Search

SUMMARY Joint inversion for the same or different geophysical parameters is proved to be an effective technique for obtaining high-resolution solutions. Thus, comprehensive geophysical interpretation based on joint inversion has been widely concerned and applied in recent years. To realize joint inversion conveniently and efficiently, we proposed a new inversion strategy based on the alternating direction method of multipliers. In this regard, three optimization algorithms were presented respectively to attain the joint inversion of body wave traveltime and surface wave dispersion data, to obtain the joint inversion of magnetotelluric and seismic data with cross-gradient constraints, and to acquire gravity constrained inversion. A complex model with inconsistent structures in terms of resistivity, velocity and density was designed to evaluate the accuracy and effectiveness of the multiparameter joint inversion algorithms. In our joint inversion processes, each method was optimized independently and the jointly inverted results were significantly more accurate than those of separate inversions. Finally, we applied the algorithms to the field data involving gravity anomaly data, magnetotelluric data and Rayleigh wave dispersion data. The reliable underground structure was achieved by the joint interpretation of density, resistivity and velocity profiles, which verified the practicality of the inversion strategy in the actual data.

International audience; A receiver-extension strategy is presented as an alternative to recently promoted source-extension strategies, in the framework of high resolution seismic imaging by full waveform inversion. This receiver-extension strategy is directly applicable in time-domain full waveform inversion, and unlike source-extension methods it incurs negligible extra computational cost. After connections between difference source-extension strategies are reviewed, the receiver-extension method is introduced and analyzed for single-arrival data. The method results in a misfit function convex with respect to the velocity model in this context. The method is then applied to three exploration scale synthetic case studies representative of different geological environment, based on: the Marmousi model, the BP 2004 salt model, and the Valhall model. In all three cases the receiver-extension strategy makes it possible to start full waveform inversion with crude initial models, and reconstruct meaningful subsurface velocity models. The good performance of the method even considering inaccurate amplitude prediction due to noise, imperfect modeling, and source wavelet estimation, bodes well for field data applications.

This letter is concerned with the decentralized $H_{\infty }$ control problem of discrete-time interconnected systems. The studied interconnected system is transformed equivalently into a single linear time invariant system with matrix inversion terms in the system matrices. This letter derives novel necessary and sufficient conditions such that the considered interconnected system is asymptotically stable with the prescribed $H_{\infty }$ performance. The new conditions are computationally attractive because of the elimination of matrix inversion terms. Then these conditions are transformed into linear matrix inequalities. The decentralized controllers can be obtained by solving linear matrix inequalities to guarantee the stability and the $H_{\infty }$ performance of the closed-loop interconnected system. Finally, the effectiveness and the advantages of the proposed results are demonstrated by one numerical example.

The perfluoroalkylsulfonylation (CF3SO2, C2F5SO2 and CHF2SO2) in the enaminone C H bonds has been developed simply via the promotion of molecular iodine by using stable and cheap sodium perfluoroalkyl sulfinates as coupling partners. The stereoselective synthesis of E-configurated α-perfluoroalkylsulfonyl enaminones has been realized via unprecedented C H bond elaboration and C C double bond configuration inversion by free radical process.

Majority inverter graph is a logic representation structure that along with its algebraic properties synthesizes circuits with improved area, delay, and speed metrics, as compared to conventional And-Invert graph (AIG) realization. In this paper, we propose mMIG synthesis approach, where we aim to minimize the number of inverters in such circuits by adopting minority logic in addition to majority and inversion operations in the logic representation. We propose a set of Boolean transformation methods and derived theorems for minority, majority, and inverter operations. We demonstrate that minority operation in addition to majority and inversion operations significantly optimizes the hardware footprint of combinational circuits and cryptographic primitives, such as linear operations and substitution boxes in several lightweight block ciphers. The area optimization is considered with reduction in count of complemented edges or inversion operations. As results demonstrate, the inversion operations have been reduced from 57.7% to 93.3% in mMIG synthesis approach as compared to MIG logic synthesis in EPFL combinational benchmark suite. In round function implementations of lightweight block ciphers such as SIMON, and ARX boxes such as MARX-2 and SPECKEY, the count of complemented edges in mMIG synthesis technique has been reduced by almost 50% as compared to that in MIG based implementations.

