We have developed a true amplitude solution to the seismic imaging problem. We derive a diagonal scaling approach for the normal operator approximation in the curvelet domain. This is based on the theorem that states that curvelets remain approximately invariant under the action of the normal operator. We use curvelets as essential tools for approximation and inversion. We also exploit the theorem that states that the curvelet-domain approximation should be smooth in phase space by enforcing the smoothness of curvelet coefficients in the angle and space domains. We analyze our method using a reverse time migration-demigration code, simulating the acoustic wave equation on different synthetic models. Our method produces a good resolution with reflecting dips, reproduces the true amplitude reflectors, and compensates for incomplete illumination in seismic images.

中文翻译：

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使用曲波进行真振幅深度偏移

我们已经为地震成像问题开发了一个真正的振幅解决方案。我们为曲线波域中的法线算子近似推导出对角线缩放方法。这是基于定理，即曲波在正常算子的作用下保持近似不变。我们使用曲线波作为逼近和反演的基本工具。我们还通过在角度域和空间域中强制曲线波系数的平滑性来利用该定理，即曲线域近似在相空间中应该是平滑的。我们使用逆时偏移-去偏移代码分析我们的方法，在不同的合成模型上模拟声波方程。我们的方法通过反射倾角产生良好的分辨率，再现真实振幅反射器，