Improved Inversion Algorithm Research Articles

Determining the Moho topography using an improved inversion algorithm: a case study from the South China Sea

The Parker-Oldenburg method, as a classical frequency-domain algorithm, has been widely used in Moho topographic inversion. The method has two indispensable hyperparameters, which are the Moho density contrast and the average Moho depth. Accurate hyperparameters are important prerequisites for inversion of fine Moho topography. However, limited by the nonlinear terms, the hyperparameters estimated by previous methods have obvious deviations. For this reason, this paper proposes a new method to improve the existing Parker-Oldenburg method by taking advantage of the invasive weed optimization algorithm in estimating hyperparameters. The synthetic test results of the new method show that, compared with the trial and error method and the linear regression method, the new method estimates the hyperparameters more accurately, and the computational efficiency performs excellently, which lays the foundation for the inversion of more accurate Moho topography. In practice, the method is applied to the Moho topographic inversion in the South China Sea. With the constraints of available seismic data, the crust-mantle density contrast and the average Moho depth in the South China Sea are determined to be 0.535 g/cm3 and 21.63 km, respectively, and the Moho topography of the South China Sea is inverted based on this. The results of the Moho topography show that the Moho depth in the study area ranges from 5.7 km to 32.3 km, with more obvious undulations. Among them, the shallowest part of the Moho topography is mainly located in the southern part of the Southwestern sub-basin and the southern part of the Manila Trench, with a depth of about 6 km. Compared with the CRUST 1.0 model and the model calculated by the improved Bott’s method, the RMS between the Moho model and the seismic point difference in this paper is smaller, which proves that the method in this paper has some advantages in Moho topographic inversion.

An improved inversion algorithm to reconstruct 2D temperature fields of long sparks with high-speed schlieren technique

The temperature measurement for discharge channels plays an important role in studying the mechanism of long sparks and natural lightning, in which cases the high-speed schlieren technique is usually applied. However, the high-speed schlieren images are noisy, and the discharge channel axis is not discernibly determined from the discrete pixels, which can sometimes cause huge errors using the traditional inversion algorithm. This may be the reason why two-dimensional (2D) temperature fields of long sparks are rarely reported at present. To fill the gap, an improved inversion algorithm is proposed, in which the dichotomy and the high order total variation (TV) regularization methods are introduced. The proposed algorithm is verified to have better performance compared with the traditional ones by numerical tests. At last, 2D temperature fields of discharge channels are reconstructed and discussed.

An improved inversion algorithm for spatio-temporal retrieval of soil moisture through modified water cloud model using C- band Sentinel-1A SAR data

An approach to incorporate vegetation fraction into Modified Water Cloud Model (MWCM) and the evaluation of potential of multi-target random forest regression (MTFER) were done for the retrieval of spatio-temporal variability of soil moisture (SM) in Varanasi district of Uttar Pradesh, India. The Sentinel-1A SAR images were acquired for three different dates (19/12/2016, 05/02/2017 and 25/03/2017) for two types of spatial regions covered with vegetated and sparse vegetated soil field for SM retrieval. The vegetation fraction (fveg), computed from Landsat – 8 satellite data, was inserted into the modified water cloud model (MWCM) as a modification factor. Leaf area index (LAI) was used as a vegetation descriptor parameter (V) in the MWCM. Subsequently, a machine learning based MTRFR algorithm with a regularization routine was used for stable and optimum solution for complex problems related to the inversion of the MWCM for the accurate estimation of SM. The coefficient of determination (R2), root mean square error (RMSE) and nash sutcliffe efficiency (NSE) indicated significantly better results in the region-2 for all the temporal changes occurred than those of region-1. The results showed that incorporation of fveg to the MWCM provided high potential to retrieve spatio-temporal SM in the region-2 where soil fields were mostly covered with wheat and barley crops rather than in region-1 having sparse vegetated soil field. The overall accuracy of spatio-temporal retrieval of SM after incorporating vegetation factor to MWCM showed significantly better R2 = 0.82, RMSE = 3.18 (%) and NSE = 0.85. The inversion results proximate that the MTRFR techniques applied to the MWCM, including vegetation factor, has great a capability for an accurate SM retrieval in the vegetated soil field.

