Parametric estimation of phase and group slownesses from sonic logging waveforms

Geophysics ◽  
1992 ◽  
Vol 57 (8) ◽  
pp. 978-985 ◽  
Author(s):  
Kai Hsu ◽  
Cengiz Esmersoy
Keyword(s):  
Parametric Method ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Flexural Wave ◽  
Smooth Functions ◽  
Dispersive Waves ◽  
Prony Method ◽  
Receiver Array ◽  
Frequency Independent ◽  
Sonic Logging

Sonic logging waveforms consist of a mixture of nondispersive waves, such as the P‐ and S‐headwaves, and dispersive waves, such as the Stoneley and pseudo‐Rayleigh waves in monopole logging and the flexural wave in dipole logging. Conventionally, slowness dispersion curves of various waves are estimated at each frequency, independent of data at other frequencies. This approach does not account for the fact that slowness dispersion functions in sonic logging are continuous and, in most cases, smooth functions of frequency. We describe a parametric slowness estimation method that uses this property by locally approximating the wavenumber of each wave as a linear function of frequency. This provides a parametric model for the phase and group slownesses of the waves propagating across the receiver array. The estimation of phase and group slownesses is then carried out by minimizing the squared difference between the predicted and observed waveforms. The minimization problem is nonlinear and is solved by an iterative algorithm. Examples using synthetic and field data are shown and the results are compared with those obtained by the conventional Prony method. Based on the comparison, we conclude that the parametric method is better than the conventional Prony method in providing robust and stable slowness estimates.

scholarly journals Parameter estimation in a Black Scholes

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 117-122
Author(s):  
Mustafa Bayram ◽  
Buyukoz Orucova ◽  
Tugcem Partal
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Parametric Method ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Likelihood Method ◽  
Observation Data ◽  
Unknown Parameters ◽  
Black Scholes ◽  
Non Parametric

In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.

Estimating the distribution of a stochastic sum of IID random variables

2020 ◽  
Vol 70 (3) ◽  
pp. 759-774
Author(s):  
Viktor Witkovský ◽  
Gejza Wimmer ◽  
Tomas Duby
Keyword(s):  
Probability Distribution ◽  
Heavy Tails ◽  
Expert Knowledge ◽  
Parametric Method ◽  
Estimation Method ◽  
Random Variables ◽  
Parametric Estimation ◽  
Empirical Characteristic Function ◽  
Parametric Modelling ◽  
Non Parametric

AbstractSuggested is a non-parametric method and algorithm for estimating the probability distribution of a stochastic sum of independent identically distributed continuous random variables, based on combining and numerically inverting the associated empirical characteristic function (CF) derived from the observed data. This is motivated by classical problems in financial risk management, actuarial science, and hydrological modelling. This approach can be naturally generalized to more complex semi-parametric modelling and estimating approaches, e.g., by incorporating the generalized Pareto distribution fit for modelling heavy tails of the considered continuous random variables, or by considering the weighted mixture of the parametric CFs (used to incorporate the expert knowledge) and the empirical CFs (used to incorporate the knowledge based on the observed or historical data). The suggested numerical approach is based on combination of the Gil-Pelaez inversion formulae for deriving the probability distribution (PDF and CDF) from the associated CF and the trapezoidal quadrature rule used for the required numerical integration. The presented non-parametric estimation method is related to the bootstrap estimation approach, and thus, it shares similar properties. Applicability of the proposed estimation procedure is illustrated by estimating the aggregate loss distribution from the well-known Danish fire losses data.

Reliability assessment of offshore dynamic scour protections using copulas

2018 ◽  
Vol 43 (5) ◽  
pp. 506-538 ◽  
Author(s):  
T Fazeres-Ferradosa ◽  
F Taveira-Pinto ◽  
X Romão ◽  
MT Reis ◽  
L das Neves
Keyword(s):  
Wind Farm ◽  
Estimation Method ◽  
Information Criterion ◽  
Probability Of Failure ◽  
Parametric Estimation ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Spectral Parameters ◽  
Peak Period ◽  
Kendall’S Τ

