Potentials and displacements for two theoretical seismic sources

Theoretical, P, SV, and SH displacement potentials and displacements for a double couple or point shear dislocation source and for a ‘mixed quadrupole’ source at any arbitrary orientation in an isotropic homogeneous elastic space are expressed as multiple integral and derivative operations on the source history in the time domain and their algebraic equivalent in the frequency domain. These sources have the same angle orientation functions, which are given explicitly. The double couple and ‘mixed quadrupole’ are both quadrupole sources but, unlike the double couple, the P and S waves from a ‘mixed quadrupole’ have different source histories. Analytic displacements are obtained using as examples the Ohnaka shear dislocation history for a double couple and the Randall and Archambeau tectonic release histories for ‘mixed quadrupole’ sources. The displacement fields are investigated numerically, in order to establish a criterion for estimating the minimum range for applying far-field theory results to the total displacement field. The chosen criterion is the ratio of the far-field peak amplitude, which is a function of source rise or duration time, to the static displacement, which is a near-field phenomenon. The proposed criterion is found to be conservative as to the minimum range for the farfield, predicted (1/R) dependence of the total field peak amplitude, but quite satisfactory for time domain estimates of moment and corner frequency based on far-field theory

The perturbation of Love wave spectra

The equations governing the variational principles for Love wave spectra are investigated. It is shown that assumptions used by earlier authors are not necessary to the validity of the variational techniques. Moreover it is demonstrated that except for a homogeneous plate, these assumptions are false for plane multilayered media and lead to incorrect expressions for group-velocity perturbations. The correct expressions are determined and examples of their use are given

Elastic relaxation coefficients for a spherical cavity in a prestressed medium of arbitrary orientation

Archambeau gave elastic relaxation coefficients for a spherical cavity introduced into a pure shear prestress field. The technique is generalized to a stress field for which only the trace of σ_(ij)^(0) is zero. The coefficients are given for a general deviatoric prestress field of arbitrary orientation. They are then specialized to the case of a pure shear stress expressed in terms of the orientation angles commonly used in fault plane descriptions, i.e. dip and slip angle. The extension of this technique to an arbitrary homogeneous prestress field and its limitations are discussed

Surface waves in multilayered elastic media. Part II. Higher mode spectra and spectral ratios from point sources in plane layered Earth models

Phase and amplitude spectra of Rayleigh and Love waves are presented for two Earth models, one oceanic and one continental shield. The spectra of the first three Rayleigh modes and the first four Love modes are tabulated for point sources at selected depths. These tables along with computer algorithms described here allow one to estimate the amplitude spectra at nontabulated source depths. The use of spectral ratios as a means of determining source depth is investigated. A source depth of 20 km is obtained for the Fallon earthquake of July 20 1962. This depth agrees with previous estimates but the technique requires a fault-plane orientation which differs from radiation pattern solutions

Theoretical and observed acoustic-gravity waves from explosive sources in the atmosphere

A matrix formulation is used to derive the pressure variation for acoustic-gravity waves from an explosive source in an atmosphere modeled by a large number of isothermal layers. Comparison of theoretical and observed barograms from large thermonuclear explosions leads to the following conclusions: (1) The major features on the barogram can be explained by the superposition of four modes, (2) different parts of the vertical temperature structure of the atmosphere control the relative excitation of these modes, (3) a scaled point source is sufficient to model thermonuclear explosions, (4) the observed shift in dominance of certain frequencies with yield and altitude can be explained by means of the empirical scaling laws derived from the direct wave near the explosion, and (5) out to 50° from the source, the observed variation of amplitude with distance can be accounted for by geometrical spreading over a spherical surface

The early years of computational seismology at Caltech

Early this year I was asked to make some "remarks" at the 100th anniversary of the Berkeley station as President of the SSA. Not knowing exactly what was expected, I decided to do some background research on the history of the Berkeley station as found in papers, letters, and reports to the Bulletin. I found these very informative and some very entertaining. Even though a lot of the information was obviously hearsay and written well after the events, I felt that there was a place for this type of anecdotal "history" in the Bulletin and probably no better place for it than in the Presidential Address

The Krakatoa Air-Sea Waves: an Example of Pulse Propagation in Coupled Systems

The theory of pulse propagation in an atmosphere coupled to an ocean is applied to the air-sea waves excited by the explosion of the volcano Krakatoa. Numerical results for a realistic atmosphere-ocean system show that the principal air pulse corresponds to the fundamental gravity mode GR_0. A small sea wave is associated with the mode GW_0 with phase velocities close to the √(gh) velocity of the ocean. Free waves with this velocity exist in the atmosphere and transfer energy to the ocean in an efficient manner. These air waves ‘jump’ over land barriers and re-excite the sea waves. An explosion of 100–150 megatons is required to produce the equivalent of the Krakatoa pressure disturbance

Propagation of acoustic-gravity waves in the atmosphere

Homogeneous wave guide theory is used to derive dispersion curves, vertical pressure distributions, and synthetic barograms for atmospheric waves. A complicated mode structure is found involving both gravity and acoustic waves. Various models of the atmosphere are studied to explore seasonal and geographic effects on pulse propagation. The influence of different zones in the atmosphere on the character of the barograms is studied. It is found that the first arriving waves are controlled by the properties of the lower atmospheric channel. Comparison of theoretical results and experimental data from large thermonuclear explosions is made in the time and frequency domains, and the following conclusions are reached: (1) The major features on barograms are due to dispersion; (2) superposition of several modes is needed to explain observed features; (3) scatter of data outside the range permitted by extreme atmospheric models shows the influence of winds for A1; wind effects and higher modes are less important for A_2 waves. A discussion is included on atmospheric terminations and how these affect dispersion curves

Radiation patterns of seismic surface waves from buried dipolar point sources in a flat stratified Earth

Explicit compact expressions were obtained for the far displacement field of Rayleigh and Love waves generated by force configurations which served to simulate shear-type faults with arbitrary dip and slip. The medium transfer functions for dipolar sources were computed for a Gutenberg flat continental earth model with 23 layers. These were then used to obtain universal radiation pattern charts for couple- and double-couple-type sources at various depths over the period range 50 to 350 sec. It was demonstrated by means of few typical examples that the radiation patterns of Rayleigh waves may depend strongly on the depth of the source, and unlike the fundamental Love mode may be rather sensitive to small variations in frequency. For a given source and frequency the radiation pattern may differ considerably from one mode to another