The problem of direct interpretation of apparent resistivity curves from horizontally layered models is accomplished by using the generalized linear inverse theory. The method permits the resolution of the model parameters to be determined. The method also indicates which data points contain relatively important information necessary to resolve the model parameters. Two models were chosen to test the inversion scheme. One model has increasing resistivity with depth, and the other model possesses an intermediate resistive layer. Both models were resolved with a very high degree of accuracy from noise‐free data. When noise was added to the data, the values of the parameters oscillated about a mean value. The noise had little effect on the well‐resolved parameters but the poorly resolved parameters were in error by as much as 15 percent. The importance of each data point relative to the model was analyzed. The effect of certain data points on specific parameters was also determined. The generalized inverse method requires that the eigenvalues and eigenvectors of the system matrix be found. A comparison of the eigenvalues indicates those parameters that are well‐resolved and those that are poorly resolved from a given set of data.
Integral expressions for the electromagnetic field components produced by a horizontal loop, carrying a current IeiUt and placed on or above the surface of an n-layered half-space, are deduced in a form such that numerical integration can be performed easily. The expressions are free of approximations and completely general for all frequencies. They are constrained only to the uniformity of current around the transmitting loop. The resulting computed electromagnetic fields are valid for arbitrary values of the electrical parameters u, p, and E. The quasi-static approximation for the region above the half-space, wherein the wave equation is replaced by the Laplace equation, can be avoided.Measurements outside the loop constitute indzrction depth sounding. Induction depth sounding curves of field components and magnetic polarization parameters show good resolution of subsurface layering. In particular, it is suggested that the measurements of tilt angle and/or ellipticity of the magnetic polarization ellipse should be made to determine earth layering because of the rapidity and ease of these measurements in field operation. It is shown that the
In this experimental study, the effect of the recycled aggregate on interfacial property, permeability and strength characteristics of the concrete was evaluated in order to examine the relationship between the recycled aggregate and the performance of the hardened concrete. Five types of recycled aggregate and four levels of w/c ratio were tested. The effect of the recycled aggregate was evaluated using Vickers hardness test of aggregate interface, carbonation depth test, tensile strength test, and compressive strength test. The experimental results showed that the recycled aggregate has a significant effect on the overall properties of concrete.
The focus of this paper is on multi-user multi-input multi-output (MIMO) transmissions for millimeter wave systems with a hybrid precoding architecture at the base-station. To enable multi-user transmissions, the base-station uses a cell-specific codebook of beamforming vectors over an initial beam alignment phase. Each user uses a user-specific codebook of beamforming vectors to learn the top-P (where P ≥ 1) beam pairs in terms of the observed signal-to-noise ratio (SNR) in a single-user setting.The top-P beam indices along with their SNRs are fed back from each user and the base-station leverages this information to generate beam weights for simultaneous transmissions. A typical method to generate the beam weights is to use only the best beam for each user and either steer energy along this beam, or to utilize this information to reduce multi-user interference. The other beams are used as fall back options to address blockage or mobility. Such an approach completely discards information learned about the channel condition(s) even though each user feeds back this information. With this background, this work develops an advanced directional precoding structure for simultaneous transmissions at the cost of an additional marginal feedback overhead. This construction relies on three main innovations: 1) Additional feedback to allow the base-station to reconstruct a rank-P approximation of the channel matrix between it and each user, 2) A zeroforcing structure that leverages this information to combat multi-user interference by remaining agnostic of the receiver beam knowledge in the precoder design, and 3) A hybrid precoding architecture that allows both amplitude and phase control at low-complexity This material is based upon work supported in part by the National Science Foundation under grants CCF1403458 and CNS1642982. 2 and cost to allow the implementation of the zeroforcing structure. Numerical studies show that the proposed scheme results in a significant sum rate performance improvement over naïve schemes even with a coarse initial beam alignment codebook. Index TermsMillimeter wave, multi-input multi-output, multi-user, beamforming, hybrid precoding, phase and amplitude control, zeroforcing, generalized eigenvector, channel estimation
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