A frequency-approximated approach to Kirchhoff migration
A frequency-approximated approach to Kirchhoff migration
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DOI：
10.1190/1.3491196
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发表时间：
2010-10
期刊：
影响因子：
3.3
通讯作者：
M. Vardy;T. Henstock
中科院分区：
文献类型：
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作者：
M. Vardy;T. Henstock
波动方程的积分解长期以来一直是基尔霍夫偏移成像和基尔霍夫反演地震数据反演最流行的方法之一。为了提高效率，此过程通常被表述为对每条迹线进行时域操作，通过算子的高切滤波或迁移前/迁移后倾角滤波来应用抗锯齿。然而，时域中的偏移不允许速度色散；标准抗锯齿方法假设反射器是平坦的，并且往往会过度过滤数据。我们在频域中重新构建了基尔霍夫积分，通过每个频率的适当倾角限制和真实色散的隐式调节来实现鲁棒的混叠滤波。输入地震图的全频率分解可以通过带通滤波或与线性调频/可控震源数据的带限源扫描相关来近似为一些窄带轨迹， 累积保留全部源带宽。根据源波形的先验知识，我们定义了合适的带宽，仅使用六个频带来描述宽带 3.0 倍频程数据。使用在其中心频率处确定的系数对这些窄带迹线进行基尔霍夫偏移，与传统时域抗锯齿方法相比，显着改善了较高频率的保留并消除了陡峭的混叠能量。但是，如果双频带频谱不再是稳健的方法，则我们的频率近似方法 为处理器提供对频率抽取的最终控制，平衡更多频段提供的更高分辨率与计算成本，而频段数量足够少，可以对频率相关的抗混叠滤波参数进行详细控制。
The integral solution of the wave equation has long been one of the most popular methods for imaging Kirchhoff migration and inverting Kirchhoff inversion seismic data. For efficiency, thisprocessiscommonlyformulatedasatime-domainoperation on each trace, applying antialiasing through high-cut filtering of the operator or pre-/postmigration dip filtering. Migration in the time domain, however, does not allow for velocity dispersion; standard antialiasing methods assume a flat reflector and tend to overfilter the data. We have recast the Kirchhoff integral in the frequencydomain,enablingrobustantialiasfilteringthroughappropriate dip limiting of each frequency and implicit accommodationoftruedispersion.Fullfrequencydecompositionoftheinput seismogram can be approximated by band-pass filtering or correlationwithband-limitedsourcesweepsforChirp/Vibroseis data into a few narrow-band traces that cumulatively retain the full source bandwidth. From prior knowledge of the source waveform, we have defined suitable bandwidths to describe broadband 3.0 octaves data using just six frequency bands. Kirchhoff migration of these narrow-band traces using coefficients determined at their central frequencies significantly improvesthepreservationofhigherfrequenciesandcancellationof steeplydippingaliasedenergyovertraditionaltime-domainantialiasingmethods.If,however,twobandsperoctaveceasetobea robust approach, our frequency-approximated approach providestheprocessorwithultimatecontroloverthefrequencydecimation, balancing increased resolution afforded by more bands against computing cost, whereas the number of frequency bands is few enough to permit detailed control over frequency-dependentantialiasfilteringparameters.