Effect of source spectrum on seismic attenuation measurements using the pulse‐broadening method

Abstract

Numerical examples of one‐dimensional (1-D) wave propagation, using realistic source time functions in an anelastic material characterized by frequency‐independent internal friction, demonstrate that (a) the source time function strongly influences the dependencies of initial rise time τ and pulse width w on internal friction [Formula: see text] and distance x; (b) in general, τ and w have different functional dependencies on [Formula: see text] and x; and (c) the slope ∂τ/∂x for particle displacement computed for a band‐limited source time function can be either greater than or less than the corresponding value computed for a delta‐function displacement source time function. Result (a) corroborates the result for τ given by Blair and Spathis, which implies that the commonly used linear rise time and distance relation, [Formula: see text], where T is the traveltime and C a source‐independent constant, is an oversimplification of 1-D anelastic wave propagation; the source spectrum must be considered when inferring seismic attenuation from changes in rise time. Result (c) contradicts the assertion by Blair and Spathis that ∂τ/∂x of wave trains generated by a band‐limited source time function is always less than the corresponding value generated by a delta‐function source time function. By matching first arrival times and rise times obtained by modeling 1-D wave propagation in an anelastic medium to those obtained in the field, seismic attenuation can be determined.

Size and geometry of microearthquake seismic ruptures fromPandSpulse width data

“…One may think that the source parameters inferred in this study are strictly dependent on the assumptions inherent to the adopted source model (i.e. Then, by considering the inelasticity of rocks, other than the source contribution to the pulse width, one must account for the attenuation term, given by Ct/Q, where C is dependent on the source time function, as shown in several papers (Liu 1988;de Lorenzo 1998). As we will try to show, the obtained results are slightly more general and inherent to the basic assumptions of kinematics of the seismic source.…”

Source and Qp parameters from pulse width inversion of microearthquake data in southeastern Sicily, Italy

“…The value of C was experimentally determined for ultrasonic acoustic pulses to be 0.5 [ Gladwin and Stacey , 1974], whereas a theoretical demonstration, based on an impulsive displacement source, was given by Kjartansson [1979]. Further studies [ Blair and Spathis , 1982; Liu , 1988; Wu and Lees , 1996] have shown that C depends on the shape of the source time function. A C value of 0.5, corresponding to an impulsive displacement function, is commonly used.…”

Source parameters and three‐dimensional attenuation structure from the inversion of microearthquake pulse width data: Method and synthetic tests

“…This is performed by assuming the circular crack model proposed by Sato and Hirasawa [1973]. With respect to other time domain modeling techniques [Liu, 1988;Wu and Lees, 1996;de Lorenzo, 1998] the equations we derived, constitute other theoretical evidence for nonlinearity among rise times and travel times, and are also able to account for the directivity of the seismic source. In this paper the explicit dependence of the slope of 'c versus t* on the frequency content at source through the function •P0, c, 0) has been obtained by considering the SH circular crack model.…”

“…The controversy about the applicability of the rise time method to signals generated by sources characterized by a finite frequency content is well documented in literature [Blair and Spathis, 1982;Liu, 1988;Zucca et al, 1994;Wu and Lees, 1996]. Zucca et al [ 1994] applied the rise time method to study the attenuation properties of the Geysers geothermal field.…”