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SUMMARY Post-seismic deformation caused by the 2004 Sumatra-Andaman Earthquake (M= 9.3) has been observed by space geodetic techniques such as the Global Positioning System (GPS) and the Gravity Recovery and Climate Experiment (GRACE). To estimate such deformation with a spatial scale exceeding 100 km, we can use theories of global post-seismic deformation in which the Earth is treated as a self-gravitating viscoelastic sphere. Previous theories have imposed limitations on employed earth models, such as neglecting compressibility and time variation of self-gravitation or simplifying the radial profile of the viscosity. This is because the normal mode method on which these theories are based cannot evaluate a denumerably infinite set of eigenmodes that will appear when those limitations are removed in the practical computation. To bypass this difficulty, in our previous paper, we showed that the numerical inverse Laplace integration with a rectangular path enabled us to obtain the vertical deformation without using those approximations. In this paper, we apply the same method to the horizontal deformation for a complete set of the fault mechanisms (strike-slip, dip-slip and vertical and horizontal tensile). Next, we reveal error sources in our approach. The largest error arises in different selections of the integration path. This error is less than 1 per cent in the lower-degree deformations (n∼ 10) and 0.1–0.5 per cent in the higher-degree ones (100 < n < 1000), relative to the result obtained with an independent method. Finally, we elucidate differences in far-field deformations obtained for the earth model employed in this study and those used in the previous studies for a large dip-slip event (Mw= 8.3). The result shows that (1) differences of 6–50 per cent are seen in the coseismic offset and (2) horizontal rate differences of 1–5 mm yr−1 (5–25 per cent of the rates) are observed at the epicentral distance of 100 km during the first thirty years after the event. These differences are detectable with GPS. Therefore, for theory to meet observational accuracy, effects of compressibility and stratification on global post-seismic deformation should be considered.

SUMMARY A set of Green's functions is presented for calculating the coseismic strain caused by four independent seismic sources in a spherically symmetric, non-rotating, perfectly elastic, and isotropic (SNREI) earth model. Corresponding expressions are derived assuming that the seismic sources are located at the polar axis. The proper combination of these expressions allows calculation of the coseismic strain components resulting from an arbitrary seismic source at any Earth position. Calculations of strain components are made for the near field resulting from the four independent sources at a depth of 32 km inside the 1066A earth model. Results agree well with those calculated for a half-space earth model, thus confirming the validity of the theory presented in this research. A case study is performed and earth model effects are investigated. Furthermore, this paper investigates effects of spherical curvature and the stratified structure of the Earth in computing coseismic strain changes. Curvature effects are small for three types of seismic sources, but extremely large for the horizontal tensile opening on the vertical fault plane. Because a general coseismic deformation comprises four independent solutions, the large curvature effect on the horizontal tensile opening source contributes to the general result. Effects of Earth's stratified structure are large for all depths and epicentral distances. They reach a discrepancy greater than 30 per cent almost everywhere, and 100 per cent in a very far field. Results show that effects of crustal structure mainly exist in the near field; they do not affect results for a far field.

SUMMARY We present a numerical formulation for computing elastic deformations caused by a dislocation on a ¢nite plane in a spherically symmetric earth. It is based on our previous work for a point dislocation (Sun & Okubo 1993). The formulation enables us to compute the displacement, potential and gravity changes due to an earthquake modelled as spatially distributed dislocations. As an application of the ¢nite-fault dislocation theory, we make a case study of the theoretical and observed gravity changes. The computed results are in excellent agreement with the observed gravity changes during the earthquake. The gravity changes in the near ¢eld can reach some 100 ]gal, which can be easily detected by any modern gravimeter. In the far ¢eld they are still signi¢cantly large:jdgj > 10 ]gal within the epicentral distance h 1 ]gal within h 0:1 ]gal within h 0:01 ]gal globally. We also calculate the geoid height changes caused by the 1964 Alaska earthquake and by the same earthquake with revised parameters and an assumed barrier. We ¢nd that the earthquake should have caused geoid height changes as large as 1.5 cm.

SUMMARY This paper studies the potential and gravity changes caused by dislocations in spherically symmetric earth models. We define dislocation Love numbers to describe the elastic deformation of the earth raised by point sources. We discuss the shear and tensile dislocations, which can be expressed by four independent components: a vertical strike-slip, a vertical dip-slip, a tensile opening on a horizontal plane, and a tensile opening on a vertical plane. The results for a homogeneous earth model agree very well, at least within lo, with those predicted from flat-earth theory. The far-field results indicate no larger than 10per cent difference within 10". It makes little difference whether we use the theory on a sphere or that for a flat earth in the near field, while it is reasonable to use the spherical theory for global calculation. We proceed to calculations with a radially heterogeneous earth model (Model 1066A). The results are as a whole similar to those for a homogeneous sphere. In some cases, however, the difference between the two becomes significant. For example, the locations of the nodal lines of the gravity change differ significantly between the two models. This indicates that the vertical layering can cause considerable effects on the deformation fields.

SUMMARY We derive expressions in closed form which give the gravity potential changes caused by point dislocations. They enable us to evaluate coseismic changes in surface gravity and geoid height. Numerical simulation shows that a great earthquake could cause a geoid height change of order 1 m.

Summary This paper treats two principal problems on the Chandler wobble Q(Qw); (1) the most probable estimate for Qw (present estimates range from 30 to 600), and (2) the relation between the mantle Q(Qm) and Qw (present estimates vary over an order of magnitude). We must resolve both problems to discuss the frequency dependence of Qm and mantle rheology on firm ground. We modify Maximum Entropy Spectral Analysis to be suitable for estimating the Q value and show Qw exists in the range 50≲ Qw≲ 100. We compute the complex Love number k for the anelastic earth to reveal Qw/Qm≃ 1.5. If Qm depends on the frequency f such that Qm(f) ∝ fα and the mantle is the principal sink of the wobble energy, then 0.14 < α < 0.2.If the mantle absorbs only a minor fraction of the wobble energy, α should be less than the above values.

Summary Natural remanent magnetization (NRM) and saturation isothermal remanent magnetization (SIRM) of deep-sea sediments from the equatorial Pacific and south-western Indian Ocean were subjected to time series analysis. Three different approaches were employed to investigate the variation of geomagnetic total force. At both sites, these analyses show periodicities of 25 000 and 18 000 yr. The period of 25 000 yr, which is nearly equal to the Earth's precessional period (25 800yr), suggests that the precession plays some role in the generation of the geomagnetic field. Fluctuations of palaeo-magnetic declination and inclination seem to have no remarkable periodicities.

SUMMARY This paper treats the spheroidal deformation when the harmonic order tends to infinity. Asymptotic solutions for a spherically symmetric model are presented in an analytical form. The formulas are indispensable in computing (i) partials of the Green's functions and (ii) coseismic deformation, such as strain steps detected far away from epicentres.

Summary. This paper treats the static spheroidal deformation of degree 1 in detail. We give a physical interpretation of the consistency relation imposed on it. The relation serves as a guiding principle to find out all of its members. Following Okubo & Saito, we derive the partial derivatives of the degree 1 Love numbers with respect to density, bulk modulus and rigidity.

Summary. This paper investigates whether the Chandler period is variable in time. The first step is to develop an Instantaneous Frequency Analysis to trace the time-varying spectrum for a non-stationary , complex-valued time series. The method is then applied to the observed polar motion to find no significant fluctuation of the Chandler period. Next, the observational grounds of the variable period hypothesis are re-examined. It is shown that the previous analytical technique does yield a fluctuating Chandler period even for simulation data of a constant frequency. We cannot find any positive evidence for the hypothesis.