In the article by Prof. Осhapovskogo: "About the best way to eliminate the inversion of the eyelids with trachoma" (R. O. Zh,, 1929, No. 6) there is a question: "How do you treat, how do you operate?". For practitioners working in a remote province, the coverage of such issues on the pages of the press is very valuable and useful. Working in the dark wilderness, where there is a sea of trachoma, passing thousands of patients through the hospital every year and more than 30 thousand through the laboratory, it is possible to conduct sometimes very interesting observations and draw appropriate conclusions From the article by Prof. Ochayovsky can be seen that operations against trachomatous beyond the gate in his clinic for 19 years have been done in total-2055. We make almost the same figure in our hospital in one year. So, in the last year of 1929, we performed operations against inversion in the hospital1767. My goal was to comprehensively study the Lagleyze method. Therefore, out of 1767 operations, 1331 fall to the share of this method, the remaining 436 operations are other methods.

SUMMARY The Bayesian slip inversion offers a powerful tool for modelling the earthquake source mechanism. It can provide a fully probabilistic result and thus permits us to quantitatively assess the inversion uncertainty. The Bayesian problem is usually solved with Monte Carlo methods, but they are computationally expensive and are inapplicable for high-dimensional and large-scale problems. Variational inference is an alternative solver to the Bayesian problem. It turns Bayesian inference into an optimization task and thus enjoys better computational performances. In this study, we introduce a general variational inference algorithm, automatic differentiation variational inference (ADVI), to the Bayesian slip inversion and compare it with the classic Metropolis–Hastings (MH) sampling method. The synthetic test shows that the two methods generate nearly identical mean slip distributions and standard deviation maps. In the real case study, the two methods produce highly consistent mean slip distributions, but the ADVI-derived standard deviation map differs from that produced by the MH method, possibly because of the limitation of the Gaussian approximation in the ADVI method. In both cases, ADVI can give comparable results to the MH method but with a significantly lower computational cost. Our results show that ADVI is a promising and competitive method for the Bayesian slip inversion.

SUMMARY In an attempt to overcome the difficulties of the full waveform inversion (FWI), several alternative objective functions have been proposed over the last few years. Many of them are based on the assumption that the residuals (differences between modelled and observed seismic data) follow specific probability distributions when, in fact, the true probability distribution is unknown. This leads FWI to converge to an incorrect probability distribution if the assumed probability distribution is different from the real one and, consequently it may lead the FWI to achieve biased models of the subsurface. In this work, we propose an objective function which does not force the residuals to follow a specific probability distribution. Instead, we propose to use the non-parametric kernel density estimation technique (KDE) (which imposes the least possible assumptions about the residuals) to explore the probability distribution that may be more suitable. As evidenced by the results obtained in a synthetic model and in a typical P-wave velocity model of the Brazilian pre-salt fields, the proposed FWI reveals a greater potential to overcome more adverse situations (such as cycle-skipping) and also a lower sensitivity to noise in the observed data than conventional L2- and L1-norm objective functions and thus making it possible to obtain more accurate models of the subsurface. This greater potential is also illustrated by the smoother and less sinuous shape of the proposed objective function with fewer local minima compared with the conventional objective functions.

Compaction effects can obscure the impedance separation between hydrocarbon-bearing and fully brine-saturated sandstones. We have improved their discrimination by removing depth-related trends from inverted seismic impedance. Although the ratio of compressional- to shear-wave velocity versus seismic compressional-wave impedance crossplots shows differences among pay, brine sand, and shale trends, using absolute inverted impedances only imperfectly distinguishes hydrocarbon sands from brine sands due to outliers. In a given locality, statistical comparison of well log and seismic-derived impedances enables us to obtain a shale impedance model for a lithology baseline to detrend the impedance from the effects of burial and overburden. This has the effect of unmasking anomalies associated with hydrocarbon-bearing sands and serves as a reliable fluid discriminator. For an offshore Gulf of Mexico data set on the flank of a salt dome, with pay occurring over a wide range of depths, we identify hydrocarbon-bearing sands with a greater success rate after detrending the absolute seismic impedance.

