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.

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.

Inversion of Seabed Geotechnical Properties in the Arctic Chukchi Deep Sea Basin Based on Time Domain Adaptive Search Matching Algorithm

The chirp sub-bottom profiler,for its high resolution,easy accessibility and cost-effectiveness,has been widely used in acoustic detection.In this paper,the acoustic impedance and grain size compositions were obtained based on the chirp sub-bottom profiler data collected in the Chukchi Plateau area during the 11th Arctic Expedition of China.The time-domain adaptive search matching algorithm was used and validated on our established theoretical model.The misfit between the inversion result and the theoretical model is less than 0.067%.The grain size was calculated according to the empirical relationship between the acoustic impedance and the grain size of the sediment.The average acoustic impedance of sub-seafloor strata is 2.5026×10^(6) kg(s m^(2))^(-1)and the average grain size(θvalue)of the seafloor surface sediment is 7.1498,indicating the predominant occurrence of very fine silt sediment in the study area.Comparison of the inversion results and the laboratory measurements of nearby borehole samples shows that they are in general agreement.

Horizontal-to-vertical spectral ratio inversion method based on multimodal forest optimization algorithm

The exploration of urban underground spaces is of great significance to urban planning,geological disaster prevention,resource exploration and environmental monitoring.However,due to the existing of severe interferences,conventional seismic methods cannot adapt to the complex urban environment well.Since adopting the single-node data acquisition method and taking the seismic ambient noise as the signal,the microtremor horizontal-to-vertical spectral ratio(HVSR)method can effectively avoid the strong interference problems caused by the complex urban environment,which could obtain information such as S-wave velocity and thickness of underground formations by fitting the microtremor HVSR curve.Nevertheless,HVSR curve inversion is a multi-parameter curve fitting process.And conventional inversion methods can easily converge to the local minimum,which will directly affect the reliability of the inversion results.Thus,the authors propose a HVSR inversion method based on the multimodal forest optimization algorithm,which uses the efficient clustering technique and locates the global optimum quickly.Tests on synthetic data show that the inversion results of the proposed method are consistent with the forward model.Both the adaption and stability to the abnormal layer velocity model are demonstrated.The results of the real field data are also verified by the drilling information.

Metaheuristic algorithms for groundwater model parameter inversion:Advances and prospects

Groundwater inverse modeling is a vital technique for estimating unmeasurable model parameters and enhancing numerical simulation accuracy.This paper comprehensively reviews the current advances and future prospects of metaheuristic algorithm-based groundwater model parameter inversion.Initially,the simulation-optimization parameter estimation framework is introduced,which involves the integration of simulation models with metaheuristic algorithms.The subsequent sections explore the fundamental principles of four widely employed metaheuristic algorithms-genetic algorithm(GA),particle swarm optimization(PSO),simulated annealing(SA),and differential evolution(DE)-highlighting their recent applications in water resources research and related areas.Then,a solute transport model is designed to illustrate how to apply and evaluate these four optimization algorithms in addressing challenges related to model parameter inversion.Finally,three noteworthy directions are presented to address the common challenges among current studies,including balancing the diverse exploration and centralized exploitation within metaheuristic algorithms,local approxi-mate error of the surrogate model,and the curse of dimensionality in spatial variational heterogeneous pa-rameters.In summary,this review paper provides theoretical insights and practical guidance for further advancements in groundwater inverse modeling studies.

Application of the Adaptive Shrinkage Genetic Algorithm in the Feasible Region to TEM Conductive Thin Layer Inversion

Combining the adaptive shrinkage genetic algorithm in the feasible region with the imaging of apparent vertical conductance differential, we have inverted the TEM conductive thin layer. The result of the inversion demonstrates that by adaptive shrinkage in the feasible region, the calculation speed accelerates and the calculation precision improves. To a certain extent, in this method we surmount the transient electromagnetic sounding equivalence and reduced equivalence scope. Comparison of the inverted result with the forward curve clearly shows that we can image the conductive thin layer.

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.