Physically Based Polarimetric Volumetric Scattering From Cylindrically Dominated Vegetation Canopies

To advance the utility of polarimetric synthetic aperture radar observations for extracting biophysical information about vegetation canopies, it is important to develop good understanding of the scattering mechanisms that give rise to the polarimetric scattering response and to apply it toward the development of effective decomposition models of the polarimetric covariance matrices. In this paper, we introduce a more rigorous approach to characterizing the volume scattering component of the three-component scattering model developed by Freeman and Durden. The improved rigor has two aspects: 1) the use of a T-matrix model for computing the polarimetric scattering by an inclined dielectric cylinder and 2) the incorporation of the change in local incidence angle as a function of the orientation of the vegetation cylinders. The improvements address some of the current limitations of the Freeman–Durden model. This paper also provides a sensitivity analysis of the various components of the covariance matrix as a function of several physical parameters including cylinder size, its dielectric constant, and the orientation distribution of cylinders. Such an analysis is a precursor to the development of improved inversion algorithms.

颗粒粒径分布测量反演算法的改进

颗粒粒径分布测量反演算法的改进

An Improved 3D Joint Inversion Method of Potential Field Data Using Cross-Gradient Constraint and LSQR Method

The joint interpretation of two sets of geophysical data related to the same source is an appropriate method for decreasing non-uniqueness of the resulting models during inversion process. Among the available methods, a method based on using cross-gradient constraint combines two datasets is an efficient approach. This method, however, is time-consuming for 3D inversion and cannot provide an exact assessment of situation and extension of anomaly of interest. In this paper, the first attempt is to speed up the required calculation by substituting singular value decomposition by least-squares QR method to solve the large-scale kernel matrix of 3D inversion, more rapidly. Furthermore, to improve the accuracy of resulting models, a combination of depth-weighing matrix and compacted constraint, as automatic selection covariance of initial parameters, is used in the proposed inversion algorithm. This algorithm was developed in Matlab environment and first implemented on synthetic data. The 3D joint inversion of synthetic gravity and magnetic data shows a noticeable improvement in the results and increases the efficiency of algorithm for large-scale problems. Additionally, a real gravity and magnetic dataset of Jalalabad mine, in southeast of Iran was tested. The obtained results by the improved joint 3D inversion of cross-gradient along with compacted constraint showed a mineralised zone in depth interval of about 110–300 m which is in good agreement with the available drilling data. This is also a further confirmation on the accuracy and progress of the improved inversion algorithm.

Inversion Algorithm to Calculate Charge Density on Solid Dielectric Surface Based on Surface Potential Measurement

Charge accumulation on a solid dielectric surface is one of the critical concerns for the design and optimization of the insulation system in a high-voltage power equipment, since it will lead to the overstress of electrical insulation. Therefore, it is important to obtain the charge density distribution on a solid dielectric surface with high accuracy. The acquisition of surface charge for insulators requires multipoint potential measurements to establish the inverse calculation for the determination of an unknown charge distribution. Up to now, extensive studies have been conducted on this subject; nevertheless, the methods are either too complicated and time consuming, or only applicable for specific arrangements, or with poor accuracy. In this paper, the problem is divided into two categories, i.e., shift-variant system and shift-invariant system, and the basic principle of an improved inversion algorithm is interpreted to solve the problem. The 2-D Fourier transform and Wiener filter techniques are employed in the algorithm for shift-invariant system thus the relationship between potential and charge density can be processed in spatial frequency domain, which tremendously simplifies the conventional procedure. The accuracy and resolution of the algorithm are discussed in detail with the aid of numerical examples. In the end, experiments are conducted and the effectiveness of the algorithm is verified.

Multi-GPU parallel algorithm design and analysis for improved inversion of probability tomography with gravity gradiometry data

In this paper, we make a study on the inversion of probability tomography (IPT) with gravity gradiometry data at first. The space resolution of the results is improved by multi-tensor joint inversion, depth weighting matrix and the other methods. Aiming at solving the problems brought by the big data in the exploration, we present the parallel algorithm and the performance analysis combining Compute Unified Device Architecture (CUDA) with Open Multi-Processing (OpenMP) based on Graphics Processing Unit (GPU) accelerating. In the test of the synthetic model and real data from Vinton Dome, we get the improved results. It is also proved that the improved inversion algorithm is effective and feasible. The performance of parallel algorithm we designed is better than the other ones with CUDA. The maximum speedup could be more than 200. In the performance analysis, multi-GPU speedup and multi-GPU efficiency are applied to analyze the scalability of the multi-GPU programs. The designed parallel algorithm is demonstrated to be able to process larger scale of data and the new analysis method is practical.

