A varying Q factor with depth induces modifications of seismic wave features due to anelastic propagation but also reflections at the discontinuities. Standard signal analysis methods often neglect the reflection contribution when assessing Q values from seismic data. We have developed an analytical quantification of the cumulative effects of both the propagation and reflection contributions by considering Kjartansson's model and a seismic plane wave at normal incidence on a step-like discontinuity. We show that the cumulative effects are equivalent to a frequency filter characterised by a bandform and phase that both depend on the ratio between the elastic and anelastic contrasts. When considering this filter applied to a Ricker wavelet, we establish an analytical expression of the peak-frequency attribute as a function of propagation and reflection properties. We demonstrate that this seismic attribute depends on the anelastic contrast, which cannot be neglected when assessing Q factors: the error in Q estimate is not linearly dependent on the anelastic contrast and we establish an analytical expression for the case where this contrast is weak. An unexpected phenomenon for a step-like interface is an increase in the peak frequency that is observed when the anelastic and elastic contrasts have opposite signs, with a constraint on the anelastic propagation properties. This behaviour allows for assessment of the elastic and anelastic parameters.

中文翻译：

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非弹性地震波传播和反射引起的瑞克小波滤波

随深度变化的Q因子会由于非弹性传播以及不连续点处的反射而引起地震波特征的变化。当从地震数据评估Q值时，标准信号分析方法通常会忽略反射贡献。通过考虑Kjartansson模型和法向入射的阶梯状不连续面上的地震平面波，我们已经对传播和反射贡献的累积效应进行了分析量化。我们表明，累积效应等效于以频带和相位为特征的频率滤波器，这两者都取决于弹性和非弹性对比之间的比率。当考虑将此滤波器应用于Ricker小波时，我们建立了峰值频率属性作为传播和反射特性的函数的解析表达式。我们证明了这种地震属性取决于非弹性对比，在评估Q因子时不可忽略：Q估计的误差并不线性地取决于非弹性对比，并且针对这种对比较弱的情况建立了解析表达式。对于阶梯状界面的未预料到的现象是，当非弹性和弹性对比具有相反的符号时，观察到峰值频率增加，从而限制了非弹性传播特性。此行为允许评估弹性和非弹性参数。在评估Q因子时不能忽略这一点：Q估计中的误差并不线性地取决于非弹性对比，对于这种对比较弱的情况，我们建立了一个解析表达式。对于阶梯状界面的意外现象是当非弹性和弹性对比具有相反的符号时观察到的峰值频率增加，从而限制了非弹性传播特性。此行为允许评估弹性和非弹性参数。这在评估Q因子时不能忽略：Q估计的误差并不线性地取决于非弹性对比，我们针对这种对比较弱的情况建立了一个解析表达式。对于阶梯状界面的意外现象是当非弹性和弹性对比度具有相反的符号时观察到的峰值频率增加，从而限制了非弹性传播特性。此行为允许评估弹性和非弹性参数。限制了弹性传播特性。此行为允许评估弹性和非弹性参数。限制了弹性传播特性。此行为允许评估弹性和非弹性参数。