Construction of Structural Geological Model using Monte Carlo Simulation

To optimize the prediction of structural geological conditions in the underground as of data collected at the surface, due to the usual great uncertainties involved, we discuss new perspectives for the construction of structural geological models, bearing in mind the common doubts involved and their implications in the safety of infrastructure works, mining, etc. This paper presents a statistical simulation applied to structural geological measures (dip-dip direction) obtained from schists during the design and construction of civil works through a correlation between surface data with different depth levels. Angular structural geological measures of joints and foliations converted in direction cosines were subjected to the PERMANOVA test to verify the amplitude of differences at different depth levels. The asymptotic results allowed to determine regions of confidence built around centroids through statistical simulation, allowable consistency was considered in regions where the differences in the simulated values were small enough from a practical point of view, taking into account that the difference between joint structures and foliation structures is smaller in the former. The foliation is a characteristic structure of rock deformation just like the joints.

Quaternion Method of Calculating Angles while Measuring via Goniometric Precision Instrument System

The article is devoted to the topical problem: increasing accuracy and performance of angle measurements necessary in various branches of science and technology. One of the ways of increasing accuracy and performance of angle measurements is using modern algorithmic methods and mathematic devices for processing measurement information. Thus, in order to increase accuracy and speed of angle measurements on the example of the well-known goniometric precision instrument system (GPIS), it was offered quaternion calculation of angle values while performing goniometric measurements in the work. The efficiency of quaternion calculation is unquestioned as quaternions unlike other traditional methods (in particular matrix with the use of Euler angles, direction cosines) are presented only with four parameters describing angle positions of the objects and have only one connection equation unlike six equations for matrix methods, in particular for direction cosines. The suggested quaternion calculation is used in GPDS as general theoretic and information basis of contactless precision goniometric measurements in preliminary setting navigation sensitive elements (NSE), plane angles, pyramid prisms etc. The usage of the developed quaternion calculation enabled to increase accuracy by 0,25 (in 3 times) and measurement performance in 9 times (up to 6.5 sec.) in comparison with the famous ones. Applying quaternion calculation of angle values implies using a smaller RAM capacity of PC that increases performance of system work. Besides, a smaller amount of mathematic operations performed in quaternion way of calculating angles, except increasing performance, enables to decrease a rounding error in calculation results that is accumulated in multiple measurements and may reach great values. Thus, accuracy and performance of measurements increase.

Efficient Two-Dimensional Direction Finding Algorithm for Rectilinear Sources Under Unknown Mutual Coupling

Digital communication signals in wireless systems may possess noncircularity, which can be used to enhance the degrees of freedom for direction-of-arrival (DOA) estimation in sensor array signal processing. On the other hand, the electromagnetic characteristics between sensors in uniform rectangular arrays (URAs), such as mutual coupling, may significantly deteriorate the estimation performance. To deal with this problem, a robust real-valued estimator for rectilinear sources was developed to alleviate unknown mutual coupling in URAs. An augmented covariance matrix was built up by extracting the real and imaginary parts of observations containing the circularity and noncircularity of signals. Then, the actual steering vector considering mutual coupling was reparameterized to make the rank reduction (RARE) property available. To reduce the computational complexity of two-dimensional (2D) spectral search, we individually estimated y-axis and x-axis direction-cosines in two stages following the principle of RARE. Finally, azimuth and elevation angle estimates were determined from the corresponding direction-cosines respectively. Compared with existing solutions, the proposed method is more computationally efficient, involving real-valued operations and decoupled 2D spectral searches into twice those of one-dimensional searches. Simulation results verified that the proposed method provides satisfactory estimation performance that is robust to unknown mutual coupling and close to the counterparts based on 2D spectral searches, but at the cost of much fewer calculations.

Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse

This paper proposes a new sensor-array geometry (the 2-circle concentric array geometry), that maximizes the array's spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem. The proposed geometry provides almost invariant azimuth angle coverage and oers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing of only an half wavelength (for non-ambiguity withrespect to the Cartesian direction cosines). A better-accurate performance in direction nding of the proposed array grid over a single ring array geometry termed as uniform circular array (UCA) is hereby analytically veried via Cramer-Rao bound analysis. Further, the authors demonstrate that the proposed sensor-array geometry has better estimation accuracy than a single ring array.

The Effect of the Anisotropy of Single Crystal Silicon on the Frequency Split of Vibrating Ring Gyroscopes

This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the n = 2 wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the n = 2 mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.

Three-Dimensional Instability of Opposite Polarity Nonthermal Dusty Plasma

Nonlinearity properties of obliquely wave propagation and instability in collisionless magnetized nonthermal dusty plasmas containing fluid of negative-positive grains are investigated. Zakharov-Kuznetsov equation is obtained and the three-dimensional wave instability is studied. The parameters such as polarity charge ratio, cyclotron frequency and fast nonthermal effectiveness of the instability properties and growth rate are theoretically studied. It is found that both positive and negative soliton profiles are formed depending on the fraction ratio of electron-ion nonthermality. Also, the growth rate was dependent nonlinearly on the direction cosines, the cyclotron frequency and the positive (negative) grain charge ratio, but independent of the fractional ratio of electron-ion nonthermality. Present discussion may be very significant regarding the observations of nonlinear phenomena in space.

Recovering a Rotation Matrix From Three Direction Cosines

In this paper, we propose a new parameterization method to represent rotation matrices using the angles ϕ→ recovered from the three direction cosines that lie on the diagonal. The map from the possible configuration space of the new variable ϕ→ to the solid ball model in axis-angle coordinates is constructed. We also introduce a bi-invariant metric and two left-invariant metrics for measuring the distance in configuration space which could be the foundation for path planning in ϕ→ space. We further analyze the Jacobian matrix and singularities to better understand the manipulability.

Bimodal or quadrimodal? Statistical tests for the shape of fault patterns

Natural fault patterns formed in response to a single tectonic event often display significant variation in their orientation distribution. The cause of this variation is the subject of some debate: it could be noise on underlying conjugate (or bimodal) fault patterns or it could be intrinsic signal from an underlying polymodal (e.g. quadrimodal) pattern. In this contribution, we present new statistical tests to assess the probability of a fault pattern having two (bimodal, or conjugate) or four (quadrimodal) underlying modes and orthorhombic symmetry. We use the eigenvalues of the second- and fourth-rank orientation tensors, derived from the direction cosines of the poles to the fault planes, as the basis for our tests. Using a combination of the existing fabric eigenvalue (or modified Flinn) plot and our new tests, we can discriminate reliably between bimodal (conjugate) and quadrimodal fault patterns. We validate our tests using synthetic fault orientation datasets constructed from multimodal Watson distributions and then assess six natural fault datasets from outcrops and earthquake focal plane solutions. We show that five out of six of these natural datasets are probably quadrimodal and orthorhombic. The tests have been implemented in the R language and a link is given to the authors' source code.