Seismic amplitude-variation-with-offset (AVO) inversion from prestack seismic data plays a significant role in estimating elastic parameters and characterizing reservoir properties. In general, sparse regularization is widely used to solve ill-posed inverse problems by reducing the solution space of subsurface parameters, which makes seismic AVO inversion more stable. However, the traditional sparse constraint inversion only focuses on the vector sparsity of reflectivity, instead of the structural sparse characteristics of the estimated parameters. Consequently, various elastic parameters demonstrate different formation structural features in the same location of stratum. In this study, we have developed a novel approach that combines the structural sparsity and the vector sparsity of the model reflectivity to establish the posterior probability density distribution and solve the objective function of the model parameters. Based on the relationship among multiple elastic parameters, we divide the model parameters to be inverted into several groups according to intrinsic structural sparse characteristics of elastic parameters. In this case, all of the model parameters at the same sampling point are classified into the identical group, which ensures that different estimated parameters indicate the same characteristic in terms of stratigraphic structure. From the perspective of Bayesian inference, we use the modified Cauchy probability density function (PDF) to characterize the group sparsity and describe the relationship among model parameters in the same group by Gaussian PDF. Furthermore, we estimate the optimum solution corresponding to the maximum a posteriori probability under Bayesian inference. Synthetic experiments on a Marmousi model prove that the estimated P-velocity, S-velocity, and density are consistent with those of the real models, and the application of field data confirms the availability and feasibility of group sparse inversion.

The biocatalyzed conversion of hyocholic acid (3?,6?,7?-trihydroxy-5?-cholan-24-oic acid) into ?-muricholic acid (3?,6?,7?-trihydroxy-5?-cholan-24-oic acid) has been obtained exploiting a small library of 7?- and 7?-HSDHs (hydroxysteroid dehydrogenases). The process has been optimized and performed avoiding the isolation of the 7-oxo intermediate using the appropriate coupled enzymes for the in situ cofactor regeneration. Moreover, the biocatalyzed reduction of 6,7-dioxolithocholic acid (3?-hydroxy-6,7-dioxo-5?-cholan-24-oic acid) was also investigated.

This paper presents a novel comparator, which is operated in weak inversion to achieve the excellent energy efficiency. Detailed theoretical calculation has been given. Simulation results in a 65-nm CMOS technology match well with the theoretical analysis. This comparator achieves a high-resolution of 4 $$\mu $$ V at the clock frequency of 200 MHz. The power dissipation is 1.002 $$\mu $$ W and the offset standard deviation is about 9 $$\mu $$ V at 0.65 V power supply. Simulation results demonstrate the delay time is 1.304 ns for 4 $$\mu $$ V input difference and the Figure-of-Merit is only 3.08 $$\times $$ $$10^{-5}$$ fJ/conversion-step while operating at 200 MHz. Finally, the comparator is analyzed and compared with the conventional double-tail dynamic comparator and prior art in terms of the low-power, low-offset and high-resolution.

This study introduces a conceptually new solvent suppression scheme with adiabatic inversion pulses for 1H-detected multidimensional solid-state NMR (SSNMR) of biomolecules and other systems, which is termed “Solvent suppression of Liquid signal with Adiabatic Pulse” (SLAP). 1H-detected 2D 13C/1H SSNMR data of uniformly 13C- and 15N-labeled GB1 sample using ultra-fast magic angle spinning at a spinning rate of 60 kHz demonstrated that the SLAP scheme showed up to 3.5-fold better solvent suppression performance over a traditional solvent-suppression scheme for SSNMR, MISSISSIPPI (Zhou and Rienstra, J Magn Reson 192:167–172, 2008) with 2/3 of the average RF power.

Supramolecular DNA complexes consisting of both DNA duplexes and tetrameric G-quadruplexes are fabricated successfully by utilizing a single short DNA strand that contains one 5'-5' polarity of inversion site in the middle of G-tract. The resulting DNA supramolecules exhibit significantly high peroxidase activities after interaction with hemin due to the presence of various G-quadruplex-duplex (G4-duplex) interfaces. Significantly, we find that the addition of a C-rich fragment to the designed sequence not only allows the self-assembly of two-dimensional porous DNA nanostructures via the formation of dimeric i-motif structures but also could act as a control element to facilitate the generation of pH-sensitive G4-based DNAzymes. The enhanced catalytic activity obtained from specific sequence modifications as well as the controllable feature of these DNA nanostructures can significantly benefit further applications of DNA functional materials in complex biological systems.

A Gaussian mixture Hamiltonian Monte Carlo (HMC) Bayesian method has been developed for the inversion of petrophysical parameters such as pyrolysis parameter S1, which is driven by a statistical shale rock-physics model. Pyrolysis parameter S1 can be used to indicate the content of free or adsorbed hydrocarbons in source rock, and it is an important indicator to evaluate the production of shale oil reservoirs. However, most studies on pyrolysis parameters are based on pyrolysis experiments and there is no relevant study to inverse pyrolysis parameter S1 from seismic data. In addition, compared to the total organic carbon content, pyrolysis S1 is more accurate for evaluating gas and oil in shale. In particular, high values of pyrolysis S1 can directly indicate the content of shale oil. We have developed a strategy for assessing shale oil sweet spots through estimating pyrolysis S1 and other petrophysical parameters. Based on the Gaussian mixture assumptions for the prior distribution of the model, we build a joint distribution to link the pyrolysis parameter S1 with elastic attributes, and then we derive a formulation to inverse S1 with the Bayesian model. Due to the components of the Gaussian mixture, the HMC method has been used to sample the posterior distribution. Our study finds that the HMC method for sampling can improve the efficiency and allow a more robust quantification of the uncertainty; also, application to real seismic data sets indicates that the delineation of sweet spots is more accurate combined with pyrolysis S1.

