Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements
Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements
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DOI：
10.1111/j.1365-246x.2011.04970.x
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发表时间：
2011-05-01
影响因子：
2.8
通讯作者：
Tromp, Jeroen
中科院分区：
文献类型：
--
作者：
Bozdag, Ebru;Trampert, Jeannot;Tromp, Jeroen
P>地震层析成像的分辨率密切取决于数据覆盖范围，地震图的不同部分对地球结构的不同部分敏感。在经典地震层析成像中，由于波动方程的近似，可用数据量通常受到限制。波传播的 3D 数值模拟通过选择直接控制 Frechet 导数的适当失配函数，为增加地震图中的可用数据量提供了新的机会。我们基于观测地震图和合成地震图之间的瞬时相位差和包络比，提出了用于全波形断层扫描的新失配函数。目的是从单个地震图中提取尽可能多的信息。利用希尔伯特变换的特性，我们在时域中分离相位和幅度信息。为了深入了解所选错配函数的优点和缺点，我们基于互相关走时、幅度和波形差异，对相应的有限频率伴随灵敏度核与常用错配函数的核进行定性比较。我们的失配函数的主要优点是：（1）在希尔伯特域中工作减少了由于相位和幅度信息的相互作用而导致的波形非线性行为，以及（2）我们用无噪声合成地震图表明可以使用完整的地震图而不会丢失低幅度相位的信息。作为瞬时相位测量的补充，包络测量提供了一种使用波形幅度信息的方法，该方法也可以轻松扩展以约束滞弹性。核的特性使我们能够通过分离弹性反演和非弹性反演来简化层析成像问题。第一个迹象是，内核在存在噪声的情况下仍表现良好。
P>Resolution in seismic tomography intimately depends on data coverage, with different parts of seismograms sensitive to different parts of Earth's structure. In classical seismic tomography, the usable amount of data is often restricted because of approximations to the wave equation. 3-D numerical simulations of wave propagation provide new opportunities for increasing the amount of usable data in seismograms by choosing appropriate misfit functions which have direct control on Frechet derivatives. We propose new misfit functions for full waveform tomography based on instantaneous phase differences and envelope ratios between observed and synthetic seismograms. The aim is to extract as much information as possible from a single seismogram. Using the properties of the Hilbert transform, we separate phase and amplitude information in the time domain. To gain insight in the advantages and disadvantages of chosen misfit functions, we make qualitative comparisons of the corresponding finite-frequency adjoint sensitivity kernels with those from commonly used misfit functions based on cross-correlation traveltime, amplitude and waveform differences. The major advantages of our misfit functions are: (1) working in the Hilbert domain reduces non-linear behaviour of waveforms due to interaction of phase and amplitude information, and (2) we show with noise-free synthetic seismograms that it is possible to use a complete seismogram without losing information from low-amplitude phases. Complementary to instantaneous phase measurements, envelope measurements provide a way of using amplitude information of waveforms, which may also easily be extended to constrain anelastic properties. The properties of the kernels allow us to simplify the tomography problem by separating elastic and anelastic inversions. First indications are that the kernels remain well behaved in the presence of noise.