Audio-frequency magnetotelluric data inversion method based on an adaptive binary structure constraint and its application in geothermal exploration

The break-up of the supercontinent Rodinia in the late Neoproterozoic led to the formation of the Nanhua rift basin within the South China Block. The Datangpo-type manganese deposit, which developed in the Nanhua rift basin, is one of the most important types of manganese deposits in South China. Although it is widely accepted that deep sedimentary structures significantly affect the manganese ore system, the relationship between the manganese deposits in South China and the Nanhua rifting process is still unclear. The origin of the manganese ore layer remains controversial. In this paper, we integrated the audio-frequency magnetotelluric (AMT) data, gravity data, and comprehensive geological and borehole data analysis to characterize the structure of the Datangpo-type manganese deposit in Songtao, Guizhou Province. The resistivity and density models produced an inclined layered structure, which correlated well with the coeval sediment strata of the Nanhua rift basin. A high-resistivity cap was observed from the surface to a depth of 800 m, corresponding to the Cambrian Loushanguan (ϵ3−4ls) and Palang dolomite formation (ϵ2p), which has helped the storage of the manganese ore. The most significant low-resistivity anomaly (25–40 Ω·m) resides at a depth of 1400 m in the Nantuo (Nh3n) gravel sandstone and Datangpo (Nh2d) silty and carbonaceous shale, corresponding to the ore-forming layer. This distinct low-resistivity layer was possibly produced by aqueous fluids and pyrite in the syn-sedimentary fault and alteration zone. The accumulations of sulfide minerals in the rock samples suggest a possible anoxic-euxinic deposition environment during the manganese mineralization and precipitation. The fault revealed in the resistivity models is perhaps a previous fault zone produced by extension in the Nanhua rifting process, which provided migration and upwelling channels for ore-forming minerals. Based on our resistivity models, density models, and geological survey, the manganese ore-forming model was derived, which can help to provide geophysical evidence for the origin of the Datangpo-type manganese deposit.

Two accurate finite-difference frequency-domain (FDFD)-based iterative inverse methods, referred to as FDFD-based iterative method (FIM) and distorted FDFD-based iterative method (DFIM), are proposed for electromagnetic inverse scattering. They can be considered as FDFD-based versions of BIM and DBIM and inherit the advantage of the traditional direct FDFD inversion method, i.e., there is no need for Green’s function of complex background, especially for the inhomogeneous medium. The difference is that full-wave consideration is implemented in the proposed methods to build an iterative framework. Then, the scattered field and object parameter profile are updated in each iteration. Using the high-order components in iteration formulation, both the methods are able to reconstruct high-contrast objects and provide accurate reconstruction results. Compared with other full-wave methods based on differential equation, the two methods also have a distinct characteristic that the inversion accuracy is not limited by extra constraints. The difference between the two proposed methods is whether the background coefficient matrix is updated. Generally, DFIM has faster convergence than FIM due to the updated background coefficient matrix in the iterations. To demonstrate the effectiveness of both the methods, several typical 2-D experiments are conducted. The results show that the proposed methods could achieve good accuracy and high imaging quality.

ABSTRACT: Volume fracturing is an important means to achieve efficient development of shale reservoirs. However, the complexity of the seepage process in shale oil reservoirs due to the distribution characteristics of fracture networks makes the fracture network and reservoir parameter characterization significantly a non-linearity and non-Gaussianity problem. This limits the application of traditional automatic history matching methods. In order to balance the computational efficiency and inversion accuracy, an efficient and high-precision complex fracture network inversion method that can sample from a reconstructed continuous posterior probability density distribution adaptatively is established in this work. A reference model is established to validate the practicality of the proposed method. It was found that: (a) the real posterior probability density distribution with complex non-Gaussian multimodal distribution can be reconstructed effectively by solving a convex Quadratic programming problem so that the inversion accuracy is guaranteed and the uncertainty of each parameter to be fitted can be quantified. (b) the required number of particles at each iterative step can be adjusted according to the filter accuracy so that the computational effort is reduced significantly and the disadvantage of determining the number of particles required for different problems in standard particle filter is avoided. (c) the main features and statistical characteristics of the fracture distribution can be characterized and the effective inversion results of the reference model can be obtained. (d) the proposed method has the potential to be applied in more complex inversion problems such as the inversion problems of multiphase and multi well. 1. INTRODUCTION Shale oil reservoirs are widely distributed and play an important role in the world energy supply chain (Yi et al., 2022; Zou et al., 2013; Liu et al., 2023). Due to the fact that these type of reservoirs are limited by complex pore structure and ultralow permeability of the shale matrix as compared to conventional reservoirs, a practical and cost-effective method commonly employed in developing shale oil reservoirs is the volume fracturing technique(He et al., 2020; Chen et al., 2021; Wu et al., 2021; Zhao et al., 2023). The complex fracture networks generated by volume fracturing have complex distribution characteristics which is difficult to accurately and directly characterize. This is due to the strong heterogeneity of the formation and the commonly developed natural fractures. This leads to high uncertainties of established numerical models which are formulated stochastically with the information of the input parameters of the model obtained mostly by indirect methods (Xue et al., 2020). Moreover, the lack of accurate estimation of reservoir physical parameters and fracture network characterization parameters bring more risks to the formulation of reasonable development plans for the volume fracturing of shale oil reservoirs. Meanwhile, the complex fracture geometry coupled with significant differences in permeability between the matrix and fracture systems may pose special challenges. Therefore, establishing an accurate, efficient, and applicable method for complex fracture network inversion in volume fractured shale reservoirs remains a challenging issue.