Wave-equation traveltime inversion (WTI) is a useful tool for background velocity model building. It is generally formulated and implemented in the time domain, in which the gradient is calculated by temporally crosscorrelating the source- and receiver-side wavefields. The time-domain source-side snapshots are either stored in memory or are reconstructed through back propagation. The memory requirements and computational cost of WTI are thus prohibitively expensive, especially for 3D applications. To partially alleviate this problem, we provide an implementation of WTI in the frequency domain with a monofrequency component. Because only one frequency is used, it is affordable to directly store the source- and receiver-side wavefields in memory. There is no need for wavefield reconstruction during gradient calculation. In such a way, we have dramatically reduced the memory requirements and computational cost compared with the traditional time-domain WTI realization. For practical implementation, the frequency-domain wavefield is calculated by time-domain finite-difference forward modeling and is transformed to the frequency domain by an on-the-fly discrete Fourier transform. Numerical examples on a simple lateral periodic velocity model and the Marmousi model demonstrate that our method can obtain accurate background velocity models comparable with those from time-domain WTI and frequency-domain WTI with multiple frequencies. A field data set test indicates that our method obtains a background velocity model that well predicts the seismic wave traveltime.

Some further theoretic properties of scheme called Γ1 non deranged permutations, the permutation which fixes the first element in the permutations were identified and studied in relation to admissible inversion in this paper. This was done first through some computation on this scheme using prime number p ≥ 5, the admissible inversion descent aid (ωp-1) is equi-distributed with descent number des (ωp-1) and also showed that the admissible inversion set Ai (ωi ) and admissible inversion set Ai (ωp-i ) are disjoint.

Mobius transformation is a very important information inversion tool. Mobius transformation is sought after by many experts and scholars at home and abroad, and is a hot research topic at present. Mobius transformation can use the known information to reverse the unknown information, indicating that it has a strong ability to process information. Generalized evidence theory is an extension of classical evidence theory. When belief degree of the null subset is 0, then the generalized evidence theory will be degenerated as classical Dempster-Shafer evidence theory. However, how to apply Mobius transformation to generalized evidence theory is still an open problem. This paper proposes Mobius transformation in generalized evidence theory, which can perform function inversion of generalized evidence theory effectively. Numerical examples are used to prove the validity of Mobius transformation in generalized evidence theory. The experimental results show that the Mobius transformation in generalized evidence theory can effectively invert the generalized evidence theory and is a very effective function inversion method.

Time-lapse (TL) seismic has great potential in monitoring and interpreting time-varying variations in reservoir fluid properties during hydrocarbon exploitation. Obtaining the disparities of reservoir elastic parameters by inversion is essential for TL reservoir monitoring. Conventional TL inversion is carried out by stages without coupling processing and leads to inaccurate results. We directly use the differences in seismic data responses from different vintages, namely, difference inversion, to improve the results’ credibility. It may reduce the deviations of the subtraction of base and monitor inversions in traditional methods. Moreover, most existing studies involving prestack inversion methods use the Zoeppritz equation or its approximants, which failed to consider the wave-propagation effects. We have developed a new TL difference inversion based on the modified reflectivity method (MRM), in which the internal multiples and transmission losses are taken into consideration to fine-tune the characterization of the seismic wave propagating underground. The new method is modified on the basis of the reflectivity method making it feasible in TL difference inversion, and it is derived from the Bayesian theorem. For further delineating the boundaries between layers, the differentiable hyper-Laplacian blocky constraint (DHLBC) is introduced into the prior information of a Bayesian framework, which heightens the sparseness in the vertical gradients of the inversion results and leads to sharp interlayer boundaries of the difference parameters. Synthetic and field data experiments demonstrate that our TL difference inversion method has clear advantages in accuracy and resolution compared with the Zoeppritz method and MRM without DHLBC.

This study focuses on advancing the inversion of aerosol data measured by a cascade impactor. We aim to find and validate a comprehensive and robust mathematical model for reconstructing a particle...

