Accurate Inversion Method Research Articles

Retrieval of tropospheric ozone profiles using ground-based MAX-DOAS

In recent years, surface ozone concentrations have increased in many cities in China. Ground-based multi-axis differential optical absorption spectroscopy (MAX-DOAS) is a powerful technique for retrieving the profiles of tropospheric trace gases, such as NO2, SO2, and HCHO. However, since the difficulties in deducting the effects of stratospheric ozone, there are few studies on the retrieval of tropospheric ozone profiles using MAX-DOAS measurements. Here, we developed an accurate inversion method to retrieve tropospheric ozone concentrations during the PRIDE-GBA Campaign, wherein the ozone differential slant column densities (DSCDs) were retrieved in QDOAS software using the “time-interpolated zenith spectrum” as the reference spectrum. The tropospheric DSCDs (DSCDstrop) were then calculated by subtracting the simulated stratospheric DSCDs (DSCDsstr, simulated from the SCIATRAN model) from the DSCDs. Tropospheric ozone profiles were retrieved from the DSCDstrop using the optimal estimation method (OEM). The results showed that high values of tropospheric ozone were mainly distributed below 1 km, which is consistent with lidar measurements. In addition, the observed surface ozone concentrations were highly correlated with the in-situ measurements, with correlation coefficients (R) of 0.75 and 0.81, respectively. Combined with the retrieved NO2 and HCHO profiles using the MAX-DOAS measurements, we found that the planetary boundary layer ozone pollution of HeShan Observatory during the PRIDE-GBA Campaign are controlled by the NOx-limited regime. The results of this study indicate that the MAX-DOAS technique has the potential to retrieve tropospheric ozone profiles with high temporal and spatial resolution.

بهبود شناسایی گسل‌ها با تلفیق شبکه عصبی پرسپترون چندلایه و نشانگرهای لرزه‌ای غیرمتعارف

Revealing the faults, one of the essential steps in seismic interpretation, provides valuable information for modeling static and dynamic characteristics of hydrocarbon reservoirs. Several methods developed for automatic fault and fracture detection, which seismic attributes integrated with artificial neural networks, and fuzzy systems are the most common ones. In this study, a 3D seismic data set of the F3 Block, offshore Netherland, was utilized for enhanced fault detection using an artificial neural network and unconventional seismic attributes integration. A steering cube was computed using a phase-based dip calculation technique to enhance seismic attributes’ accuracy and target detection capability. The fault enhancement filter, as a combination of the diffusion and median filters, and conventional attributes are modified and redefined along with the dip and azimuth information. A supervised, fully connected multi-layer perceptron neural network was constructed to integrate the previous traditional seismic attributes with optimum parameters to generate a fault probability cube. For an improved interpretation, the fault probability cube is then treated through the unconventional seismic attributes. Finally, the end product is subjected to the voxel connectivity filter to visualize the detected faults’ three-dimensional nature. Our proposed workflow results were superposed with the ones derived from the color-based inversion cube as an accurate inversion method. The proposed automatic fault extraction workflow can yield considerable savings in time and result in a highly detailed mapping of discontinuities.

A Review of Flow Mechanism and Inversion Methods of Fracture Network in Shale Gas Reservoirs

The pore structure of shale gas reservoirs has strong heterogeneity, and the flow mechanism in multiscale media is complex. The fracture network of hydraulic fracturing is significantly affected by reservoir in situ stress, rock mechanical properties, and natural fracture distribution. At present, there is no efficient and accurate inversion method for fracture networks. Accurately describing fracture network morphology and flow capacity distribution of induced fracture is an important basis for production analysis, fracturing evaluation, and production plan. This article focuses on the hot issues of shale gas development, from three aspects: flow parameter characterization method of organic/inorganic matter, multiscale mass transfer simulation of shale gas reservoir, and inversion method of fracture network morphology and flow capacity, to introduce relevant research progress in detail. At the same time, the advantages and shortcomings of current related researches are compared and analyzed. Based on this, the key scientific problems existing on flow mechanisms and inversion method of fracture network in shale gas reservoirs are proposed, which can provide guidance for further research.