A new inverse method for contaminant source identification under unknown solute transport boundary conditions

In this paper, we present an inversion estimation method of thin film parameters based on thermal effects induced by laser irradiation. Firstly, the theoretical model of classical Fourier heat conduction of thin film irradiated by laser is established, and the analytical solutions of temperature fields are obtained by using Laplace transform. Then, the inversion model and the iteration algorithm are established based on the nonlinear conjugate gradient method on condition that the thermal conductivities of the film and the substrate are selected as inversion parameters and the temperature fields of the thin film surface in different irradiation times are selected as measured data. In view of the fact that the sensitivity coefficient plays a decisive role in determining the accuracy and efficiency of the nonlinear conjugate gradient iteration inversion algorithm, we derive the closed form expressions of the sensitivity coefficients for the thermal conductivities of the film and the substrate based on the above analytical solutions of the temperature fields, and this closed form expressions can improve the accuracy and efficiency of the thin film parameter inversion significantly. Taking four kinds of metal films (aluminum, silver, copper and gold) with glass substrate for example, the accuracies of the analytical solutions of temperature fields are verified by comparing with the numerical results from the finite element method in the existing literature, and it can ensure the accuracies of the sensitivity coefficients in the process of iteration inversion. Finally, the thermal conductivities of the above four kinds of thin films are estimated by using the presented iteration inversion method. The accuracy and efficiency of the parameter inversion are verified by investigating and analyzing the inversion results of the parameters for different random noises and different iterative initial values. The inversion results show that this method has a high accuracy and efficiency, and it only needs less than 20 iteration times to convergence when the iteration stop error is 10-7. The smaller random noise is added in the measured data, and the less iteration times to convergence are needed. It can achieve higher convergence efficiency even in the iterative initial values from the inversion results that differ greatly for the case of 5% random noise. This inversion method of thin film parameters is not only applicable to the inversion of the thermal conductivity, but can also be used to inverse the parameters such as the reflection coefficient or the absorption coefficient. The presented method has a certain guiding significance for the parameters inversion and the parameters optimization in the process of the laser processing or the laser damage.

PurposeVertical electrical sounding (VES) and Rayleigh wave exploration are widely used in the exploration of near-surface structure, but both have limitations. This study aims to make full use of the advantages of the two methods, reduce the multiple solutions of single inversion and improve the accuracy of the inversion. Thus, a nonlinear joint inversion method of VES and Rayleigh wave exploration based on improved differential evolution (DE) algorithm was proposed.Design/methodology/approachBased on the DE algorithm, a new initialization strategy was proposed. Then, taking AK-type with high-velocity interlayer model and HA-type with low-velocity interlayer model near the surface as examples, the inversion results of different methods were compared and analyzed. Then, the proposed method was applied to the field data in Chengde, Hebei Province, China. The stratum structure was accurately depicted and verified by drilling.FindingsThe synthetic data and field data results showed that the joint inversion of VES and Rayleigh wave data based on the improved DE algorithm can effectively improve the interpretation accuracy of the single-method inversion and had strong stability and large generalizable ability in near-surface engineering problems.Originality/valueA joint inversion method of VES and Rayleigh wave data based on improved DE algorithm is proposed, which can improve the accuracy of single-method inversion.

