Research into the inversion of the induced polarization relaxation time spectrum based on the uniform amplitude sampling method

The induced polarization relaxation time spectrum（RTS） reflects the distribution of rock pore size,which is a key factor in estimating the oil or water storage capacity of strata.However,as the data acquisition and transmission abilities of well logging instruments are much limited due to the underground environment,it is necessary to explore suitable sampling methods which can be used to obtain an accurate RST with less sampling data.This paper presents a uniform amplitude sampling method（UASM）,and compares it with the conventional uniform time sampling method（UTSM） and logarithm time sampling method（LTSM） in terms of the adaptability to different strata,RTS inversion accuracy,and stratum vertical resolution.Numerical simulation results show that the UASM can obtain high inversion accuracy of RTS with different kinds of pore size distribution formation,with high dynamic ranges of pore size,and with a small number of sampling points.The UASM,being able to adapt to the attenuation speed of polarization curve automatically,thus has the highest vertical resolution.The inversion results of rock samples also show that the UASM is superior to the UTSM and LTSM.

Dynamic bivariate normal copula

Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.

Normalized estimation of fundamental frequency and measurement of harmonics/interharmonics

An adaptive notch filter is presented to estimate the fundamental frequency and measure both harmonics and interharmonics of an almost periodic signal with unknown time-variant fundamental frequency, which has the ro- bustness that the convergence speed is determined by neither amplitude nor frequency of fundamental component. The algorithm forms a one-dimensional slow adaptive integral manifold whose existence and stability are proved by averaging method and Lyapunov stability theorem. The local exponential stability and the ultimate boundedness of fundamental fre- quency estimation are proved. The local exponential stability makes sure that the fundamental frequency, the harmonic and interharmonic components can be all fast tracked. The principle for adjusting the parameters with their influences on tran- sient and steady-state performance is investigated and decreasing parameters can improve noise characteristic. The validity is verified by simulation results.

Learning conditional photometric stereo with high-resolution features

Photometric stereo aims to reconstruct 3D geometry by recovering the dense surface orientation of a 3D object from multiple images under differing illumination.Traditional methods normally adopt simplified reflectance models to make the surface orientation computable.However,the real reflectances of surfaces greatly limit applicability of such methods to real-world objects.While deep neural networks have been employed to handle non-Lambertian surfaces,these methods are subject to blurring and errors,especially in high-frequency regions(such as crinkles and edges),caused by spectral bias:neural networks favor low-frequency representations so exhibit a bias towards smooth functions.In this paper,therefore,we propose a self-learning conditional network with multiscale features for photometric stereo,avoiding blurred reconstruction in such regions.Our explorations include:(i)a multi-scale feature fusion architecture,which keeps high-resolution representations and deep feature extraction,simultaneously,and(ii)an improved gradient-motivated conditionally parameterized convolution(GM-CondConv)in our photometric stereo network,with different combinations of convolution kernels for varying surfaces.Extensive experiments on public benchmark datasets show that our calibrated photometric stereo method outperforms the state-of-the-art.