Atraves da bibliografia de base, do tema sugerido na disciplina “Projeto Laboratorial: Ensaio Academico”, do conhecimento adquirido nas aulas de “Teoria do Jornalismo” com o Professor Roberto Nicolato e com a orientacao do Professor Doutor Guilherme de Carvalho, foi possivel uma analise do novo ambiente virtual que se estabeleceu a partir do seculo XXI e trouxe os debates publicos para um mundo digital, invertendo a Teoria do Agendamento. Com isso identificou-se o novo papel de emissor e receptor de informacao entre a imprensa e a populacao.

The Gabor quaternionic offset linear canonical transform (GQOLCT) is defined as a generalization of the quaternionic offset linear canonical transform (QOLCT). In this paper, we investigate the 2D GQOLCT. A new definition of the GQOLCT is provided along with its several important properties, such as boundedness, orthogonality relation, Plancherel and inversion formulas, are derived based on the spectral representation of the GQOLCT. Further, we establish a version of Lieb’s and logarithmic inequalities. Finally we will prove a type of the Heisenberg inequality by using local uncertainty principle.

In this paper, we introduce a new two-dimensional fractional Stockwell transform using the kernel of the coupled fractional Fourier transform. We establish that the two-dimensional fractional Stockwell transform satisfies all the expected properties including Parseval identity and inversion formula. We also characterize the range of the fractional Stockwell transform on $$\mathscr {L}^2(\mathbb {R}^2)$$ and prove a convolution theorem of the transform. Finally, we prove the uncertainty principles for the coupled fractional Fourier transform as well as for the two-dimensional fractional Stockwell transform.

In this paper we present an algorithm for solving quasi-pentadiagonal Toeplitz linear systems, that is based on Du et al. method (Du et al., 2014) and the Sherman–Morrison–Woodbury inversion formula. All algorithms have been implemented in Matlab and numerical experiments are given in order to illustrate the validity and efficiency of our algorithm. An application of the proposed algorithm to the Lax–Wendroff scheme is also considered.

We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased (SIRD) compartmental model of epidemiology, which is achieved by replacing compartmental populations by their densities. Building on our recent work (Computat Mech 66:1177, 2020), we replace our earlier use of global polynomial basis functions with those having local support, as epitomized in the finite element method, for the spatial representation of the SIRD parameters. The time dependence is treated by inferring constant parameters over time intervals that coincide with the time step in semi-discrete numerical implementations. In combination, this amounts to a scheme of field inversion of the SIRD parameters over each time step. Applied to data over ten months of 2020 for the pandemic in the US state of Michigan and to all of Mexico, our system inference via field inversion infers spatio-temporally varying PDE SIRD parameters that replicate the progression of the pandemic with high accuracy. It also produces accurate predictions, when compared against data, for a three week period into 2021. Of note is the insight that is suggested on the spatio-temporal variation of infection, recovery and death rates, as well as patterns of the population's mobility revealed by diffusivities of the compartments. Supplementary information The online version contains supplementary material available at 10.1007/s11831-021-09643-1.

The stereoselective Suzuki–Miyaura cross-coupling of (Z)-β-enamido triflates is demonstrated. Depending on the nature of the ligand in the palladium catalyst, either retention or inversion of the configuration during the synthesis of β,β-diaryl-substituted enamides is observed. Thus, the method provides synthetic access to both isomers of the target enamides from (Z)-β-enamido triflates.

Denoisers can help solve inverse problems via a recently proposed framework known as regularization by denoising (RED). The RED approach defines the regularization term of the inverse problem via explicit denoising engines. Simultaneous source separation techniques, themselves being a combination of inversion and denoising methods, provide a formidable field to explore RED. We investigate the applicability of RED to simultaneous-source data processing and introduce a deblending algorithm called REDeblending (RDB). The formulation permits developing deblending algorithms in which the user can select any denoising engine that satisfies RED conditions. Two popular denoisers are tested, but the method is not limited to them: frequency-wavenumber thresholding and singular spectrum analysis. We offer synthetically blended data examples to showcase the performance of RDB.

Waveform inversion is an approach used to find an optimal model for the velocity field of a ground structure such that the dynamic response is close enough to the given seismic data. First, a suitable numerical approach is employed to establish a realistic forward computer model. The forward problem is solved in the frequency domain using higher-order finite elements. The velocity field is inverted over a specific number of discrete frequencies; thereby, reducing the computational cost of the forward calculation and the nonlinearity of the inverse problem. The results are presented for different frequency sets and with different source and receiver locations for a two-dimensional model. The influence of attenuation effects is also investigated. The results of two blind tests are presented where only the seismic records of an unknown synthetic model with an inhomogeneous material parameter distribution are provided to mimic a more realistic case. Finally, the result of the inversion in a three-dimensional space is illustrated.