Adaptive Antenna Utilizing Power Inversion and Linearly Constrained Minimum Variance Algorithms

This paper presents a new algorithm based on the power inversion （PI） and the linearly constrained minimum variance （LCMV）. This algorithm is capable of adjusting the weights of the antenna array in real time to respond to and improve the global positioning system （GPS） received signals coming from the desired directions and at the same time to highly suppress the jammers coming from the other directions. The simulation is performed for fixed and moving jammers. It indicates that this structure can give deeper nulls, more than 115 dB depths for fixed jammers and more than 94 dB depths for moving jammers.

Performance evaluation for intelligent optimization algorithms in self-potential data inversion

The self-potential method is widely used in environmental and engineering geophysics. Four intelligent optimization algorithms are adopted to design the inversion to interpret self-potential data more accurately and efficiently: simulated annealing, genetic, particle swarm optimization, and ant colony optimization. Using both noise-free and noise-added synthetic data, it is demonstrated that all four intelligent algorithms can perform self-potential data inversion effectively. During the numerical experiments, the model distribution in search space, the relative errors of model parameters, and the elapsed time are recorded to evaluate the performance of the inversion. The results indicate that all the intelligent algorithms have good precision and tolerance to noise. Particle swarm optimization has the fastest convergence during iteration because of its good balanced searching capability between global and local minimisation.

New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm （SFLA）, into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

The inversion of 3-D crustal structure and hypocenter location in the Beijing-Tianjin-Tangshan-Zhangjiakou area by genetic algorithm

This paper discusses the inversion of velocity structure and hypocenters location in the Beijing Tianjin Tangshan Zhangjiakou area by genetic algorithm. The hypocenters location of selected earthquakes and crustal structure of this area are obtained using the travel time data of local earthquakes acquired by the Telemetered Seismic Network of Northern China. The mean and standard residuals of hypocenter location acquired by this method are much less than those provided by the report of respective earthquakes. The crustal structure of the first and the second layers obtained interpret the outline of the plain and mountain area in the region successfully and the crustal structure of the third layer nearly coincides with the Moho discontinuity obtained by artificial seismic sounding. These show the genetic algorithm is effective to the inversion of hypocenter location and three dimensional velocity structure.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit （GPU） and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation （SSOR） technique and the incomplete Choleksy decomposition conjugate gradient algorithm （ICCG）. Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noise- contaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit （CPU）. Real airbome gravity-gradiometry data from Vinton salt dome （south- west Louisiana, USA） are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Parametric inversion of viscoelastic media from VSP data using a genetic algorithm

Viscoelastic parameters are becoming more important and their inversion algorithms are studied by many researchers. Genetic algorithms are random, self-adaptive, robust, and heuristic with global search and convergence abilities. Based on the direct VSP wave equation, a genetic algorithm （GA） is introduced to determine the viscoelastic parameters. First, the direct wave equation in frequency is expressed as a function of complex velocity and then the complex velocities estimated by GA inversion. Since the phase velocity and Q-factor both are functions of complex velocity, their values can be computed easily. However, there are so many complex velocities that it is difficult to invert them directly. They can be rewritten as a function of Co and C∞ to reduce the number of parameters during the inversion process. Finally, a theoretical model experiment proves that our algorithm is exact and effective.

Nonlinear amplitude inversion using a hybrid quantum genetic algorithm and the exact zoeppritz equation

The amplitude versus offset/angle(AVO/AVA)inversion which recovers elastic properties of subsurface media is an essential tool in oil and gas exploration.In general,the exact Zoeppritz equation has a relatively high accuracy in modelling the reflection coefficients.However,amplitude inversion based on it is highly nonlinear,thus,requires nonlinear inversion techniques like the genetic algorithm(GA)which has been widely applied in seismology.The quantum genetic algorithm(QGA)is a variant of the GA that enjoys the advantages of quantum computing,such as qubits and superposition of states.It,however,suffers from limitations in the areas of convergence rate and escaping local minima.To address these shortcomings,in this study,we propose a hybrid quantum genetic algorithm(HQGA)that combines a self-adaptive rotating strategy,and operations of quantum mutation and catastrophe.While the selfadaptive rotating strategy improves the flexibility and efficiency of a quantum rotating gate,the operations of quantum mutation and catastrophe enhance the local and global search abilities,respectively.Using the exact Zoeppritz equation,the HQGA was applied to both synthetic and field seismic data inversion and the results were compared to those of the GA and QGA.A number of the synthetic tests show that the HQGA requires fewer searches to converge to the global solution and the inversion results have generally higher accuracy.The application to field data reveals a good agreement between the inverted parameters and real logs.