An accurate inversion method of aerosol extinction coefficient about ground-based lidar without needing calibration

<sec> How to accurately calibrate the lidar data about haze in the presence of some cloud layers over the haze has always been a subject to be solved for data inversion of Mie scattering lidar. It is difficult for laser to penetrate the haze and clouds simultaneously, so the backscattering signal of lidar cannot be calibrated by using a clear air layer when the haze is under the low clouds. For the portable Mie scattering lidar with a detecting range of less than 6 km, it is also difficult to calibrate the lidar signals by using a clear air layer. An iterative algorithm for aerosol extinction coefficient is proposed based on the characteristics of the Fernald forward integral equation in this paper. By specific settings for the inversion process, the difference between the inversion value and the expected one of aerosol extinction coefficient is reduced after each iteration. After several iterations, the difference between the inversion value and the expected one of aerosol extinction coefficient is small enough to be negligible.</sec><sec>The disadvantage of the iterative algorithm for aerosol extinction coefficient is that the inversion results are affected by the overlap factor of lidar. The errors of lidar overlap factor measured experimentally at different times are slightly different. However, the influence about the overlap factor of lidar measured experimentally at different times on the inversion results is slightly different when the iterative algorithm for aerosol extinction coefficient is used to calculate aerosol extinction coefficient.</sec><sec>The results of preliminary calculation show that the iterative algorithm of aerosol extinction coefficient can accurately reproduce aerosol extinction coefficient profile without needing calibration of the lidar data. For the haze detection signal that cannot be calibrated by a clear air layer, the vertical distribution of the haze extinction coefficient can be accurately retrieved by the iterative algorithm for aerosol extinction coefficients. The vertical distribution of aerosol extinction coefficients can also be accurately retrieved by using the iterative algorithm of aerosol extinction coefficients for the Mie backscattering lidar data with the measuring height less than 6 km. Through comparative analysis and research, it is found that for the same lidar data, the aerosol extinction coefficient obtained by the iterative algorithm for aerosol extinction coefficient is closer to the actual value than that by the slope method. </sec>

Retrieval method of cirrus microphysical parameters at terahertz wave based on multiple lookup tables

Cirrus is an important regulator for the flow of radiant energy in the earth-atmosphere system through the processes of scattering and absorption of radiation. In order to satisfy the urgent requirement for accurate retrieval of cirrus microphysical properties, terahertz wave is expected to be the best waveband for inverting cirrus particle size and ice water path, with terahertz wavelengths on the order of the size of typical cirrus particles. There is an urgent need for establishing stable and accurate inversion method. A new retrieval method for particle size and ice water path is developed based on multiple lookup tables for spaceborne measurements of brightness temperature spectrum of 183 GHz, 325 GHz, 462 GHz, 664 GHz, and 874 GHz channels. Five parameters are derived to quantify the effects of particle size and ice water path on terahertz radiation spectrum due to the scattering of ice clouds, manifested by brightness temperature difference, brightness temperature difference slope, etc. To retrieve cirrus microphysical parameters, a weighted least square fit that matches the modeled parameters is used. The analysis of retrieval errors are conducted by a simulated data series and the results are compared with those retrieved by the other two methods, i. e., difference method and slope method. The results retrieved by the multiple lookup table method are much closer to the simulated data series than those from the other two methods. It is indicated that the method introduced here is a stable and valid method of inverting particles between 50 and 500 m and ice water path between 10 and 500 g/m2. Compared with the errors from the difference-featured method and slope-featured method, the retrieval errors are reduced by 68.78% and 60.28% for particle size, 78.17% and 49.01% for ice water path. The analyses of retrieval uncertainties show that, in general, uncertainties of particle size and ice water path vary with particle size and ice water path. The ice water path uncertainties mainly spread in a range of 0-15 g/m2. The particle size uncertainties fluctuate within a range of 0-20 m. In other words, for small particle size range, the uncertainties are 0-5 m for thick clouds and 5-20 m for thin clouds. However, for large particle size range, the uncertainties are 0-5 m for particles larger than 300 m and 5-15 m for those smaller than 300 m. The results will be helpful for further developing the terahertz wave remote sensing of cirrus microphysical parameter technology. Moreover, it is also an important reference to the improvement of cirrus retrieval accuracy.