Knowledge graph embedding, as the upstream task of link prediction which aims to predict new links between entities under the premise of known relations, its reliability greatly affects the performance of link prediction. However, previous distance-based models focus on modeling complicated relation patterns while ignoring the semantic hierarchy of knowledge graph, from TransE to RotatE. In this setting, all entities are regarded as the same type, and the fact that different entities belong to different levels is neglected. Therefore, we propose the general form of RotatE, the hierarchical-aware relation rotational knowledge graph embedding (HA-RotatE), to model the hierarchical-aware knowledge graph. HA-RotatE represents entities and relations as complex vectors and uses different moduli of entity embeddings to indicate the different hierarchical levels they belong to. The transformation of modulus and rotation from head entity to tail entity depends on different relations. Some relations are used to link entities of the same level, and others are used to link entities of different levels. We adopt the shared modulus transformation parameter method for avoiding overfitting. As the general form of RotatE, HA-RotatE also has the ability to model and infer various relation modes, i.e., symmetry/antisymmetric, inversion and composition. On benchmark datasets WN18RR and FB15k-237, the experiments on link prediction tasks show that: (1) HA-RotatE can effectively model the semantic hierarchy of the knowledge graph; (2) Compared with competitive benchmarks, our model substantially outperforms them in most metrics.

Microseismic location methods based on diffraction stacking, which does not require arrival picking, can yield accurate and reliable source locations for data with a low signal-to-noise ratio. However, due to the complex radiation pattern from a rupturing source, variation in the waveform polarities brings challenges to diffraction stacking-based methods. The current implementations of joint source mechanism inversion and location methods that only use compressional wave (P-wave) amplitudes have limitations in noise resistance and location accuracy. To mitigate those issues, we have developed a new method for joint microseismic moment-tensor inversion and event location using diffraction stacking with P- and S-waves amplitudes, both of which are used to invert for the moment tensor of a microseismic event; then, the inverted moment tensor is used to correct the waveform polarity changes before stacking. In addition, to expedite the large amount of calculations required for moment-tensor inversion at each potential source position and origin time, we develop an optimized grid search scheme and implement the algorithm with GPUs. Our location method does not require manual picking of the first arrivals, and it can automatically detect and locate microseismic events from continuous data. We first validated the method with two synthetic examples, and then we apply it to a surface monitoring data set for hydraulic fracturing at a shale gas well pad in the southern Sichuan Basin, China, where billions of cubic meters of shale gas are being produced annually. The locations of the microseismic events are nicely correlated with the fracturing stages, and the determined source mechanisms are also consistent with the expected fracture growth. Our method is feasible for microseismic surface monitoring with dense nodal arrays and can provide important information for fracture growth and regional stress characterization.

We have developed a method to automatically relate events between observed and synthetic data for wave-equation traveltime (WT) inversion. The scheme starts with local similarity measurements by applying crosscorrelation to localized traces. We then develop a differentiable alternative for the argmax function. By applying the differentiable argmax to each time slice of the local similarity map, we build a traveltime difference function but keep this process differentiable. WT inversion requires only the traveltime difference of related events through a phase shift. Thus, we must reject events that are not apparently related between observed and synthetic data. The local similarity map implies the possibility of doing so but indicates abrupt changes with time and offset. To mitigate this problem, we have introduced a dynamic programming algorithm to define a warping function. Wave packets in the observed and synthetic data are assumed to be related if they are connected by this warping function and if they exhibit high local similarity. Only such related events are considered in the subsequent calculation of misfit and adjoint source. Numerical examples demonstrate that our method successfully retrieves an informative model from roughly selected data. In contrast, WT inversion based on crosscorrelation or deconvolution fails to do so.