Improved inversion algorithms for near-surface characterization

Improved inversion algorithms for near-surface characterization

Evaluation of Joint Inversion Algorithm with Logarithmic Treatment for Resistivity Log

The joint inversion of dual laterolog and dual-induction log was evaluated from the linear inversion theory. The generalized inversion method was used for the inverse calculation. A couple of parameters in the inversion algorithm were treated using logarithmic method. The abnormal states resulting from the logarithmic treatment on equations were analyzed. The effects of both the data-resolution matrix and model-resolution matrix on convergence of inversion process were discussed. It indicated that the logarithm treatment can not only weaken the abnormal state obviously, but also can reduce the spread of the data-resolution matrix. The improved inversion algorithm is efficient to enhance the stability and to improve the behaviors of convergence during the inversion process.

An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography

An adjoint field approach is used to formulate a general numerical framework for Fisher information-based sensitivity analysis in electrical impedance tomography. General expressions are given for the gradients used in standard least-squares optimization, i.e. the Jacobian related to the forward problem, and it is shown that these gradient expressions are compatible with commonly used electrode models such as the shunt model and the complete electrode model. By using the adjoint field formulations together with a variational analysis, it is also shown how the computation of the Fisher information can be integrated with the gradient calculations used for optimization. It is furthermore described how the Fisher information analysis and the related sensitivity map can be used in a preconditioning strategy to obtain a well-balanced parameter sensitivity and improved performance for gradient-based quasi-Newton optimization algorithms in electrical impedance tomography. Numerical simulations as well as reconstructions based on experimental data are used to illustrate the sensitivity analysis and the performance of the improved inversion algorithm in a four-electrode measurement set-up.

Accurate inversion of high‐resolution snow penetrometer signals for microstructural and micromechanical properties

Measurements of snow using a high‐resolution micropenetrometer can be used to discriminate between different snow types; in lower‐density snow the signal is sensitive to microstructure, and micromechanical properties can be estimated. Although a physics‐based snow penetration theory was first developed almost a decade ago, since that time the majority of studies using snow micropenetrometers have focused on using direct hardness measurements in statistical relationships. We use Monte‐Carlo simulations to rigorously test the existing physics‐based snow micropenetration theories over a wide range of parameters. These tests revealed four major sources of error in the inversion, which are corrected in this analysis. It is shown that this improved inversion algorithm can recover micromechanical parameters in synthetic data with much greater accuracy over the entire range of micromechanical properties observed in natural snow. Detailed examples of the inversion results are shown for eight different snow types, collected in both Alaskan and alpine snowpacks. The resulting micromechanical properties are distinctly different, indicating that a snow characterization from snow micropenetrometer estimates of micromechanical properties is likely possible. Estimates of the microscale elastic modulus, microscale strength, and structural element length make sense physically when compared to the qualitative descriptions of the different snow types. Microscale strength estimates are used to estimate macroscale strength values, and results from 33 different snow samples, covering a wide range of densities and snow types, are consistent with previously reported values from macroscale tests.

Study on measurement lower limit of DOAS system based on kalman filter

Differential Optical Absorption Spectroscopy (DOAS) technique put forward by Platt in 1970s has been widely applied to the measurement of atmospheric trace gas. The key procedures in the retrieval algorithm are the separation of the absorption cross section into two parts and the solution of linear equations about concetration with the least-squares method. However, the above procedures can't be effectively applied to the monitoring of low concentration gases at short light path length. Here, an improved inversion algorithm based on kalman filter is applied to the optimal estimation of gas concentration instead of applying the least squares. Thus, it is not necessary to select specific wavelengths and subtraction of background spectroscopy. The concentration is treated as the state variable and is calculated with linear recursion. Research on experiment of quantitative measurement for SO2 show that the accuracy of inversion is greatly improved with kalman filter at low ratio of signal to noise and the measurement lower limit is less than 28.6mg/m3 at a light path length of 0.5 m. Zero drift of the DOAS system based on the improved algorithm is less than 2.9mg/m3. It is also found that dynamic measurement range can be broadened by combining traditional DOAS algorithm with the improved algorithm by setting an appropriate threshold for the differential optical density.

