhomogeneous waves and various loss mechanisms, and consider the analogy between elastic and electromagnetic waves. We discuss physical theories describing relaxation peaks, bounds on Q and experiments showing the behaviour of Q as a function of frequency, saturation and pore pressure. Finally, we propose an application example where Q can be used to estimate porosity and saturation.

Blended acquisition offers significant cost and period reduction in seismic data acquisition. However, fired blended sources are usually deployed at off-the-grid (OffG) samples due to obstacle limitation and economic cost considerations. The irregular distribution of coordinates, along with the blending noise, has a detrimental effect on the performance of subsequent seismic processing and imaging. The interpolated multichannel singular spectrum analysis (I-MSSA) algorithm effectively provides on-the-grid deblended results by employing an interpolator, in conjunction with a projected gradient descent strategy. However, the deblending accuracy and computational efficiency of the I-MSSA are still a concern due to the limitations of the traditional singular value decomposition (SVD). To address these limitations, we propose an interpolated fast damped multichannel singular spectrum analysis (I-FDMSSA) rank-reduction algorithm. The proposed algorithm incorporates the damping operator, the randomized SVD (RSVD) and the fast Fourier transform (FFT) strategy. The damping operator can further attenuate the remaining noise in the estimated signal obtained from the truncated SVD, resulting in an improved deblending performance. The RSVD accelerates the rank-reduction process by shrinking the size of the Hankel matrix. To expedite the rank-reduction and anti-diagonal averaging stages without explicitly constructing large-scale block Hankel matrices, the FFT strategy is employed. By incorporating a 2D separable sinc interpolator, the I-FDMSSA enables an efficient and accurate deblending of 3D OffG blended data. The deblending performance and operational efficiency improvements of the proposed I-FDMSSA algorithm over the traditional I-MSSA algorithm are demonstrated through OffG synthetic and field blended data examples.