We have developed a multiscale approach for solving 2D and 3D nonlinear inverse problems of gravity data in estimating the basement topography. The inversion is carried out in two stages in which the long-wavelength features of the basement are first estimated from smoothed gravity data via a stochastic optimization algorithm. The solution of this stage is used as the starting model for a deterministic optimization algorithm to reconstruct the short-wavelength features from the full-spectrum gravity data. The forward problem is capable of handling lateral and vertical variations in the density of sediments. Two cases are considered regarding prior knowledge about the density: (1) The density contrast between sediments at the surface and the underlying basement and its vertical variations are a priori known, and (2) only the density contrast at the surface is known with its vertical gradient to be recovered in the inversion. In the former case, the unknowns of the problem are the depths, whereas in the latter case, they are the depths and density gradients defined individually for each prism. Therefore, the inverse problem is ill-posed and has many local minima. The stochastic optimization algorithm uses a random initial model and estimates a coarse model of the basement topography. By repeating the stochastic inversion, an ensemble of solutions is formed defining an equivalent domain in the model space supposed to be within the neighborhood of the global minimum of which several starting solutions are extracted for the secondary deterministic inversion. The presented methodology has been tested successfully in converging to the global minima in 2D and 3D cases with 50 and 2352 total number of prisms, respectively. Finally, the inversion algorithm is used to calculate the thickness of the sediments in the South Caspian Basin using the EIGEN-6c4 global gravity model.

The Golcuk (Isparta) is on the southern side of the city of Isparta in the Mediterranean region of Turkey. The investigation of magnetic field strength variations over subterranean layers may reveal their locations on Earth's surface and provide physical and geometrical characteristics. Magnetic studies were carried out around Golcuk caldera lake using proton magnetometers to identify subsurface volcanic structures. The acquired data were inverted using four different edge detection algorithms such as analytic signal, tilt angle, theta map, horizontal gradient. Afterwards, the results were used to determine the locations of the anomalous structures. We also used pseudo-gravity and reduction-to-pole techniques for interpretation.

Continuing advances within unmanned aerial vehicles and scalar magnetic sensor technology are revolutionizing geophysical remote sensing. For perspective, examples of high resolution, low noise data presented in this study enabled detection and accurate positioning of human-made objects ferrous objects with a total mass of 0.5 kg, from altitudes around and above 2 m. However, with these new possibilities come a requirement of higher fidelity, where good sensor position estimates in particular are key to achieving a data quality sufficient for reliable data interpretation and geophysical inversion. Apart from inherent instrument properties, typical factors that hamper sensor position estimation are lag and parallax errors. Lag errors arise from time-stamping delays between the positioning system and sensor reading, while parallax errors stem from the imperfect recovery of sensor positions due to a decoupling and/or distancing of the positioning system and sensor head. The impact from each of these error sources is typically similar and partially or even completely inseparable. A number of correctional techniques exist, typically based on large-scale data correlations, or collection of specific additional data. We present a survey data adjustment method based on the simultaneous inversion of source parameters and a number of independent survey shifts or lags in pre-specified sections of a survey. The method is particularly suited for surveys where the sensor path through space can be assumed well known, but the sensor position itself may suffer lags or shifts relative to the position measurement. The approach is based on modelling an existing source signature within the data and requires no data transformations, such as continuation to a two-dimensional plane, or enforcing of smoothness. The approach is an amendment to independent source inversion and is ideal for scenarios where the source behaviour is thought to be well known, such as processing efforts in which the objective is source–parameter inversion. In this study, we validate the approach using a simple point-dipole model to adjust synthetic data and subsequently demonstrate it on an unmanned airborne scalar magnetic survey for small unexploded ordnance targets, where a hardware malfunction resulted in unknown time-shifts between magnetic sensor readings and positioning unit output. The adjustment procedure was carried out on line data, based on a single anomaly from a 155 mm shell, and enabled the recovery of signatures from several other ferrous unexploded ordnance targets as small as 0.5 kg. Subsequent inversion on the corrected signatures provided unexploded ordnance positions with an accuracy suitable for recovery purposes.

We have designed a target-oriented methodology to perform full-waveform inversion (FWI) using a frequency-domain wave propagator based on the so-called patched Green’s function (PGF) technique. Originally developed in condensed matter physics to describe electronic waves in materials, the PGF technique is easily adaptable to the case of wave propagation in spatially variable media in general. By dividing the entire computational domain into two sections, namely the target area and the outside target area, we calculate the Green’s functions related to each section separately. The calculations related to the section outside the target are performed only once at the beginning of the inversion, whereas the calculations in the target area are performed repeatedly for each iteration of the inversion process. With the Green’s functions of the separate areas, we calculate the combined Green’s function of the two systems patched together through application of a recursive Dyson equation. The calculation is exact; that is, it is the same as the Green’s function calculated by directly solving the Helmholtz equation. By performing 2D and time-lapse experiments on the Marmousi and a Brazilian presalt velocity models, we determined that the target-oriented PGF reduces the computational time of the inversion without compromising accuracy. In fact, when compared with conventional FWI results, the PGF-based calculations are identical but done in a reduced time according to the target size.

