Engineering topics

Chao, B. F.

Publications and source records attributed to Chao, B. F..

31 records · Page 2

NASA NTRS1991

The earth's equatorial principal axes and moments of inertia

The earth's equatorial principal moments of inertia are given as A and B, where A is less than B, and the corresponding principal axes are given as a and b. Explicit formulas are derived for determining the orientation of a and b axes and the difference B - A using C(22) and S(22), the two gravitational harmonic coefficients of degree 2 and order 2. For the earth, the a axis lies along the (14.93 deg W, 165.07 deg E) diameter, and the b axis lies perpendicular to it along the (75.07 deg E, 104.93 deg W) diameter. The difference B - A is 7.260 x 10 to the -6th MR2. These quantities for other planets are contrasted, and geophysical implications are discussed.

Liu, H. S.↗

NASA NTRS1988

Global surface-water-induced seasonal variations in the earth's rotation and gravitational field

The effects of seasonal changes in continental surface-water storage on the low-degree gravitational-field coefficients (J), the annual wobble excitation (Psi), and the seasonal length-of-day (LOD) variations are investigated by means of numerical simulations based on compiled meteorological data (Willmott et al., 1985) and satellite snow-load estimates (Chao et al., 1987). The formulation of the model equations and the overall characteristics of the data sets are discussed in detail, and the computation results are presented in tables and graphs. The effect on Psi is found to be relatively small due to longitudinal cancellation, but those on LOD and J are considered significant.

Chao, B. F.↗

NASA NTRS1985

Excitation study of the Lageos-derived Chandler wobble

Euler (1765) has deduced that any nonspherical rigid body which is rotating about some axis that is not its principal moment of inertia axis will experience a wobble as it rotates. The earth's wobble predicted by Euler was actually detected by Chandler (1891). The present paper is concerned with this wobble which is now known as the Chandler wobble. The Chandler wobble has now been under observation for more than 80 years. During part of this time, the amplitude of the wobble has actually been seen to grow. It follows that there must be some mechanisms operating to maintain (or excite) the Chandler wobble preventing it from decaying. Possible excitation mechanisms considered include earthquakes and meteorological variations. In this paper, an analysis is conducted of Lageos polar motion data for the period 1977-1983 to find out what can be learned from these data about the excitation mechanisms.

Gross, R. S.↗

NASA NTRS1985

Excitation of the Earth's Chandler wobble by southern oscillation/El Nino, 1900-1979

The southern oscillation/El Nino (ENSO) is the single most prominent interannual signal in global atmospheric/oceanic fluctuations. The following question is addressed: how important is the angular momentum carried by ENSO in exciting the Earth's Chandler wobble? The question is attacked through a statistical analysis of the coherence spectra (correlation as a function of frequency) between two data sets spanning 1900 to 1979-the southern oscillation index (SOI) time series and the excitation function psi (with x-component psi sub x and y-component psi sub y) of the Chandler wobble derived from the homogeneous ILS (International Latitude Service) polar motion data. The coherence power and phase in the Chandler frequency band (approx. 0.79 to 0.89 cpy) are studied. It is found that, during 1900 to 1979 the coherence between SOI and psi sub x is significant well over the 95% confidence threshold whereas that between SOI and psi sub y is practically nil. Quantitatively, the coherence study shows that ENSO provides some 20% of the observed Chandler wobble excitation power. Since earlier investigations have shown that the total atmospheric/oceanic variation can account for the Chandler wobble excitation at about 20% level, the implication is that ENSO maybe an important (interannual) part of the atmospheric/oceanic variation that is responsible for the Chandler wobble excitation during 1900 to 1979.

Chao, B. F.↗

NASA NTRS1985

On the excitation of the earth's polar motion

Reference is made to recent studies by Barnes et al. (1983) and Hide (1984) in which a conclusion is made that atmospheric excitation alone is sufficient to account for the earth's polar motion over the studied periods. It is then shown through a physical 'thought' experiment and a numerical simulation that this conclusion is unjustified since the information about the Chandler wobble presented in these papers is insufficient. Whether the conclusion is true or not, however, remains an open question.

Chao, B. F.↗

NASA NTRS1984

On the excitation of the earth's free wobble and reference frames

The excitation of the earth's polar motion in connection with problems that are associated with the diversity of reference frames involved in observations and theoretical computations is studied. Following the dynamics of the earth's polar motion, the kinematics that relates observations from different reference frames is developed. The conventional procedures of studying the seismic excitation of polar motion are re-examined, subject to the question: relative to what reference frame? It is concluded that an inconsistency in reference frames has prevailed in the literature. While this inconsistency is indeed far from trivial, the resultant discrepancy, however, is small for all practical purposes.

