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

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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.

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