The arrest of a semi-infinite longitudinal shear crack is caused by either (1) the finiteness of available strain energy, or (2) an increase in fracture energy along the trajectory of the running crack. In the former case the following relationship may be used to evaluate the fracture energy:where yo is the fracture energy per unit length along the crack edge per unit extension of the cracktip (erg cm-2), R is the characteristic radius of the fault (cm), ACJ is the stress drop (dyne cm-2) and p is the rigidity (dyne cm-2). This leads to the following relationship:log Aa = -3 log R +f log (2ptny0) or from the Keylis-Borok relationship (1959):where M , is the seismic moment in dyne cm-'. These two relationships are statistically acceptable for Southern California faults and the Tonga-Kermadec Arc earthquakes. The fracture energy is found to vary from lo3 to lo9 erg cm-' with fresh fracture being associated with 10'-lQ9 erg cm-2 while frictional rupture with 103-107 erg cm-2. These values are in good agreement with other independent estimates.

This paper is the first of a series that will examine the effect of earth structure on earthquake displacement, strain and tilt fields at the Earth's surface. Its purpose is to develop the numerical techniques to be applied in the papers that foliow. A general computational procedure for the evaluation of the integral expressions for the surface displacements due to an arbitrary point dislocation source in a layered medium is described. It is shown to be rapid and inexpensive to use, and its accuracy appears to be entirely adequate for practical purposes.

Detailed lithologic interpretation of seismic sections and/or pseudo‐sonic logs generated from seismic data requires that the seismic trace can be modeled as a reflection series convolved with a zero‐phase broadband wavelet. Ghosting and marine signature deconvolution processing is a prerequisite for assuring that the seismic wavelet on a marine CDP section will be zero phase. A deterministic approach to deconvolution is centered around the concept of abandoning the purely statistical method of wavelet estimation and actually measuring the seismic wavelet. A proper signature recording for marine data is, therefore, a crucial component of deterministic deconvolution. Another important element in the deterministic deconvolution sequence is the application of a deghosting filter to remove near‐surface reflections. Proper application of a deghosting filter significantly improves the correlation between log synthetics and the seismic trace. It has been found that statistical deconvolution schemes, because of the number of statistical hypotheses required to produce a deconvolution filter, produce residual wavelets that are highly variable in character and whose average phases cover the entire phase spectrum, modulo 2π. Examples of a Gulf Coast marine line which was shot with Aquapulse™, air gun, and Maxipulse™ sources by the RV Hollis Hedberg are presented to demonstrate the differences between statistical and deterministic deconvolution processing sequences. It will be shown, using sonic logs from wells adjacent to the seismic line, that the deterministic deconvolution sections for all three sources are close to zero phase while the statistical deconvolution sections have residual average phase errors between 180 and 270 degrees. The deterministic deconvolution sections have a high degree of correlation among themselves and to the wells adjacent to the line, while the statistical deconvolution sections correlate poorly to each other and to the wells. Synthetic seismograms and their impedance logs, and the seismic sections and their corresponding pseudo‐sonic logs, are used to demonstrate how deconvolution influences lithologic interpretation. ™Western Geophysics Co.

The static displacement and strain fields caused by the introduction of a shear dislocation point source into a layered elastic half space have been evaluated using a Thomson-Haskell matrix method (Singh). The point source was found to be an adequate representation of a fault at distances greater than four fault lengths. Gross earth structure (oceanic, shield and tectonic models) cause fields that differ little from those of a uniform half space. However, significant departures from the uniform half-space fields are found to be caused by low rigidity layers, both at the surface (representing sediment cover) and at depth (representing possible zones of partial melt). Both of these features cause complexities in the strain fields that depend on the source orientation and source-receiver distance, and these may result in amplification or attenuation of the uniform halfspace fields by factors of up to 10.