Random Spatial Variation Research Articles

Estimation and implications of instrumental drift, random measurement error and nugget variance of soil attributes—a case study for soil pH

SUMMARYWe propose a general model for soil pH measurement that includes instrumental drift, random measurement error, and random and correlated spatial variation. Methods for estimating these four components are described in detail. For soil pH in water, instrumental drift, random measurement error and random spatial variation (nugget effect) were greater than the corresponding quantities for soil pH in CaCl2. For both pH measurements, instrumental drift was quite marked. Measurement error and nugget effect were of a similar size. A modified kriging method is presented that takes into account the four‐component model proposed here. It is concluded that, for measuring soil chemical attributes, grid layouts should be supplemented by additional sites for the estimation of short‐range variation, that laboratory sampling designs should include controls, and that field measurements should be adjusted for instrumental drift prior to being used for spatial contouring or kriging.

Thermodynamic behavior of random-field Ising ferromagnets.

We study the thermodynamic behavior of an Ising ferromagnet in the presence of an external magnetic field of binary random spatial variation ${H}_{i}$=\ifmmode\pm\else\textpm\fi{}${H}_{0}$. We show the behavior of the system to be equivalent to a two-species (A,B) Ising ferromagnet with opposite magnetic moments (${\ensuremath{\mu}}_{A}$=-${\ensuremath{\mu}}_{B}$) in a constant magnetic field ${H}_{0}$, and we study this system in the Bethe lattice. The phase diagram (${H}_{0}$-T) of the system presents regions where two or more phases may exist, and we study their thermodynamic stability. We find a general qualitative agreement of the obtained behavior to existing results, with a slight difference in the stability region of the ferromagnetic phase, which we find to be stable throughout the whole region of its existence.

Ultrasound attenuation estimation using the lmse filters and the median filter

The ultrasound attenuation coefficient in known to increase with frequency in soft biological tissue within the diagnostic frequency range. The frequency dependent attenuation coefficient is an important parameter in clinical tissue characterization, especially in liver, and in ultrasonic quantitative B-scan imaging. But, because of the random spatial variation in the backscattered signal amplitude, the estimator variance becomes very large, making it difficult to estimate the attenuation slope from the backscattered ultrasound signal. In this paper we suggest a new ultrasound attenuation estimator based on the calibrated log spectral difference. The proposed estimation process consists of Wiener filtering, Kalman filtering, and median filtering in this order. The simulation results and experimental results with tissue equivalent (TE) phantoms show that combination of the above filterings yields a considerably reduced estimator variance compared with the conventional estimators.

Spatial variation of bandgap energy in In 0.53Ga 0.47As

We report the observation of spatial variation of the bandgap energy of In 0.53Ga 0.47As in high quality epitaxial samples grown lattice matched to InP. Nine samples grown by three different techniques (LPE, VPE and MBE) were investigated and they all showed this apparently random spatial variation. A bandgap variation as large as 15 meV was observed over distances of the order of 1 mm, an effect corresponding to two percent of bandgap energy.

Hydraulic conductivity of deeply weathered materials in the Darling Range, Western Australia

The hydraulic conductivity (K) of unconsolidated, deeply weathered material was measured by the slug test method In 214 boreholes distributed over five distinct areas in the Darling Range of Western Australia. Most of the measurements were made in the zone 0-3 m above hard rock. Theory of the method was extended to include a layer of material with lower K about the slotted pipe. The frequency distribution of K in each area was well fitted by the log-normal function. Parameters of the linear regression of logK against the inverse Gaussian function of cumulative frequency differed significantly (P<0.001) between areas. In one area of 134 ha, measurements were made in 54 boreholes located on a grid. There was a very poor correlation between values of K at the smallest separation of grid points (100 m), which suggests that there is an essentially random spatial variation of K measured by this method in this study area. Assuming log-normal frequency distributions and random spatial distributions, bulk conductivities were estimated for each area. On the basis of these investigations, it is concluded that the bulk hydraulic conductivity of the weathered material in the Darling Range is slow to moderately slow, and relatively uniform on the broad scale.

Holography in a Random Spatially Inhomogeneous Medium

The Huygens-Fresnel principle, extended to a medium that exhibits a random spatial variation in the index of refraction, is used to calculate the resulting fringe patterns in the Fresnel-Fraunhofer and pointreference Fourier-transform methods of holography. The resolution limits pertaining to these two methods are derived. In the Fresnel-Fraunhofer method, the effect of the medium is a lateral reduction in the size of the hologram that leads to a corresponding loss of resolution. In the point-reference Fourier-transform method, on the other hand, the medium does not limit the lateral extent of the hologram but gives a uniform reduction in amplitude to the resulting fringe pattern. Thus in the latter method, resolution is not degraded; but the medium does limit the size of objects that can form holograms. Numerical results pertaining to underwater holography are given.