A bio-optical inversion model to retrieve absorption contributions and phytoplankton size structure from total minus water spectral absorption using genetic algorithm

We propose a bio-optical inversion model that retrieves the absorption contributions of phytoplankton and colored detrital matter(CDM),as well as the phytoplankton size classes(PSCs),from total minus water absorption spectra.The model is based on three-component separation of phytoplankton size structure and a genetic algorithm.The model performance was tested on two independent datasets(the NASA bio-Optical Marine Algorithm Dataset(NOMAD) and the northern South China Sea(NSCS) dataset).The relationships between the estimated and measured values were strongly linear,especially for aCDM(412),and the Root Mean Square Error(RMSE) of the CDM exponential slope(SCDM) was relatively low.Next,the inversion model was directly applied to in-situ total minus water absorption spectra determined by an underwater meter during a cruise in September 2008,to retrieve the phytoplankton size structure in the seawater.By comparing the measured and retrieved chlorophyll a concentrations,we demonstrated that total and size-specific chlorophyll a concentrations could be retrieved by the model with relatively high accuracy.Finally,we applied the bio-optical inversion model to investigate changes in phytoplankton size structure induced by an anti-cyclonic eddy in the NSCS.

Acoustic Velocity-Based Inversion of the Physical Properties of Sea Ice in the Central Arctic Region

Studying the Arctic sea ice contributes to a comprehensive understanding of the climate system in polar regions and offers valuable insights into the interplay between polar climate change and the global climate and environment.One of the key research aspects is the investigation of the temperature,salinity,and density parameters of sea ice to obtain essential insights.During the 11th Chinese National Arctic Research Expedition,acoustic velocity was measured on an ice core at a short-term ice station,however,temperature,salinity,and density were not measured.In the present work,we utilized a genetic algorithm to invert these obtained acoustic velocity data to sea ice temperature,salinity,and density parameters on the basis of the relationship between acoustic velocity and the physical properties of Arctic summer sea ice.We validated the effectiveness of this inversion procedure by comparing its findings with those of other researchers.The results indicate that within the normalized depth range of 0.43-0.94,the ranges for temperature,salinity,and density are -0.48--0.29℃,1.63-3.35,and 793.1-904.1 kg m^(-3),respectively.

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.

Optimization algorithm for rapid 3D gravity inversion

The practical application of 3D inversion of gravity data requires a lot of computation time and storage space.To solve this problem,we present an integrated optimization algorithm with the following components:(1)targeting high accuracy in the space domain and fast computation in the wavenumber domain,we design a fast 3D forward algorithm with high precision;and(2)taking advantage of the symmetry of the inversion matrix,the main calculation in gravity conjugate gradient inversion is decomposed into two forward calculations,thus optimizing the computational efficiency of 3D gravity inversion.We verify the calculation accuracy and efficiency of the optimization algorithm by testing various grid-number models through numerical simulation experiments.

Genetic algorithm in seismic waveform inversion and its application in deep seismic sounding data interpretation

A genetic algorithm of body waveform inversion is presented for better understanding of crustal and upper mantle structures with deep seismic sounding （DSS） waveform data. General reflection and transmission synthetic seismogram algorithm, which is capable of calculating the response of thin alternating high and low velocity layers, is applied as a solution for forward modeling, and the genetic algorithm is used to find the optimal solution of the inverse problem. Numerical tests suggest that the method has the capability of resolving low-velocity layers, thin alternating high and low velocity layers, and noise suppression. Waveform inversion using P-wave records from Zeku, Xiahe and Lintao shots in the seismic wide-angle reflection/refraction survey along northeastern Qinghai-Xizang （Tibeteau） Plateau has revealed fine structures of the bottom of the upper crust and alternating layers in the middle/lower crust and topmost upper mantle.