THE MULTI-PARAMETER INVERSION OF ELASTIC WAVE IN HALF-SPACE

The multi-parameter inverse scattering problem of elastic waveequation with single fre- quency is investigated within Bornapproximation. By use of a wideband measuring scheme in which bothtransmitters and receivers scan over the half-space surface, theformula of the scattering field of elastic wave is derived. Fourtypes of mode conversion of elastic wave(P→P, P→S, S→P, S→S)areseparated from the scattering field. These components containsufficient information for usto recon- struct the configuration ofthe density and Lame parameters of the medium.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

Layer-Valley Hall Effect under Inversion and Time-Reversal Symmetries

Hall effects have been the central paradigms in modern physics,materials science and practical applications,and have led to many exciting breakthroughs,including the discovery of topological Chern invariants and the revolution of metrological resistance standard.To date,the Hall effects have mainly focused on a single degree of freedom(Do F),and most of them require the breaking of spatial-inversion and/or time-reversal symmetries.Here we demonstrate a new type of Hall effect,i.e.,layer-valley Hall effect,based on a combined layer-valley Do F characterized by the product of layer and valley indices.The layer-valley Hall effect has a quantum origin arising from the layer-valley contrasting Berry curvature,and can occur in nonmagnetic centrosymmetric crystals with both spatial-inversion and time-reversal symmetries,transcending the symmetry constraints of single Do F Hall effect based on the constituent layer or valley index.Moreover,the layer-valley Hall effect is highly tunable and shows a W-shaped pattern in response to the out-of-plane electric fields.Additionally,we discuss the potential detection approaches and material-specific design principles of layer-valley Hall effect.Our results demonstrate novel Hall physics and open up exotic paradigms for new research direction of layer-valleytronics that exploits the quantum nature of the coupled layer-valley DoF.

True-temperature inversion algorithm for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization

Herein,a method of true-temperature inversion for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization is proposed for difficult inversion problems with unknown emissivity.Fractional-order calculus has the inherent advantage of easily jumping out of local extreme values;here,it is introduced into the particle-swarm algorithm to invert the true temperature.An improved adaptive-adjustment mechanism is applied to automatically adjust the current velocity order of the particles and update their velocity and position values,increasing the accuracy of the true temperature values.The results of simulations using the proposed algorithm were compared with three algorithms using typical emissivity models:the internal penalty function algorithm,the optimization function(fmincon)algorithm,and the conventional particle-swarm optimization algorithm.The results show that the proposed algorithm has good accuracy for true-temperature inversion.Actual experimental results from a rocket-motor plume were used to demonstrate that the true-temperature inversion results of this algorithm are in good agreement with the theoretical true-temperature values.

Surface wave inversion with unknown number of soil layers based on a hybrid learning procedure of deep learning and genetic algorithm

Surface wave inversion is a key step in the application of surface waves to soil velocity profiling.Currently,a common practice for the process of inversion is that the number of soil layers is assumed to be known before using heuristic search algorithms to compute the shear wave velocity profile or the number of soil layers is considered as an optimization variable.However,an improper selection of the number of layers may lead to an incorrect shear wave velocity profile.In this study,a deep learning and genetic algorithm hybrid learning procedure is proposed to perform the surface wave inversion without the need to assume the number of soil layers.First,a deep neural network is adapted to learn from a large number of synthetic dispersion curves for inferring the layer number.Then,the shear-wave velocity profile is determined by a genetic algorithm with the known layer number.By applying this procedure to both simulated and real-world cases,the results indicate that the proposed method is reliable and efficient for surface wave inversion.

A novel efficient energy absorber with free inversion of a metal foam-filled circular tube

In this paper, a novel efficient energy absorber with free inversion of a metal foam-filled circular tube(MFFCT) is designed, and the axial compressive behavior of the MFFCT under free inversion is studied analytically and numerically. The theoretical analysis reveals that the energy is mainly dissipated through the radial bending of the metal circular tube, the circumferential expansion of the metal circular tube, and the metal filled-foam compression. The principle of energy conservation is used to derive the theoretical formula for the minimum compressive force of the MFFCT over free inversion under axial loading. Furthermore, the free inversion deformation characteristics of the MFFCT are analyzed numerically. The theoretical steady values are found to be in good agreement with the results of the finite element(FE) analysis. The effects of the average diameter of the metal tube, the wall thickness of the metal tube, and the filled-foam strength on the free inversion deformation of the MFFCT are considered. It is observed that in the steady deformation stage, the load-carrying and energy-absorbing capacities of the MFFCT increase with the increase in the average diameter of the metal tube, the wall thickness of the metal tube, or the filled-foam strength. The specific energy absorption(SEA) of free inversion of the MFFCT is significantly higher than that of the metal tube alone.