This article presents a methodology to assess the reliability of dynamic scour protections used to protect offshore wind turbine foundations. The computed probabilities of failure are based on a dataset of 124 months of hindcast data from the Horns Rev 3 offshore wind farm. Copula-based models are used to obtain the joint distribution function of the significant wave height and spectral peak period and to obtain the probability of failure of scour protections. The sensitivity of the probability of failure to each model is addressed. The influence of the duration of the waves’ time series is also studied. A sensitivity analysis of the probability of failure to physical constraints, such as the water depth, current’s velocity or the mean diameter of the armour units, is performed. The results show that probability of failure is dependent on the copula used to model the spectral parameters and the associated value of Kendall’s τ. It is shown that the copula presenting the best values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) did not lead to the probabilities of failure that are closer to the non-parametric estimation, obtained by means of the bivariate version of the Kernel density estimation method. The application to the case study led to annual probabilities of failure, which are comparable with the values applied for other offshore components, according to the current offshore wind industry standards.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

Parametric estimation in boolean segment processes by a restoration-estimation method

1998 ◽  
Vol 30 (2) ◽  
pp. 274-275
Author(s):  
Joël Chadœuf ◽  
Rachid Senoussi ◽  
Jian-Feng Yao
Keyword(s):  
Estimation Method ◽  
Parametric Estimation

Time Frequency Analysis of Dispersive Waves by Means of Wavelet Transform

1995 ◽  
Vol 62 (4) ◽  
pp. 841-846 ◽  
Author(s):  
Kikuo Kishimoto ◽  
Hirotsugu Inoue ◽  
Makoto Hamada ◽  
Toshikazu Shibuya
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Gabor Wavelet ◽  
Flexural Wave ◽  
Lateral Impact ◽  
Dispersive Waves ◽  
Time Frequency Analysis ◽  
Arrival Times ◽  
Time Frequency ◽  
Wide Range

A new approach is presented for investigating the dispersive character of structural waves. The wavelet transform is applied to the time-frequency analysis of dispersive waves. The flexural wave induced in a beam by lateral impact is considered. It is shown that the wavelet transform using the Gabor wavelet effectively decomposes the strain response into its time-frequency components. In addition, the peaks of the time-frequency distribution indicate the arrival times of waves. By utilizing this fact, the dispersion relation of the group velocity can be accurately identified for a wide range of frequencies.

Which One is More Important Factor for Pricing Options, Skewness or Kurtosis?

2006 ◽  
Vol 14 (2) ◽  
pp. 25-50
Author(s):  
Sol Kim
Keyword(s):  
Parametric Method ◽  
Estimation Method ◽  
Relative Importance ◽  
Pricing Options ◽  
Pricing Errors ◽  
Risk Neutral ◽  
Definition Of ◽  
Skewness And Kurtosis ◽  
Non Parametric

This paper investigates the relative importance of the skewness and kurtosis of the risk neutral distribution for pricing KOSPI200 options. The skewness and kurtosis are estimated from non parametric method of Bakshi, Kapadia, and Madan (2003) and the parametric method of Corrado and Su (1996). We show that the skewness of the risk neutral distribution is more important factor than the kurtosis irrespective of the estimation method, the definition of pricing errors, the moneyness, the type of options and a period of time.

Research and Extended of Semi-Parametric Model Additional System Parameter

2014 ◽  
Vol 580-583 ◽  
pp. 2815-2819
Author(s):  
You Ping Wu ◽  
Chun Tao Wang ◽  
Jia Bang Wang
Keyword(s):  
Calculation Method ◽  
System Parameter ◽  
Mixed Model ◽  
Estimation Method ◽  
Parametric Model ◽  
Parametric Estimation ◽  
Accuracy Evaluation ◽  
Estimation Of Parameters ◽  
System Parameters ◽  
Regularization Matrix

In this paper, a new solution to the semi-parametric estimation of a mixed model additional system parameters was conducted to derive a calculation method of parameter adjustment at the model regularization matrix, and determine the estimation of parameters and non-parameters as well as the accuracy evaluation formula of the model. The effectiveness of the semi-parametric estimation method was demonstrated through simulation examples, and the semi-parametric model additional system parameters was further extended.

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