Scattering of elastic waves causes velocity dispersion, which increases uncertainty in seismic analysis. Understanding the sources of scattering and the degree of velocity dispersion are critical to improve subsurface imaging in efforts to locate resources and study subsurface processes. In addition to scattering, other mechanisms, such as the wave-induced fluid flow in saturated rocks cause velocity dispersion. To study the effect of scattering on velocity dispersion, we conducted laboratory measurements of ultrasonic velocities on dry rock samples and performed wave-propagation simulations on CT-scanned 3D volumes of those samples. The set of samples consists of homogeneous and heterogeneous carbonate rocks with porosities between 3% and 26%. Ultrasonic velocities were measured at frequencies between 0.3 and 1 MHz, and numerical wave propagation simulations on the digital volumes were performed using an elastic approximation and a finite-difference method. The homogeneous sample and the corresponding numerical simulations exhibit negligible velocity dispersion. On the other hand, heterogeneous samples exhibit significant dispersion, and the corresponding numerical simulations accurately reproduce the observed dispersion in terms of magnitude and frequency shift. We conclude that scattering has a first-order effect on the velocities of the elastic waves in heterogeneous samples. This effect should be considered in conjunction with laboratory measurements in heterogeneous carbonates similar to those studied here. Furthermore, we illustrate a method to characterize frequency-dependent ultrasonic velocities (i.e., dispersion) and show that finite-difference modeling can reproduce the laboratory-observed dispersion.

中文翻译：

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散射和频率对碳酸盐岩超声速度的影响


弹性波的散射会导致速度分散，这增加了地震分析的不确定性。了解散射源和速度色散的程度对于在定位资源和研究地下过程时改进地下成像至关重要。除了散射之外，其他机制（例如饱和岩石中的波诱导流体流动）也会导致速度分散。为了研究散射对速度色散的影响，我们对干岩石样品的超声速度进行了实验室测量，并对这些样品的 CT 扫描 3D 体积进行了波传播模拟。该样品组由孔隙度在 3% 至 26% 之间的均质和非均质碳酸盐岩组成。在 0.3 到 1 MHz 的频率下测量超声速度，并使用弹性近似和有限差分方法对数字体积进行数值波传播模拟。均匀样品和相应的数值模拟表现出可忽略不计的速度色散。另一方面，非均质样品表现出明显的色散，相应的数值模拟在幅度和频移方面准确地再现了观察到的色散。我们得出结论，散射对异质样品中弹性波的速度具有一阶效应。这种影响应与异质碳酸盐的实验室测量一起考虑，类似于此处研究的那些。此外，我们说明了一种表征频率相关超声速度（即色散）的方法，并表明有限差分建模可以再现实验室观察到的色散。