Multi-scale data joint inversion of minerals and porosity in altered igneous reservoirs—A case study in the South China Sea

There are abundant igneous gas reservoirs in the South China Sea with significant value of research,and lithology classification,mineral analysis and porosity inversion are important links in reservoir evaluation.However,affected by the diverse lithology,complicated mineral and widespread alteration,conventional logging lithology classification and mineral inversion become considerably difficult.At the same time,owing to the limitation of the wireline log response equation,the quantity and accuracy of minerals can hardly meet the exploration requirements of igneous formations.To overcome those issues,this study takes the South China Sea as an example,and combines multi-scale data such as micro rock slices,petrophysical experiments,wireline log and element cutting log to establish a set of joint inversion methods for minerals and porosity of altered igneous rocks.Specifically,we define the lithology and mineral characteristics through core slices and mineral data,and establish an igneous multi-mineral volumetric model.Then we determine element cutting log correction method based on core element data,and combine wireline log and corrected element cutting log to perform the lithology classification and joint inversion of minerals and porosity.However,it is always difficult to determine the elemental eigenvalues of different minerals in inversion.This paper uses multiple linear regression methods to solve this problem.Finally,an integrated inversion technique for altered igneous formations was developed.The results show that the corrected element cutting log are in good agreement with the core element data,and the mineral and porosity results obtained from the joint inversion based on the wireline log and corrected element cutting log are also in good agreement with the core data from X-ray diffraction.The results demonstrate that the inversion technique is applicable and this study provides a new direction for the mineral inversion research of altered igneous formations.

Three-dimensional constrained gravity inversion of Moho depth and crustal structural characteristics at Mozambique continental margin

Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.

Crustal and uppermost mantle structure of the northeastern Qinghai-Xizang Plateau from joint inversion of surface wave dispersions and receiver functions with P velocity constraints

Lithospheric structure beneath the northeastern Qinghai-Xizang Plateau is of vital significance for studying the geodynamic processes of crustal thickening and expansion of the Qinghai-Xizang Plateau. We conducted a joint inversion of receiver functions and surface wave dispersions with P-wave velocity constraints using data from the Chin Array Ⅱ temporary stations deployed across the Qinghai-Xizang Plateau. Prior to joint inversion, we applied the H-κ-c method(Li JT et al., 2019) to the receiver function data in order to correct for the back-azimuthal variations in the arrival times of Ps phases and crustal multiples caused by crustal anisotropy and dipping interfaces. High-resolution images of vS, crustal thickness, and vP/vSstructures in the Qinghai-Xizang Plateau were simultaneously derived from the joint inversion. The seismic images reveal that crustal thickness decreases outward from the Qinghai-Xizang Plateau. The stable interiors of the Ordos and Alxa blocks exhibited higher velocities and lower crustal vP/vSratios. While, lower velocities and higher vP/vSratios were observed beneath the Qilian Orogen and Songpan-Ganzi terrane(SPGZ), which are geologically active and mechanically weak, especially in the mid-lower crust.Delamination or thermal erosion of the lithosphere triggered by hot asthenospheric flow contributes to the observed uppermost mantle low-velocity zones(LVZs) in the SPGZ. The crustal thickness, vS, and vP/vSratios suggest that whole lithospheric shortening is a plausible mechanism for crustal thickening in the Qinghai-Xizang Plateau, supporting the idea of coupled lithospheric-scale deformation in this region.

Statistical Inversion Based on Nonlinear Weighted Anisotropic Total Variational Model and Its Application in Electrical Impedance Tomography

Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e., the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.

Elastic direct envelope inversion based on wave mode decomposition for multi-parameter reconstruction of strong-scattering media

The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures imaging without the need of low-frequency seismic data.However,the current DEI methods are all based on the acoustic approximation.Whereas,in real cases,seismic records are the combined effects of the subsurface multi-parameters.Therefore,the study of DEI in elastic media is necessary for the accurate inversion of strong-scattering structures,such as salt domes.In this paper,we propose an elastic direct envelope inversion(EDEI)method based on wave mode decomposition.We define the objective function of EDEI using multi-component seismic data and derive its gradient formulation.To reduce the coupling effects of multi-parameters,we introduce the wave mode decomposition method into the gradient calculation of EDEI.The update of Vp is primarily the contributions of decomposed P-waves.Two approaches on Vs gradient calculation are proposed,i.e.using the petrophysical relation and wave mode decomposition method.Finally,we test the proposed method on a layered salt model and the SEG/EAGE salt model.The results show that the proposed EDEI method can reconstruct reliable large-scale Vp and Vs models of strong-scattering salt structures.The successive elastic FWI can obtain high-precision inversion results of the strong-scattering salt model.The proposed method also has a good anti-noise performance in the moderate noise level.

