Slip distribution inversion of seismic sub-fault dip iteration using gradient based optimizer algorithm

This paper considers setting different dips for different sub-faults to fit the actual rupture situation based on the fault rupture of the 2013 Lushan M_(S)7.0 earthquake.Meanwhile,combined with the coseismic GNSS data of the Lushan earthquake,the source parameters and sliding distribution of the Lushan earthquake fault are inversed.Firstly,we use the gradient based optimizer(GBO)in nonlinear inversion to obtain the source parameters of this seismic fault.The inversion results indicate that the strike of the fault is 206.52°,the dip is 44.10°,the length is 21.92 km,and the depth is 12.79 km.To refine the sliding distribution of the seismic fault,the seismic fault is divided into 3×3 sub-faults.Then,we fix the central sub-fault dip of 44.10°;the dip of other sub-faults is obtained by iteration.After that,the model is further divided into a fault layer model composed of 23×19 sub fault slices,and using the Matlab fitting function is used to fit the dip of the 23×19 sub faults.Finally,the Lushan seismic fault plane is established as a shovel structure with steep upper and gentle lower,steep south and gentle north.The slip distribution inversion results indicate that the depth of the slip peak is 13 km,the corresponding maximum slip momentum is 0.67 m,the seismic moment is 1.10×10^(19)N·m and the corresponding moment magnitude is MW6.66.The results above are consistent with the research results of seismology.

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

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.

Recent Advances in the Geodesy Data Processing

Geodetic functional models,stochastic models,and model parameter estimation theory are fundamental for geodetic data processing.In the past five years,through the unremitting efforts of Chinese scholars in the field of geodetic data processing,according to the application and practice of geodesy,they have made significant contributions in the fields of hypothesis testing theory,un-modeled error,outlier detection,and robust estimation,variance component estimation,complex least squares,and ill-posed problems treatment.Many functional models such as the nonlinear adjustment model,EIV model,and mixed additive and multiplicative random error model are also constructed and improved.Geodetic data inversion is an important part of geodetic data processing,and Chinese scholars have done a lot of work in geodetic data inversion in the past five years,such as seismic slide distribution inversion,intelligent inversion algorithm,multi-source data joint inversion,water reserve change and satellite gravity inversion.This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years,analyzes the methods used by scholars and the problems solved,and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

A new polar motion prediction method combined with the difference between polar motion series

After the first Earth Orientation Parameters Prediction Comparison Campaign(1 st EOP PCC),the traditional method using least-squares extrapolation and autoregressive(LS+AR)models was considered as one of the polar motion prediction methods with higher accuracy.The traditional method predicts individual polar motion series separately,which has a single input data and limited improvement in prediction accuracy.To address this problem,this paper proposes a new method for predicting polar motion by combining the difference between polar motion series.The X,Y,and Y-X series were predicted separately using LS+AR models.Then,the new forecast value of X series is obtained by combining the forecast value of Y series with that of Y-X series;the new forecast value of Y series is obtained by combining the forecast value of X series with that of Y-X series.The hindcast experimental comparison results from January 1,2011 to April 4,2021 show that the new method achieves a maximum improvement of 12.95%and 14.96%over the traditional method in the X and Y directions,respectively.The new method has obvious advantages compared with the differential method.This study tests the stability and superiority of the new method and provides a new idea for the research of polar motion prediction.

Penalized total least squares method for dealing with systematic errors in partial EIV model and its precision estimation

When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To solve this problem,we propose to add the nonparametric part(systematic errors)to the partial EIV model,and build the partial EIV model to weaken the influence of systematic errors.Then,having rewritten the model as a nonlinear model,we derive the formula of parameter estimations based on the penalized total least squares criterion.Furthermore,based on the second-order approximation method of precision estimation,we derive the second-order bias and covariance of parameter estimations and calculate the mean square error(MSE).Aiming at the selection of the smoothing factor,we propose to use the U curve method.The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information,which validates the feasibility and effectiveness of the proposed method.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

A complete solution of an improved universal 3D coordinate similarity transformation model

When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.

Scaled unscented transformation method and adaptive Monte Carlo method used for effects of fault parameters estimation on green function matrix in slip distribution inversion

The elements of Green function matrix are the nonlinear functions of fault parameters estimation, the randomness of fault parameters estimation causes that the slip distribution inversion turns to be the parameter estimation problem of total least squares. Second-order approaching function method, scaled unscented transformation(SUT) method and adaptive Monte Carlo method are designed for biases of displacements in rectangular dislocation model. They are used to analyze effects of the length, width,depth and dip of fault with different variances on the corresponding displacements of unit strike slip dislocation fault, unit dip slip dislocation fault and unit tensile dislocation fault. Results of the simulated fault show that compared with second-order approaching function method and adaptive Monte Carlo method, SUT method has better computational efficiency. The second-order term has dominant effects on nonlinear relationship between displacements and the fault parameter in the rectangular dislocation model. The main biases of displacements are near to fault. The corresponding displacements of unit tensile dislocation are mostly susceptible to fault parameters estimation, followed by the unit dip slip dislocation and unit strike slip dislocation. In addition, the vertical displacement is more sensitive to fault parameters estimation than horizontal displacements.