A ray theoretical traveltime inversion method in two dimensional arbitrarily dipping layers has been developed and applied to synthetic and real field data. The method is based on Durbaum's formula and may be applied to single-fold as well as CMP raw data. The advantage of Durbaum's formula is that we can estimate dipping angles as well as accurate velocities in dipping layers. In addition, the number of traces which can be utilized for velocity estimations is drastically increased. Also, a statistical method can be used to estimate normal incident times (t$\sb{\rm o}$) and the take-off angles at the surface (B$\sb{\rm o}$) which are measured manually from a stacked section in other methods. Basically, two different statistical ways of interval parameter estimations are discussed. One is Gauss-Newton's nonlinear least squares which applies to sampled traveltime data. The other is the coherency measures technique which does not need picking. To visualize the coherency measures, three different types of plotting are proposed depending on which parameter is fixed with respect to the others. The velocity-B$\sb{\rm o}$ analysis display which plots semblance coefficients on the axes of Vnmo and B$\sb{\rm o}$ at a fixed t$\sb{\rm o}$ is the most efficient method of presentation. An analytical method and an iterative method for velocity inversion from interval parameters are discussed. A computer algorithm to trace rays efficiently in arbitrarily dipping plane layers is also presented because both inversion methods need ray tracing to solve the inversion equation. The accuracy of inversion is studied through models. This study shows that velocity-B$\sb{\rm o}$ analysis is superior to Dix's and Hubral's method for estimating the interval velocities, depths, and dipping angles. Even in the presence of random errors, the method gives a better prediction than the others. The inversion from curved layers and the effect of multiples and diffractions on velocity-B$\sb{\rm o}$ analysis are examined. Application of Velocity-B$\sb{\rm o}$ analysis to real seismic data shows that it successfully predicts both velocity and dipping angle. These accurate velocities and dipping angles are essential in subsequent processing stages.

The characterisation of the thickness and geology of cover sequences significantly improves targeting for mineral exploration in buried terrains. Audio-frequency Magnetotelluric (AMT) data is applicable to characterise cover sequences, where their conductivity (inverse resistivity) can be differentiated. We present a regional study from the under-cover East Tennant region in the Northern Territory (Australia) where we have applied deterministic and probabilistic inversion methods to derive 2D and 1D resistivity models. We integrated these models with information of co-located basement penetrating boreholes (lithological and geophysical logs) to ground-truth and validate the models and to improve geophysical interpretations. In the East Tennant region, borehole lithology and wireline logging demonstrate that the modelled AMT response is largely controlled by the mineralogy of the cover and basement rocks. The bulk conductivity is due primarily to bulk mineralogy and the success of using the AMT models to predict cover thickness is shown to be dependent on whether the bulk mineralogy of cover and basement rocks are sufficiently different to provide a detectable conductivity contrast. Our investigation of a range of geological scenarios that differ in thickness, complexity and geology of the cover and basement rocks suggests that in areas where there is sufficient difference in bulk mineralogy and where the stratigraphy is relatively simple, AMT models predict the cover thickness with high certainty. In more complex scenarios interpretation of AMT models may be more ambiguous and requires integration with other data (e.g. drilling, wireline logging, potential field modelling). Overall, we conclude that the application of the method has been validated and the results compare favourably with borehole stratigraphy logs once geological (i.e. bulk mineralogical) complexity is understood. This demonstrates that the method is capable of identifying major litho-stratigraphic units with resistivity contrasts. Our results have assisted with the planning of regional drilling programs and have helped to reduce the uncertainty and risk associated with intersecting targeted stratigraphic units in covered terrains.