Chao, B. F.↗

NASA NTRS1984

Analysis of the Earth's variable rotation

The objective was to analyze the Earth's rotation, and to compare the observations with the atmospheric and seismic excitation functions. The variation in the Earth's rotation can be separated into the length-of-day (LOD) variation and the polar motion. Possible driving mechanisms include: atmospheric/oceanic circulations, seismic activities, solar-lunar tides, mantle convection, core-mantle coupling, and solar activities. The major problem of concern was the identification of these dynamical processes as primary driving mechanisms for the various features in the variation of the Earth's rotation.

Chao, B. F.↗

NASA NTRS1984

Interannual length-of-day variation with relation to the southern oscillation/El Nino

The atmospheric and oceanic mass transport associated with the southern oscillation/El Nino will inevitably induce an interannual variation in the length of day. An empirical correlation study is conducted by comparing the Southern Oscillation Index time series and the interannual length-of-day variation (obtained by removing the long-period and short-period variations from a BIH length-of-day series) for the period 1957-1983. The two series have an encouraging qualitative correlation, in particular with respect to El Nino events; and the linear correlation coefficient is found to be 0.55. It is believed that much, if not most, interannual length-of-day variation is caused by the southern oscillation, and the true correlation is considerably higher than its apparent value considering the fact that the Southern Oscillation Index is merely an indicator derived from two local atmospheric measurements.

Chao, B. F.↗

NASA NTRS1984

Predictability of the Earth's polar motion

A comprehensive, experimental study of the predictability of the polar motion using a homogeneous BIH (Bureau International de l'Heure) data set is presented. Based on knowledge of the physics of the annual and the Chandler wobbles, the numerical model for the polar motion is constructed by allowing the wobble periods to vary. Using an optimum base length of 6 years for prediction, this floating-period model, equipped with a non-linear least-squares estimator, is found to yield polar motion predictions accurate from 0.012 to 0.024 inches depending on the prediction length up to one year, corresponding to a predictability of 91-83%. This represents a considerable improvement over the conventional fixed-period predictor, which does not respond to variations in the apparent wobble periods. The superiority of the floating-period predictor to other predictors based on critically different numerical models is also demonstrated.

Chao, B. F.↗

NASA NTRS1984

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗

NASA NTRS1983

Autoregressive harmonic analysis of the earth's polar motion using homogeneous International Latitude Service data

The homogeneous set of 80-year-long (1900-1979) International Latitude Service (ILS) polar motion data is analyzed using the autoregressive method (Chao and Gilbert, 1980), which resolves and produces estimates for the complex frequency (or frequency and Q) and complex amplitude (or amplitude and phase) of each harmonic component in the data. The ILS data support the multiple-component hypothesis of the Chandler wobble. It is found that the Chandler wobble can be adequately modeled as a linear combination of four (coherent) harmonic components, each of which represents a steady, nearly circular, prograde motion. The four-component Chandler wobble model 'explains' the apparent phase reversal during 1920-1940 and the pre-1950 empirical period-amplitude relation. The annual wobble is shown to be rather stationary over the years both in amplitude and in phase, and no evidence is found to support the large variations reported by earlier investigations. The Markowitz wobble is found to be marginally retrograde and appears to have a complicated behavior which cannot be resolved because of the shortness of the data set.

Chao, B. F.↗

NASA NTRS1983

Normal mode study of the earth's rigid body motions

In this paper it is shown that the earth's rigid body (rb) motions can be represented by an analytical set of eigensolutions to the equation of motion for elastic-gravitational free oscillations. Thus each degree of freedom in the rb motion is associated with a rb normal mode. Cases of both nonrotating and rotating earth models are studied, and it is shown that the rb modes do incorporate neatly into the earth's system of normal modes of free oscillation. The excitation formula for the rb modes are also obtained, based on normal mode theory. Physical implications of the results are summarized and the fundamental differences between rb modes and seismic modes are emphasized. In particular, it is ascertained that the Chandler wobble, being one of the rb modes belonging to the rotating earth, can be studied using the established theory of normal modes.

Chao, B. F.↗

NASA NTRS1983

On excitation of Earth's free wobble and reference frames

The excitation of the Earth's polar motion in connection with problems that are associated with the diversity of reference frames involved in observations and theoretical computations is studied. Following the dynamics of the Earth's polar motion, the kinematics that relates observations from different reference frames is developed. The conventional procedures of studying the seismic excitation of polar motion are re-examined, subject to the question: relative to what reference frame? It is concluded that an inconsistency in reference frames has prevailed in the literature. While this inconsistency is indeed far from trivial, the resultant discrepancy, however, is small for all practical purposes.

Chao, B. F.↗