3-D multi-parameter type traveltime tomography in a spherical coordinate frame: comparison of double and triple class simultaneous inversions

It is now common practice to perform simultaneous traveltime inversion for the velocity field and the reflector geometry in reflection/refraction tomography, or the velocity field and the hypocenter locations in regional earthquake tomography, but seldom are all three classes of model parameters updated simultaneously. This is mainly due to the trade-off between the different types of model parameters and the lack of different seismic phases to constrain the model parameters. Using a spherical-coordinate ray tracing algorithm for first and later（primary reflected） arrival tracing algorithm in combination with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model parameters in regional or global tomographic studies. In this paper we incorporate the multistage irregular shortest-path ray tracing algorithm（in a spherical coordinate system） with a subspace inversion solver to formulate a simultaneous inversion algorithm for triple model parameters updating using direct and later arrival time information.Comparison tests for two sets of data（noise free and added noise） indicate that the new triple-class parameter inversion algorithm is capable of obtaining nearly the same results as the double-class parameter inversion scheme. Furthermore,the proposed multi-parameter type inversion method is not sensitive to a modest level of picking error in the traveltime data, and also performs well with a relatively large uncertainty in earthquake hypocentral locations. This shows it to be a feasible and promising approach in regional or global tomographic applications.

Rapid source inversions of the 2023 SE Türkiye earthquakes with teleseismic and strong-motion data

We conducted rapid inversions of rupture process for the 2023 earthquake doublet occurred in SE Türkiye,the first with a magnitude of M_(W)7.8 and the second with a magnitude of M_(W)7.6,using teleseismic and strong-motion data.The teleseismic rupture models of the both events were obtained approximately 88 and 55 minutes after their occurrences,respectively.The rupture models indicated that the first event was an asymmetric bilateral event with ruptures mainly propagating to the northeast,while the second one was a unilateral event with ruptures propagating to the west.This information could be useful in locating the meizoseismal areas.Compared with teleseismic models,the strong-motion models showed relatively higher resolution.A noticeable difference was found for the M_(W)7.6 earthquake,for which the strong-motion models shows a bilateral event,rather than a unilateral event,but the dominant rupture direction is still westward.Nevertheless,all strong-motion models are consistent with the teleseismic models in terms of magnitudes,durations,and dominant rupture directions.This suggests that both teleseismic and strong-motion data can be used for fast determination of major source characteristics.In contrast,the strong-motion data would be preferable in future emergency responses since they are recorded earlier and have a better resolution ability on the source ruptures.

GBO algorithm for seismic source parameters inversion

The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault parameters inversion has nonlinear characteristics, and the gradient-based optimizer(GBO) has the characteristics of fast convergence speed and falling into local optimum hardly. This paper applies GBO algorithm to simulated earthquakes and real LuShan earthquakes in the nonlinear inversion of the Okada model to obtain the source parameters. The simulated earthquake experiment results show that the algorithm is stable, and the seismic source parameters obtained by GBO are slightly closer to the true value than the multi peak particle swarm optimization(MPSO). In the 2013 LuShan earthquake experiment, the root mean square error between the deformation after forwarding of fault parameters obtained by the introduced GBO algorithm and the surface observation deformation was 3.703 mm, slightly better than 3.708 mm calculated by the MPSO. Moreover, the inversion result of GBO algorithm is better than MPSO algorithm in stability. The above results show that the introduced GBO algorithm has a certain practical application value in seismic fault source parameters inversion.

Multi-Parameter Influence Analysis of Interaction Between Internal Solitary Wave and Fixed Submerged Body

To obtain the interaction characteristics between Internal solitary waves(ISWs)and submerged bodies,a three-dimensional numerical model for simulating ISWs was established in the present study based on the RANS equation.The velocity entrance method was adopted to generate the ISWs.First,the reliability of this numerical model was validated by comparing it with theoretical and literature results.Then,the influence of environmental and navigation parameters on interactions between ISWs and a fixed SUBOFF-submerged body was studied.According to research,the hydrodynamic performance of the submerged body has been significantly impacted by the ISWs when the body is nearing the central region of the wave.Besides,the pitching moment(y')will predominate when the body encounters the ISWs at a certain angle between 0°and 180°,and the lateral force is larger than the horizontal force.Additionally,the magnitude of the force acting on the body is mostly affected by the wave amplitude.The variation of the vertical force is the main way that ISWs affect the hydrodynamic performance of the bodies.The investigations and findings discussed above can serve as a guide to forecast how ISWs will interact with submerged bodies.