Characterizing anomalous diffusion by studying displacements

Subordinated Lévy processes provide very diverse conceptual models for mass transport, beside other paradigms (e.g., fractional Brownian motion) generalizing Brownian motion. Some of that many models exhibit similar empirical Mean Squared Displacements growing non-linearly with time, while their increments have very different characteristic functions. In many media, such functionals can be directly measured, but accurate inversion methods adapted to them and to subordinated processes are still lacking. We show that each such process is associated to an operator that transforms the deviation from 1 of the characteristic function of its increments into a quantity that does not depend on the wave-number. We build an inversion method based on this property: it deduces the individual identity of each subordinated Lévy process from data sampling the characteristic functions of its increments.

Tick Size, Microstructure Noise, Informed Trading and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price, as well as on the statistical technique used to estimate these metrics. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics, all statistical techniques used for their estimation, and all inversion methods. In addition, we document systematic differences in option market information shares between equities and exchange traded funds both before and after the tick size change, and we present strong event-type empirical evidence of informed trading in the equity option market after the tick size change, with extreme values of the IS and CS metrics in that market producing similar abnormal underlying asset returns.

Tick Size, Microstructure Noise and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Tick Size Reduction and Price Discovery in Option Markets: An Empirical Investigation

We examine the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. We first document a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the inversion method of the option value to find the implied stock price. We then introduce a more accurate inversion method that results in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. In all cases, however, we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Tick Size, Microstructure Noise and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity. However, the path that the rays travel along in media with irregular interfaces is not clear. Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements (SEMO) that can accurately evaluate waves traveling along an irregular interface. Consequently, the head waves are separated from interface waves by a time window. Thus, their energy and arrival time changes can be analyzed independently. These analyses demonstrate that, contrary to the case for head waves propagating along a flat interface, there are two mechanisms for head waves traveling along an irregular interface: a refraction mechanism and transmission mechanism. That is, the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media. Such knowledge will be helpful in constructing a more accurate inversion method, such as head wave travel-time tomography, and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas, such as the Tibetan Plateau.

Inversion of multimegameter-range acoustic data for ocean temperature

Ocean sound speed (a surrogate for temperature) derived from the ray travel times obtained from acoustic transmissions may be inaccurate when the reference ocean state is inadequate for linearized inversion. When the reference (e.g., the Levitus ocean atlas) is significantly different from the "true" ocean, the reference ray paths inaccurately represent the true sampling. In addition, natural oceanic variations, such as the evolution of a summer mixed layer, can significantly change the ray sampling over time. The guiding principle for inversion is that ray travel times associated with the inverse solution must match the measured travel times. A time-dependent reference ocean can reduce both the nonlinearities and the solution uncertainties since the model variances may be assumed to be less. The Levitus ocean atlas was employed to explore the effects of nonlinearities when inverting multimegameter-range acoustic data and to find accurate inversion methods. These methods were applied to acoustic data obtained in the North Pacific during the acoustic thermometry of ocean climate (ATOC) project using an acoustic source on Pioneer Seamount off the coast of California. In order to linearize the inversions, the annual cycle was removed by referencing the measured travel times to travel times computed using the Levitus monthly ocean atlas. This linearization results in a more accurate time series of range- and depth-averaged temperatures, but the solution for range- and depth-averaged temperature is only slightly different from that using a time-independent set of rays. Standard uncertainties for the 0-1000-m depth-averaged temperature are typically /spl plusmn/0.012/spl deg/C, while the annual peak to-peak temperature variation is about 0.4/spl deg/C. Because the travel time data are inherently averaging, the time series of range- and depth averaged temperature is insensitive to different assumptions made in the forward model, such as the model parameterization, variances, wavenumber spectra, and the data uncertainties.

