不依赖源子波的跨孔雷达时间域波形反演

波形反演是近年来较热门的反演方法,其分辨率可以达到亚波长级别.在波形反演的实际应用中,源子波的估计十分重要.传统方法使用反褶积来估计源子波并随着反演过程更新,该方法在合成数据波形反演中效果较好,但在实际数据反演过程中存在一系列的问题.由于实际数据信噪比较低,在源子波估计过程中需要大量的人为干涉,且结果并不一定可靠.本文使用一种基于褶积波场的新型目标函数,令反演过程不再依赖源子波.详细推导了针对跨孔雷达波形反演的梯度及步长公式,实现介电常数和电导率的同步反演.针对一个合成数据模型同时反演介电常数和电导率,结果表明该方法能够反演出亚波长尺寸异常体的形状和位置.接着,将该方法应用到两组实际数据中,并与基于估计源子波的时间域波形反演结果进行比较.结果表明不依赖源子波的时间域波形反演结果分辨率更高,也更准确.

Source-independent time-domain waveform inversion of cross-hole GPR data

As a highly efficient near-surface geophysical technology, cross-hole GPR can provide high-resolution images between two boreholes. Waveform inversion, of which the resolution reaches sub-wavelength, can reconstruct accurate subsurface dielectric parameters such as permittivity and conductivity. We can get accurate and high-resolution subsurface dielectric information by combining waveform inversion and cross-hole GPR data. In the waveform inversion of field data, the source wavelet is unknown. Normally, the source wavelet can be estimated by using a deconvolution method. In this method, the source wavelet is a new unknown parameter added in the inversion and updated with iteration. When the results of inversion are same as the true models, the estimated source wavelet is same as the true source wavelet. This method is useful in the inversion of synthetic data, but it does not perform well in the field data. Lots of intervention are needed to choose the best source wavelet after the estimation. The reason may be that the subsurface medium of field data is highly complex and the signal-to-noise ratio of the field data is low.#br#In this paper, we realize a source-independent time-domain waveform inversion. Firstly, the observed wavefields are convolved with a reference trace of the modeled wavefield, then the modeled wavefields are convolved with a reference trace of observed wavefield. A new object function is based on the convolved wavefields. In theory, no matter which source wavelet is used in the forward modeling. The source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the object function, so that the effect of the source wavelet is removed. Another important feature of this object function is that the modeled wavefields act as a low-pass filter of the wavefield based on the frequency range of the source used for modeling. Though it is very easy to employ a frequency-selection strategy, we don't discuss the strategy here. For each shot gather, we always choose the trace which is nearest to the antenna as the reference trace in this study.#br#To check the effect of our algorithm, we simulate three different synthetic data:1) Single cylindrical body of permittivity. 2) Single cylindrical body of conductivity. And 3) layered media with multiple embedded cylindrical inclusions of permittivity and conductivity. Finally, we apply the source-independent waveform inversion to the field data of Guizhou and Xiuyan.#br#The first two results of synthetic data show that our algorithm can provide high-resolution images. When permittivity and conductivity are simultaneously updated, the results of synthetic data are good. The layers are well reconstructed and the two pipes can be clearly distinguished. But there are many false features which are caused by the artifacts of sources. We have to do convolution and crosscorrelation to compute the gradients. These convolution and crosscorrelation operations increase the nonlinearity of the inversion. The artifacts of the sources become stronger after the convolution and crosscorrelation is hard to remove when the complex models are of a small scale. Then we apply the source-independent waveform inversion to the field data of Guizhou and Xiuyan. The signal-to-noise ratio of Guizhou field data is high, so both the source-independent and source-estimated waveform inversion can obtain accurate results. We think the results of source-independent waveform inversion are better. The reason may be the difference between the estimated source wavelet and the true source wavelet, though they are very similar. However, it is difficult to get the ideal estimated source wavelet of Xiuyan field data because its signal-to-noise ratio is low. So the results of the Xiuyan field data can better reflect the value of our source-independent waveform inversion.