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反演是搜索参数的值以使目标函数(本文中称为处理算子)取这些值时达到最大或最小的一个过程。根据这种解释可以推演出三种新的地震处理算子,它们既不需要作前期反褶积也无需知道震源与接收器的子波。三种处理算子中最有效的是四元处理算子,它适用于多炮和多检波器的数据集,即使各炮的未知特征波形不同,各检波器的未知脉冲响应不同也能适应。比四元处理算子稍逊一点的是二元处理算子,它适用于未知子波相同但增益可能不相同的二道或者多道数据集。当只有一个地震记录存在时,我们可以使用分离处理算子,分离处理器还可用于只有一个震源(检波器)且每个检波器(震源)具有不同的特征波形的场合。在四元和二元处理算子反演中,未知的子波在时间上可以是任意长的而且不要求是最小相位的,在分离处理算子反演中,子波除假定为在时间上比数据还要短外,没有其它的限制。所有这些方法都没有对Green函数作要求。
Inversion is the process of finding the parameters to maximize or minimize the value of an objective function (referred to herein as a processing operator) taking these values. Based on this interpretation, three new seismological operators can be deduced, which do not require pre-deconvolution or knowledge of the source and receiver wavelets. The most effective of the three processing operators is the quaternion operator, which is suitable for multi-gun and multi-detector datasets. Even if the unknown characteristic waveforms of the guns are different, the unknown impulse response of each detector can also be adapted. Slightly inferior to the quaternary operators is the binary operator, which applies to two or more datasets of the same but unknown gain. When only one seismic record is present, we can use the separation operator, and the separation processor can also be used where there is only one source (detector) and each detector (source) has a different characteristic waveform. In the quaternion and binary processing operator inversion, the unknown wavelet can be arbitrarily long in time and does not require to be the minimum phase. In the separation processing operator inversion, the wavelet addition is assumed to be in time ratio The data is short, with no other restrictions. None of these methods require a Green function.