Feedback control and quantum error correction assisted quantum multi-parameter estimation

Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols.

Moment tensor and stress inversion solutions of acoustic emissions during compression and tensile fracturing in crystalline rocks

We investigate the accuracy and robustness of moment tensor(MT)and stress inversion solutions derived from acoustic emissions(AEs)during the laboratory fracturing of prismatic Barre granite specimens.Pre-cut flaws in the specimens introduce a complex stress field,resulting in a spatial and temporal variation of focal mechanisms.Specifically,we consider two experimental setups:(1)where the rock is loaded in compression to generate primarily shear-type fractures and(2)where the material is loaded in indirect tension to generate predominantly tensile-type fractures.In each test,we first decompose AE moment tensors into double-couple(DC)and non-DC terms and then derive unambiguous normal and slip vectors using k-means clustering and an unstructured damped stress inversion algorithm.We explore temporal and spatial distributions of DC and non-DC events at different loading levels.The majority of the DC and the tensile non-DC events cluster around the pre-cut flaws,where macro-cracks later develop.Results of stress inversion are verified against the stress field from finite element(FE)modeling.A good agreement is found between the experimentally derived and numerically simulated stress orientations.To the best of the authors’knowledge,this work presents the first case where stress inversion methodologies are validated by numerical simulations at laboratory scale and under highly heterogeneous stress distributions.

Fast pre-stack multi-channel inversion constrained by seismic reflection features

Classical multi-channel technology can significantly reduce the pre-stack seismic inversion uncertainty, especially for complex geology such as high dipping structures. However, due to the consideration of complex structure or reflection features, the existing multi-channel inversion methods have to adopt the highly time-consuming strategy of arranging seismic data trace-by-trace, limiting its wide application in pre-stack inversion. A fast pre-stack multi-channel inversion constrained by seismic reflection features has been proposed to address this issue. The key to our method is to re-characterize the reflection features to directly constrain the pre-stack inversion through a Hadamard product operator without rearranging the seismic data. The seismic reflection features can reflect the distribution of the stratum reflection interface, and we obtained them from the post-stack profile by searching the shortest local Euclidean distance between adjacent seismic traces. Instead of directly constructing a large-size reflection features constraint operator advocated by the conventional methods, through decomposing the reflection features along the vertical and horizontal direction at a particular sampling point, we have constructed a computationally well-behaved constraint operator represented by the vertical and horizontal partial derivatives. Based on the Alternating Direction Method of Multipliers (ADMM) optimization, we have derived a fast algorithm for solving the objective function, including Hadamard product operators. Compared with the conventional reflection features constrained inversion, the proposed method is more efficient and accurate, proved on the Overthrust model and a field data set.

Rock physics and seismic reflectivity parameterization and amplitude variation with offsets inversion in terms of total organic carbon indicator

Total organic carbon (TOC) prediction with elastic parameter inversions has been widely used in the identification and evaluation of source rocks. However, the elastic parameters used to predict TOC are not only determined by TOC but also depend on the other physical properties of source rocks. Besides, the TOC prediction with the elastic parameters inversion is an indirect method based on the statistical relationship obtained from well logs and experiment data. Therefore, we propose a rock physics model and define a TOC indicator mainly affected by TOC to predict TOC directly. The proposed rock physics model makes the equivalent elastic moduli of source rocks parameterized by the TOC indicator. Combining the equivalent elastic moduli of source rocks and Gray’s approximation leads to a novel linearized approximation of the P-wave reflection coefficient incorporating the TOC indicator. Model examples illustrate that the novel reflectivity approximation well agrees with the exact Zoeppritz equation until incident angles reach 40°. Convoluting the novel P-wave reflection approximation with seismic wavelets as the forward solver, an AVO inversion method based on the Bayesian theory is proposed to invert the TOC indicator with seismic data. The synthetic examples and field tests validate the feasibility and stability of the proposed AVO inversion approach. Using the inversion results of the TOC indicator, TOC is directly and accurately estimated in the target area.