A SCR method for uncertainty estimation in geodesy non-linear error propagation: Comparisons and applications

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC(Monte Carlo), SUT(scaled unscented transformation), and SI(sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time, namely, SCR(spherical cubature rule), which is no need for setting parameters. By theoretical derivation, we prove that the precision of uncertainty obtained by SCR can reach second-order. We conduct four synthetic experiments, for the first two experiments, the results obtained by SCR are consistent with the other three methods with optimal setting parameters, but SCR is easier to operate than other three methods, which verifies the superiority of SCR in calculating the uncertainty. For the third experiment, real-time calculation is required, so the MC is hardly feasible. For the forth experiment, the SCR is applied to the inversion of seismic fault parameter which is a common problem in geophysics, and we study the sensitivity of surface displacements to fault parameters with errors. Our results show that the uncertainty of the surface displacements is the magnitude of ±10 mm when the fault length contains a variance of 0.01 km^(2).

Genetic Nelder-Mead neural network algorithm for fault parameter inversion using GPS data

The traditional genetic algorithm(GA)has unstable inversion results and is easy to fall into the local optimum when inverting fault parameters.Therefore,this article considers the combination of GA with other non-linear algorithms in order to improve the inversion precision of GA.This paper proposes a genetic Nelder-Mead neural network algorithm(GNMNNA).This algorithm uses a neural network algorithm(NNA)to optimize the global search ability of GA.At the same time,the simplex algorithm is used to optimize the local search capability of the GA.Through numerical examples,the stability of the inversion algorithm under different strategies is explored.The experimental results show that the proposed GNMNNA has stronger inversion stability and higher precision compared with the existing algorithms.The effectiveness of GNMNNA is verified by the BodrumeKos earthquake and Monte Cristo Range earthquake.The experimental results show that GNMNNA is superior to GA and NNA in both inversion precision and computational stability.Therefore,GNMNNA has greater application potential in complex earthquake environment.

Determination of Smoothing Factor for the Inversion of Co-seismic Slip Distribution

For the determination of the smoothing factor (also known as the regularization parameter) in the co-seismic slip distribution inversion, the compromise curve between the model roughness and the data fitting residual is generally used to determine (in order to distinguish the method proposed in this paper, the method is called “L curve” according to its shape). Based on the L-curve, the Eclectic Intersection curve as a new method is proposed to determine the smoothing factor in this paper. The results of the simulated experiment show that the inversion accuracy of the parameters of the seismic slip distribution with the smoothing factor determined by the Eclectic Intersection curve method is better than that of the L curve method. Moreover, the Eclectic Intersection curve method and the L curve method are used to determine the smoothing factor of L’Aquila earthquake and the Taiwan Meinong earthquake slip distribution inversion respectively, and the inversion results are compared and analyzed. The analysis results show that the L’Aquila and the Taiwan Meinong actual earthquake slip distribution results are in the range of other scholars at home and abroad, and compared with the L curve method, the Eclectic Intersection curve method has advantages of high computation efficiency, no need to depend on data fitting degree and more appropriate of smoothing factor and so on.

Many facades of CTCF unified by its coding for three-dimensional genome architecture

CCCTC-binding factor(CTCF)is a multifunctional zinc finger protein that is conserved in metazoan species.CTCF is consistently found to play an important role in many diverse biological processes.CTCF/cohesin-mediated active chromatin‘loop extrusion’architects three-dimensional(3D)genome folding.The 3D architectural role of CTCF underlies its multifarious functions,including developmental regulation of gene expression,protocadherin(Pcdh)promoter choice in the nervous system,immunoglobulin(Ig)and T-cell receptor(Tcr)V(D)J recombination in the immune system,homeobox(Hox)gene control during limb development,as well as many other aspects of biology.Here,we review the pleiotropic functions of CTCF from the perspective of its essential role in 3D genome architecture and topological promoter/enhancer selection.We envision the 3D genome as an enormous complex architecture,with tens of thousands of CTCF sites as connecting nodes and CTCF proteins as mysterious bonds that glue together genomic building parts with distinct articulation joints.In particular,we focus on the internal mechanisms by which CTCF controls higher order chromatin structures that manifest its many fa?ades of physiological and pathological functions.We also discuss the dichotomic role of CTCF sites as intriguing3D genome nodes for seemingly contradictory‘looping bridges’and‘topological insulators’to frame a beautiful magnificent house for a cell’s nuclear home.

Volunteered remote sensing data generation with air passengers as sensors

Remote sensing satellites are playing very important roles in diverse earth observation fields.However,long revisit period,high cost and dense cloud cover have been the main limitations of satellite remote sensing for a long time.This paper introduces the novel volunteered passenger aircraft remote sensing(VPARS)concept,which can partly overcome these problems.By obtaining aerial imaging data from passengers using a portable smartphone on a passenger aircraft,it has various advantages including low cost,high revisit,dense coverage,and partial anti-cloud,which can well complement conventional remote sensing data.This paper examines the concept of VPARS and give general data processing framework of VPARS.Several cases were given to validate this processing approach.Two preliminary applications on land cover classification and economic activity monitoring validate the applicability of the VPARS data.Furthermore,we examine the issues about data maintenance,potential applications,limitations and challenges.We conclude the VPARS can benefit both scientific and industrial communities who rely on remote sensing data.