Improved algorithms of differential optical absorption spectroscopy for monitoring SO2, NO2 from flue gas

Valuable achievements in differential optical absorption spectroscopy (DOAS) for monitoring atmospheric trace gas have been made in the past decades. However, in flue gas monitoring, it is difficult to monitor the pollutant gases at low optical density. In this paper, two improved inversion algorithms based on the genetic algorithm and Kalman filter, respectively, were developed to accurately calculate the concentrations of SO2 and NO2 from flue gas. Experimental results show that the improved algorithms have the detection limit of 10 ppm and have a zero drift of 1 ppm at a light path length of 0.5 m. Additionally, the improved algorithms of DOAS combined with the traditional DOAS algorithm can broaden the measurement range of pollutant gases by appropriately setting critical values for the maximum value of the differential optical density.

Shallow velocity structure and seismic site effects at Arenal volcano, Costa Rica

We use the spatial autocorrelation (SPAC) method with improved inversion algorithms to estimate the Love and Rayleigh dispersion curves at two sites at the West and Northeast flanks of Arenal volcano, Costa Rica. At the West flank site, the Rayleigh waves phase velocities vary from 765 m s − 1 at 1 Hz to 300 m s − 1 at 12 Hz and those of Love waves between 780 and 295 m s − 1 in the same frequency band. At the Northeast flank site, the Rayleigh wave velocities range from 1386 to 300 m s − 1 and those of Love from 1983 to 315 m s − 1 . From dispersion curves we derive shallow (< 400 m) P and S waves velocity models. 2D velocity models down to a depth of 150 m are also obtained by seismic refraction surveys along two radial profiles on the tephra apron at West and East flanks. They present strong vertical and lateral variations in the velocity and thickness of the layers. Strong variations in amplitude of the spectral peaks are observed for the seismic events along two radial arrays. These site effects are analysed using the H/V spectral ratio method and S-wave theoretical transfer functions. Results show that the wave amplifications are related to resonance effects of shallow structure (< 150 m) and occur only where impedance contrast with the deeper layers is strong enough. In contrast, almost no site effect are detected at the Masaya shield volcano, Nicaragua, where the structure is more homogeneous and mainly composed of lava flows. When a resonance of the shallow layers occurs, the correlation coefficients between close stations increase at the corresponding frequency. The site effects may thus produce spurious results with the SPAC method. The H/V spectral ratio, used in complement of the SPAC method, can help detecting the site effects and testing the plane layer hypothesis. Furthermore, the theoretical transfer functions calculated for the estimated velocity models is also useful to validate the models.

An improved method for determining the vertical ozone distribution using satellite measurements.

A procedure was developed for determining vertical ozone distributions from spectral measurements of UV radiances diffusely reflected from the terrestrial atmosphere. In this procedure, the inversion method of Aruga and Igarashi (1976) is improved by incorporating the effects of multiple scattering and the lower boundary of the atmosphere. The improved inversion algorithm was tested using data of NIMBUS-4 backscattered UV experiments. The results indicate that by using this method, the vertical distributions of atmospheric ozone can be obtained with high accuracy over a wide range of altitude.

Improving Twomey's Algorithm for Inversion of Aerosol Measurement Data

Inversion of aerosol size distribution data is often needed because many aerosol measurement instruments have sufficiently broad responses that assuming sharp channel boundaries when reducing their raw data may result in substantial errors. Several routines are available to do reasonable inversions on cascade impactor and optical particle counter data. However, these routines often give mediocre results when used with Electrical Aerosol Analyzer data. Twomey's algorithm has been widely used, but it depends to some extent on the initial guess and often produces oscillatory results. Adding smoothing to the Twomey algorithm and an intelligent initial guess and stopping point greatly reduce these problems. Negative results do not occur as with unconstrained inversions. If fitting tolerances cannot be met, an approximate solution is always obtained, whereas other inversion techniques may sometimes stop due to lack of convergence in a subroutine. The performance of the improved inversion algorithm is comparable to the better routines for impactor data and offers important advantages over other routines for inversion of Electrical Aerosol Analyzer data.