We develop a method to estimate relative seismic moments M₀ and corner frequencies f_c of acoustic emission events recorded in laboratory experiments from amplitude spectra of signal's coda composed of reverberated and scattered waves. This approach has several advantages with respect to estimations from direct waves that are often clipped and also are difficult to separate in experiments performed on small samples. Also, inversion of the coda spectra does not require information about the source locations and mechanisms. We use the developed method to analyze the data of two experiments: (a) on granite from the Voronezh crystal massif and (b) on Berea sandstone. The range of absolute corner frequencies estimated in both experiments is around 70 − −700 kHz. The range of relative seismic moments covers 10^3.5. The relation between f_c and M₀ observed on the first stages of both experiments, consisted of increasing isotropic confining pressure, approximately follow $M_0\sim f_c^{-3}$ scaling and the b-value of the Gutenberg-Richter distribution was found close to 1. This can be interpreted as rupturing of preexisting material defects with a nearly constant stress-drop and has a similarity with observations of “natural” earthquakes. Deviations from this “earthquake-like” behavior observed after applying axial loading and initiation of sample damaging can be interpreted as changes in stress-drop. Lower stress-drops prevail for sandstone and higher for granite sample respectively that can be related to the strength of corresponding material.

中文翻译：

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根据波形尾估计的实验室声发射事件的源参数

我们开发了一种方法，根据由混响波和散射波组成的信号尾波的幅度谱来估计实验室实验中记录的声发射事件的相对地震矩M ₀和角频率f _c 。这种方法相对于直接波的估计有几个优点，直接波经常被削波，并且在小样本上进行的实验中也很难分离。此外，尾波谱的反演不需要有关源位置和机制的信息。我们使用开发的方法来分析两个实验的数据：（a）沃罗涅日晶体地块的花岗岩和（b）伯里亚砂岩。两个实验中估计的绝对角频率范围约为 70 − −700 kHz。相对地震矩范围为10 ^3.5。在两个实验的第一阶段观察到的f _c和M ₀之间的关系，包括增加各向同性围压，大约如下${\mathrm{中号}}_0～F_C^{-3}$发现古腾堡-里希特分布的缩放比例和b 值接近 1。这可以解释为预先存在的材料缺陷在几乎恒定的应力降下破裂，并且与“自然”地震的观测结果相似。在施加轴向载荷和样品损坏开始后观察到的这种“类似地震”行为的偏差可以解释为应力降的变化。砂岩样品的应力降较低，花岗岩样品的应力降较高，这可能与相应材料的强度有关。