The reflection response of strongly scattering media often contains complicated interferences between primaries and (internal) multiples, which can lead to imaging artifacts unless handled correctly. Internal multiples can be kinematically predicted, for example by the Jakubowicz method or by the inverse scattering series (ISS), as long as monotonicity, that is, “correct” temporal event ordering, is obeyed. Alternatively, the (conventional) Marchenko method removes all overburden-related wavefield interactions by formulating an inverse problem that can be solved if the Green’s and the so-called focusing functions are separable in the time domain, except for an overlap that must be predicted. For acoustic waves, the assumptions of the aforementioned methods are often satisfied within the recording regimes used for seismic imaging. However, elastic media support wave propagation via coupled modes that travel with distinct velocities. Compared to the acoustic case, not only does the multiple issue become significantly more severe, but also violation of monotonicity becomes much more likely. By quantifying the assumptions of the conventional Marchenko method and the ISS, unexpected similarities as well as differences between the requirements of the two methods come to light. Our analysis demonstrates that the conventional Marchenko method relies on a weaker form of monotonicity. However, this advantage must be compensated by providing more prior information, which in the elastic case is an outstanding challenge. Rewriting, or remixing, the conventional Marchenko scheme removes the need for prior information but leads to a stricter monotonicity condition, which is now almost as strict as for the ISS. Finally, we introduce two strategies on how the remixed Marchenko solutions can be used for imperfect, but achievable, demultiple purposes.

中文翻译：

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逆散射序列和Marchenko弹性波解乘方法遇到的单调性挑战的比较

强散射介质的反射响应通常在原色和（内部）倍数之间包含复杂的干涉，除非正确处理，否则可能导致成像伪影。只要遵守单调性，即“正确的”时间事件顺序，就可以通过运动学例如通过雅库博维奇（Jakubowicz）方法或逆散射序列（ISS）来预测内部倍数。或者，（常规）马尔琴科方法通过制定一个反问题来消除所有与上覆层有关的波场相互作用，如果格林和所谓的聚焦函数在时域中是可分离的，则可以解决该反问题，但必须预测到有重叠。对于声波，通常在用于地震成像的记录范围内满足上述方法的假设。然而，弹性介质通过以不同速度传播的耦合模式来支持波传播。与声学情况相比，不仅多重问题变得更加严重，而且违反单调性的可能性也更大。通过量化常规Marchenko方法和ISS的假设，可以发现这两种方法的意想不到的相似之处和差异。我们的分析表明，传统的Marchenko方法依赖于较弱形式的单调性。但是，必须通过提供更多的先验信息来补偿此优势，这在弹性情况下是一项严峻的挑战。对传统的Marchenko方案进行重写或重新混合，不再需要先验信息，但会导致更严格的单调性条件，现在几乎与国际空间站一样严格。最后，我们介绍了两种策略，说明如何将重新混合的Marchenko解决方案用于不完美但可实现的多倍目的。