复数域约束最小二乘拓频

拓频的目的是为了提高地震资料的主频，拓宽频带，进而可以提高描述更小、更薄的地质体的能力。文中首先建立了拓频的正演数学模型，通过宽频约束目标谱，将拓频的正演问题转换为反问题；基于复数域最小二乘方法求解该反问题，进而得到频率域拓频算子；将拓频算子作用于原始地震的频谱，再通过傅里叶反变换，即可实现地震数据的拓频处理。该方法可以在不改变地震数据相位信息的情况下，有效提高信号的主频，拓宽频带，提高地震资料的分辨率，并可通过设定不同的控频因子来调节拓频后地震数据的频谱和约束目标谱之间的距离，以得到不同分辨率的拓频结果。将该方法应用于济阳坳陷不同层系砂泥岩薄互层和超覆尖灭点的精细识别，取得了显著的应用效果，具有广阔的应用前景。

Constrained complex-domain least-squares spectrum blueing

The purpose of frequency extension is to improve the dominant frequency of seismic data, broaden the frequency band, and thereby better describe smaller and thinner geological bodies. A forward mathematical model is built for spectrum extension, and the forward problem of spectrum extension is transformed into an inverse problem through the broadband constrained target spectrum (CTS). The spectrum extension operator (SEO) in the frequency domain is acquired through solving the inverse problem by the complex-domain least-squares method. Spectrum extension of seismic data is achieved by applying SEO to the frequency spectrum of the original seismic data and the inverse Fourier transform. This method can effectively improve the dominant frequency, broaden the frequency band, and improve the resolution of seismic data without changing the phase spectrum of the data. The distance between the frequency spectrum after frequency extension and the CTS can be adjusted by setting different spectrum control factors to obtain spectrum extension results with different resolutions. This method has been applied to the fine identification of thin layers and overlap pinch-outs in the Jiyang Depression,and has a broad application prospect.