Inversion of multimegameter-range acoustic data for ocean temperature

Ocean sound speed (temperature) derived from ray travel times obtained from multimegameter-range acoustic transmissions may be inaccurate when the reference ocean state is inadequate for linearized inversion. When the reference (e.g., the Levitus atlas) is significantly different than the ‘‘true’’ ocean, the ray paths defined by that reference inaccurately represent the true sampling. In addition, natural oceanic variations, such as the evolution of a summer mixed layer, can significantly change the ray sampling. The guiding principle for inversion is that ray travel times associated with the inverse solution must match the measured travel times. Inversion of travel times relative to an arbitrary mean can be inaccurate. Accurate inversions may be obtained by iterative methods or by a better choice of reference ocean, but the solution of this nonlinear problem is not always obvious. Inadequate depth resolution for the vertical structure in the inverse solution can make calculation of travel times difficult. A linearizing time-dependent reference ocean can reduce the solution uncertainties since the a priori model variances are less. Simulations employing the Levitus ocean atlas, so that the ‘‘true’’ ocean state is known, are used to define the problems of nonlinear inversion and to find accurate inversion methods.

Partial Derivatives of Eigenfrequencies of a Rectangular Parallelepiped and a Sphere of Elastically Anisotropic Solid.

Analytic expressions of partial derivatives of eigenfrequency with respect to elastic constants, density and size were derived for a rectangular parallelepiped and a sphere of elastically anisotropic solid, in order to provide an accurate inversion method for determining the elastic constants. The formulas were extended for determination of anisotropic dissipation constants from attenuation data of free oscillation of anelastic materials. A numerical example was given for an olivine specimen (orthorhombic) of rectangular parallelepiped.

Regularized inversion of diatomic vibration–rotation spectral data: A functional sensitivity analysis approach

We present a stable and accurate inversion method for extracting potentials from spectroscopic data of diatomic molecules. The method, which was developed previously for inverting scattering data, is based on first-order functional sensitivity analysis in conjunction with the Tikhonov regularization, singular system analysis, and an exact transformation technique. Besides being numerically stable, it requires neither explicit functional forms nor special basis function expansions for the potential corrections when solving the corresponding linearized integral equation. Instead, we solve the linear equation directly in terms of the probability densities of the unperturbed vibrotation eigenstates. For illustration, we consider the ground electronic state of the H2 molecule. Inversions have been carried out for simulated data free of noise and for those with noise of magnitude comparable to realistic experimental errors. It is found that in both cases, a relatively large deviation of the starting reference potential from the truth may be tolerated to still accurately recover the intended one. The propagation of the spectral errors is analyzed in detail based on the linearization assumption. The variance of the recovered potential reveals the reliability of various regions of the recovered potential.

Highly Accurate Inversion Methods for Three-Dimensional Stratified Media

This paper describes two highly accurate velocity inversion methods for three-dimensional isovelocity stratified media. The first one is a Born-type perturbation method based on an asymptotic, implicit Green’s function, while the second one is based on the Kirchhoff representatfnn of the reflected field. It is shown that, given a band-limited reflected signal resulting from one backscatter experiment, both methods can be used in a recursive manner to accurately reconstruct the unknown velocity profile. They are tested on both synthetic and real data sets. The tests on synthetic data demonstrate higher accuracy than has been the case for previous methods in the literature. In the most extreme test, synthetics with 10 layers and velocity variation on the order of 200% were used and extremely accurate inversion was achieved.

Generating the maximum of independent identically distributed random variables

Frequently the need arises for the computer generation of variates that are exactly distributed as Z = max( X 1, …, X n ) where X 1, …, X n form a sequence of independent identically distributed random variables. For large n the individual generation of the X i 's is unfeasible, and the inversion-of-a-beta-variate is potentially inaccurate. In this paper, we discuss and compare the corrected inversion method, the log( n)/ n-tail method and the record time method. The latter two methods have an average complexity 0(log( n)), are very accurate and do not require the inversion of a distribution function. The normal, exponential and gamma densities are treated in detail. The existence of fast and accurate inversion methods for the error function makes the corrected inversion method faster than the other ones for n large enough when the X i 's are normal random variables.