A Study On Low-Frequency Compensation Based On Compressed Sensing And Sparse Inversion

With mining for oil and gas continuously, people gradually transfer the point ofexploration to the deep part of land and sea. Low exploration precision has not meetthe requirements of the reality. High resolution seismic exploration technology isawaited development, high resolution seismic data processing technology and makefull use of collected seismic information can effectively achieve the goal ofhigh-resolution exploration. Around this theme, this paper proposes a low frequencycompensation method based on compressed sensing and sparse inversion.Full waveform inversion is make full use of seismic record contains all theinformation for underground imaging method. This imaging technology can obtainhigh accuracy in underground medium model figure, this is what we need. Since fullwaveform inversion comes out many scholars research it, they make the limitation inapplication less and less, make the calculation speed faster and faster. But thetechnology depend on initial model, under the condition of no good initial modelneeds to be relatively abundant low frequency information. Low frequencycompensation technology will be helpful to the practical application of the fullwaveform inversion.Proposed method is based on compressed sensing theory, this is a signalreconstruction theory that only appeared in recent years. Compressed sensing is usingthe sparse property of signal through the nonlinear to reconstruct single perfectly.Assume that reflection coefficient in seismic exploration is sparse, the frequencydomain of the reflection coefficient as the target signal, then using frequency domainconvolution relation between signal reconstruction. Such reconstruction signals, lowfrequency and high frequency parts can be compensated. Observation matrix in thismethod is a seismic wavelet frequency domain, which is not completely random, sowe can’t fully recover all the band.Based on compressed sensing frequency compensation method can effectivelyextend bandwidth, achieve the purpose of improving resolution. The seismic recordsinversion use the same frequency and phase wavelet, which can improve the main energy frequency part. All frequency compensation data lose some small energy. Inorder to improve the fidelity, this paper puts forward modified method in therectangular window, namely in frequency compensation within the rectangle window.Choosing the window size can also achieve the goal of denoising.Full waveform inversion need abundant low frequency information, so basedadded window sparse inversion frequency compensation method of low frequencycompensation method is put forward. The compensated low frequency spectrumcomes from combining the low frequency spectrum of compensation and the originalspectrum, the low frequency compensation through inverse discrete Fouriertransformation gets low frequency compensation of seismic records, this is retainedthe original information and includes compensation information. Throughout thewaveform inversion has obvious effect, the inversion results horizon of detailedcharacterization, speed curve is close to the original situation.The frequency and low frequency compensation method based on compressedsensing and sparse inversion can achieve the desired effect. The wavelet of allfrequency compensation data is compressed, the resolution is improved significantly.By choosing different parameters, this method can effectively suppress noise. Lowfrequency compensation correct the phase of data, result of the full waveforminversion is very well. The study of low frequency compensation method has juststarted, the theory and algorithm are awaited further improved.