The high-precision molding capability of complex surfaces and structures makes three-dimensional (3D) printing technology more widely used in underwater acoustic models and structural molding. The plastic polymer material, as the main material in the field of 3D printing, possesses the acoustic parameters that are directly related to the acoustic properties of 3D printed underwater acoustic models and structures. Based on the Rayleigh normal series solution for the acoustic scattering of underwater target and the mechanism analysis of the low-frequency resonance which is associated with subsonic Rayleigh waves on the solid plastic polymer spheres, the sensitivity characteristics of the resonance frequency and amplitude to the wave velocity and attenuation coefficient are obtained at low frequencies. It is shown that the transverse wave velocity and the transverse wave attenuation coefficient both have high inversion accuracy at low values of <i>ka</i>, where <i>a</i> is the radius of elastic sphere, as they are quite sensitive to the backscattering resonance frequency and amplitude, respectively. In the frequency band of interest, the backscattering resonance frequency is almost independent of attenuation coefficient. Considering the inversion accuracy, the longitudinal wave velocity and transverse wave velocity are inverted by the resonance frequency separately. Based on these characteristics, the cyclic search method is used to establish an acoustic parameter inversion method for plastic polymer materials, in which the frequency and amplitude of backscattering resonance peak are used as cost functions. Finally, the backscattering acoustic scattering experiment on a solid typical plastic polymer PMMA (methyl methacrylate-acrylic) sphere is conducted in the tank. The experimental results about the backscattering target strength varying with the frequency are in good agreement with the simulation results in a frequency range of 5–20 kHz. The simulation parameters such as the longitudinal wave velocity, transverse wave velocity and attenuation coefficient are obtained by the previously established inversion method. Therefore, the acoustic parameter inversion method provides reliable acoustic parameters for 3D printed underwater acoustic model and structure performance prediction for plastic polymer materials.

<title>Abstract</title> Magnetotellurics (MT) is a geophysical method used to study subsurface structures based on resistivity properties. Inversion modeling in MT is crucial to reconstructing subsurface resistivity distributions from observed data. However, traditional inversion methods often face challenges such as computational complexity, local minimum traps, and dependence on initial models. This study proposes a novel one-dimensional (1-D) MT inversion approach using a One-to-One-Based Optimizer (OOBO) algorithm. OOBO efficiently explores the solution space using information from all population members, reducing the risk of local minima and improving accuracy. The proposed method was tested on synthetic MT data with added noise 5\% using a four-layer resistivity model (Model 1) and a five-layer resistivity model (Model 2). The results showed the best resistivity reconstructions with a percentage root mean square error (RMSE) value of 5.98\% for Model 1 and 6.40\% for Model 2, demonstrating superior accuracy compared to traditional methods such as Occam’s inversion. The algorithm was also applied to field data, demonstrating its ability to efficiently explore model spaces, even when the number of layers is unknown. OOBO's stochastic nature enables the consideration of model uncertainty, providing more consistent solutions compared to probabilistic approaches such as rj-McMCMT, with smaller uncertainty ranges. This study highlights the potential of OOBO to improve the accuracy and efficiency of MT inversion, demonstrating its broad applicability to complex geophysical problems.

Three-dimensional audio-frequency magnetotelluric imaging of Akebasitao granitic intrusions in Western Junggar, NW China

Full waveform inversion (FWI) is a technique used to estimate subsurface model parameters by minimizing the difference between observed and calculated seismic data. Sparsity-promoting regularization are useful tools for traditional FWI methods to tackle complex subsurface structures. Since the traditional regularization techniques can only impose some fixed priors, it is necessary to develop a regularization strategy to obtain more flexible priors. In this way, we develop a structural sparse representation method that exploits the non-local self-similarity prior of the model, which is achieved by grouping similar patches using graph matching operators and a dynamic group selection strategy. A group-based dictionary is trained with the aim of providing the best sparse representation of complex features and variations in the entire model perturbation. The dynamic selection strategy of the training method can balance computational efficiency and inversion accuracy by constantly updating and retaining groups during the processing. In addition, two loop algorithm framework is utilized to enhance the robustness and the efficiency of the proposed method. Numerical experiments are presented to demonstrate that the proposed method outperforms the total variation regularization method and the adaptive dictionary learning with non-local self-similarity in terms of robustness and resolution. This structural sparsity-promoting regularization is incorporated into the FWI problem through a two-loop algorithm framework, enhancing the robustness and efficiency of FWI results.

Explainable machine learning-based fractional vegetation cover inversion and performance optimization – A case study of an alpine grassland on the Qinghai-Tibet Plateau

Summary A new method for NMR inversion constrained by generalized prior information was proposed. Power function transform and exponential power function transform were used to directly extract generalized prior information from echo data. Then the prior information was used as constraint conditions to construct the new objective function and from which we got the inversion results. The numerical simulation results showed that the new method improved the inversion accuracy for T2 inversion and T2-D inversion at low SNR level compared with traditional regularization method.

Crosshole radio electromagnetic tomography using apparent source intensity and logarithmic barrier