SUMMARYFull-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

In this paper, we develop a subsampling Newton’s method to efficiently approximate the maximum likelihood estimate in logistic regression, which is especially useful for large-sample problems. One distinct feature of our algorithm is that matrix inversion is not explicitly performed. We propose two algorithms which are used to construct iteratively a sequence of matrices which converge to the Hessian of the maximum likelihood function on the subsample. We provide numerical examples to show that the proposed method is efficient and robust.

We study the full-waveform inversion (FWI) problem for the recovery of velocity model/image in acoustic media. FWI is formulated as a typical nonlinear optimization problem, many regularization tec...

The even dimensional Clifford-Fourier transforms have been studied in detail in the last decade. However, the research on the odd dimension is hard to start because the closed expressions and the bounds of these kernels are not obtained. In this paper, we prove that the odd-dimensional Clifford-Fourier kernels are polynomially bounded as in the even-dimensional cases. The crucial ingredient in our proof is the closed expression of these kernels in the Laplace domain. With these bounds, various analytic properties can be established by carrying over the proof for even dimensions, such as inversion theorem and uncertainty principles.

The frequency-dependent amplitude-versus-offset (FAVO) method has become a practical method for fluid detection in sand reservoirs. At present, most FAVO inversions are based on the assumption that reservoirs are isotropy, but the application effect is not satisfactory for fractured reservoirs. Hence, we analyse the frequency variation characteristics of anisotropy parameters in tight sandstone reservoirs based on a new petrophysical model, and propose a stepwise anisotropic FAVO inversion method to extract frequency-dependent attributes from prestack seismic field data. First, we combine the improved Brie's law with the fine-fracture model to analyse frequency-dependent characteristics of velocities and Thomsen anisotropy parameters at different gas saturations and fracture densities. Then, we derive an anisotropic FAVO inversion algorithm based on Rüger's approximation formula and propose a stepwise anisotropic FAVO inversion method to obtain the dispersions of anisotropy parameters. Finally, we propose a method that combines the inversion spectral decomposition with the stepwise anisotropy FAVO inversion and apply it to tight sand reservoirs in the Xinchang area. We use P-wave velocity dispersion and anisotropy parameter ε dispersion to optimise favourable areas. Numerical analysis results show that velocity dispersion of the P-wave is sensitive to fracture density, which can be used for fracture prediction in fractured reservoirs. In contrast, anisotropic parameter dispersion is sensitive to gas saturation and can be used for fluid detection. The seismic data inversion results show that velocity dispersion of the P-wave and anisotropic parameter dispersion are sensitive to fractured reservoirs in the second member of Xujiahe Group, which is consistent with logging interpretation results.

An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful for understanding and extending this topic of study. Motivated by fractional differential equations, we present an operational calculus approach for Laplace transforms with respect to functions and their relationship with fractional operators with respect to functions. This approach makes the generalised Laplace transforms much easier to analyse and to apply in practice. We prove several important properties of these generalised Laplace transforms, including an inversion formula, and apply it to solve some fractional differential equations, using the operational calculus approach for efficient solving.

Conventional linear iterative methods for magnetotelluric sounding (MT) suffer from considerable limitations related to difficulties in selecting the initial model and local optima. On the other hand, conventional intelligent nonlinear methods exhibit slow convergence and low accuracy. In this study, we propose an inversion strategy based on the deep learning (DL) deep belief network (DBN) to realise the instantaneous inversion of MT data. A scaled momentum learning rate is introduced to improve the convergence performance of the restricted Boltzmann machine during the DBN pre-training stage, and a novel activation function (DSoft) is introduced to enhance the global optimisation capability during the DBN fine-tuning stage. To address the difficulty in designing the sample data when prior information is lacking, we employ the k-means++ algorithm to cluster the MT field data and use the clustering results as the prior information to guide the construction of the sample dataset. Then, based on the proposed DBN, we ensure end-to-end mapping directly from the apparent resistivity to the resistivity model. We implement two groups of experiments to demonstrate the validity of both improvements on the DBN. We consider six types of geoelectric model from the test set to demonstrate the feasibility and effectiveness of the proposed DBN method for MT 2D inversion, which we further compare with the well-known least-square regularisation method for several extended geoelectric models and field data. The qualitative and quantitative analyses show that the DL inversion method is promising as it can accurately delineate the subsurface structures and perform rapid inversion.