Hydrocarbon source rocks can be adequately approximated as transversely isotropic (TI) media. The elastic properties of a TI medium are defined by five stiffness parameters: $c_{11}$, $c_{33}$, $c_{44}$, $c_{66}$, and $c_{13}$. The laboratory estimation of $c_{11}$, $c_{33}$, $c_{44}$, and $c_{66}$ is straightforward, with each of the stiffness parameters determined by a single velocity measurement in an orthogonal direction. For $c_{13}$, we need the information of $c_{11}$, $c_{33}$, $c_{44}$, and at least one oblique velocity. Consequently, it is usually more difficult to estimate $c_{13}$ than the other stiffness parameters in the laboratory, and it is even more challenging to acquire it from the field. Therefore, it is important to find the relations between $c_{13}$ and the other stiffness parameters so that $c_{13}$ can be estimated from the orthogonal elastic tensor elements $c_{11}$, $c_{33}$, $c_{44}$, and $c_{66}$ that can be much more economically and reliably acquired. There are phenomenological models for estimating $c_{13}$ from the other stiffness parameters, but their accuracy is not always satisfactory. We find that $c_{13}$ has strong correlations with $c_{33}-2c_{44}$ and $c_{11}-2c_{66}$, and that $c_{33}-2c_{44}$ generally underestimates $c_{13}$ and $c_{11}-2c_{66}$ generally overestimates $c_{13}$. The average of $c_{33}-2c_{44}$ and $c_{11}-2c_{66}$ can be a much more precise phenomenological model to approximate $c_{13}$. We also find that $c_{11}-2c_{66}$ is generally greater than $c_{33}-2c_{44}$ for hydrocarbon source rocks. Therefore, we determine that $c_{13}$ should lie between $c_{33}-2c_{44}$ and $c_{11}-2c_{66}$ for hydrocarbon source rocks.

中文翻译：

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横向各向同性烃源岩 c13 估计和约束的唯象模型

烃源岩可以充分近似为横向各向同性 (TI) 介质。TI 介质的弹性特性由五个刚度参数定义：$C_{11}$, $C_{33}$, $C_{44}$, $C_{66}$， 和 $C_{13}$. 实验室估计$C_{11}$, $C_{33}$, $C_{44}$， 和 $C_{66}$很简单，每个刚度参数都由正交方向上的单个速度测量确定。为了$C_{13}$，我们需要的信息 $C_{11}$, $C_{33}$, $C_{44}$，以及至少一个斜速度。因此，通常更难以估计$C_{13}$与实验室中的其他刚度参数相比，从现场获取它更具挑战性。因此，找到它们之间的关系很重要$C_{13}$ 和其他刚度参数，以便 $C_{13}$ 可以从正交弹性张量元素估计 $C_{11}$, $C_{33}$, $C_{44}$， 和 $C_{66}$可以更经济、更可靠地获得。存在用于估计的现象学模型$C_{13}$从其他刚度参数来看，但它们的准确性并不总是令人满意。我们发现$C_{13}$ 有很强的相关性 $C_{33}-2C_{44}$ 和 $C_{11}-2C_{66}$， 然后 $C_{33}-2C_{44}$ 普遍低估 $C_{13}$ 和 $C_{11}-2C_{66}$ 通常高估 $C_{13}$. 的平均值$C_{33}-2C_{44}$ 和 $C_{11}-2C_{66}$ 可以是一个更精确的现象学模型来近似 $C_{13}$. 我们还发现$C_{11}-2C_{66}$ 一般大于 $C_{33}-2C_{44}$为烃源岩。因此，我们确定$C_{13}$ 应该介于 $C_{33}-2C_{44}$ 和 $C_{11}-2C_{66}$ 为烃源岩。