Structural Dependence of the Apparent Initial Phase of Rayleigh Wave

Abstract

Summary For Rayleigh waves generated by buried point sources, we investigate the effect of incomplete knowledge of the structure beneath the epicentre on the apparent initial phase. The effect is described in terms of a critical distance between epicentre and receiver, beyond which we expect an overall error in phase velocity which does not exceed 0.04 km s−1. A quarter of this error is due to uncertainty in the subepicentral structure. The main classes of focal mechanisms are treated explicitly. For the common classes of shallow‐crustal continental, and crustal oceanic sources, the effect is unimportant. The main, deep‐crustal continental mechanisms require critical distances of 1600–2200 km, with avoidance of a 30‐s period range. The results for the common, shallow‐subcrustal mechanisms show strong effects due to structural uncertainty. For an oceanic source depth of 34 km, one must accept large critical distances of 5100–6900 km if only a 40‐s period range is to be avoided; for the smaller critical distances of 2600–2100 km, the period ranges to be avoided become quite large—up to 100 s in extent. Of the common classes of sources at depths of about 72 km, only vertical dip slip in an oceanic structure gives fairly good results. Other combinations of source class and environment result in critical distances of up to 11000 km, as well as some excessively large period ranges to be avoided. The results for the deeper, vertical dip‐slip mechanisms are better: maximum critical distances of 4600 and 2000 km for source depths of about 150 and 300 km, respectively.

Bias in the estimate of seismic moment tensor by the linear inversion method

“…Neither source depth nor the geometric property of the moment tensor is biased by the differences in these earth models. This is consistent with previous results from focal depth and focal mechanism studies based on amplitude (Tsai & Aki 1970;Mendiguren 1971) and from s t d i e s based on initial phase delay (Weidner 1972;Frez & Schwab 1976). It is noteworthy that the seismic moment obtained in Table 15 is reduced by a factor of 2.…”

Source and Propagation Effects of Rayleigh Waves from Central Asian Earthquakes

“…Neither source depth nor the geometric property of the moment tensor is biased ,by the differences in these earth models. This is consistent with previous results from focal depth and focal mechanism studies based on amplitude (Tsai and Aki, 1970;Mendiguren, 1971) and from studies based on initial phase delay (Weidner, 1972;Frez and Schwab, 1976). It is noteworthy that the seismic moment obtained in Table 3-3.4 is reduced by a factor of two.…”

Source mechanisms and focal depths of East African earthquakes using Rayleigh-wave inversion and body-wave modelling

“…Several authors have concluded that variations in the assumed source model do not seriously affect the theoretical Rayleigh radiation pattern (Weidner 1972;Patton 1978). In a theoretical study of the dependence of Rayleigh phase on source structure, Frez & Schwab (1976) showed that the effects of uncertainties in the source model were in general unimportant for shallow crustal sources. They further suggested that the presence of a pronounced amplitude minimum at a given period over many stations of a dataset could indicate the presence of a significant error in phase propagation time due to incomplete knowledge of the source structure.…”