Absorption Compensation Based On Curvelet Transform

Due to the affection of Wavefront divergence and formation absorption, Source waveletenergy attenuation, phase distortion, and bandwidth narrowing when seismic signal propagatein viscoelastic media, cause deep reflection seismic wave reduced resolution, thereby makingit difficult to track the reflected wave in-phase axis, unable to accurately recognize the deepstructure and trap characteristics, is not conducive to the subsequent processing andinterpretation work. Thus, compensation is essential to the formation due to absorption ofseismic wave attenuation.Existing stratigraphic absorption compensation method are two categories: one is theformation absorption compensation method based on strike the quality factor, the methodrequires the calculation of the quality factor Q in the time domain or frequency domain,most of the Q value extraction methods are dependent on the ratio of deep spectrum andshallow spectrum，should estimate seismic wavelet before calculation. In noise-free synthetictheoretical data, wavelet is time-invariant, the Q value can be extracted to compare with thetheoretical value. Due to the formation of viscoelastic absorption the wavelet of actual seismicdata is change by time, the extracted Q value does not necessarily correspond to the realsituation of formation absorption, which limits the application of the anti-Q filtering. Theother is the formation absorption compensation method based on time-frequency analysis,such methods do not need to strike a Q value, can compensate by point, adapt to the constantQ and variable Q. But such methods have certain requirements on the signal-to-noise ratio, ineffective compensation signal attenuation at the same time is also correspondingly increasethe energy of the noise and random interference.We propose the strata absorption compensation method based on Curvelet transform onaccount of some problems for the the existing formations absorption compensation method.Curvelet transform is a new multi-scale geometric analysis methods。The sparsity of Curvelettransform can make it accurately describe the seismic signal with the least coefficient and lessrestricted by signal-to-noise ratio, the directivity makes Curvelet transform can represent theedges of the image more sparse,and have efficient, stable and near-optimal representation forthe smooth singularity curve of objective function. The effective signal and the random noisein Curvelet domain stored separately,we can only extract the effective signal processingwithout corresponding enhancement of the energy of the noise and random interference.The amplitude spectrum of depth layer reflected wave and shallow layer reflected wavewas same when seismic wave propagation in elastic media. We assume that there is no strataabsorption, then the energy distribution relations of the time between seismic records of thedifferent frequency bands have similarity, The energy of all frequency bands of deepreflection should be the same as that of shallow reflection of the same frequency band energyratio, but the absolute energy of the different bands have different sizes.Because of thelow-frequency energy loss less, when the high-frequency record is multiplied by time-varyingfactor,the energy ratio of deep layer would be the same to that with low frequency, playingthe role of the compensation. This method first use Curvelet transform to divide the frequency of seismic data,then use the directional characteristics of Curvelet transform toselect the signal of each frequency band selected angle, extract the weighting factor of eachtime point and reciprocal weighting to make sure that the ratio of deep and shallow energy ofrelative angle signal for each frequency band was same, And then reconstruct the weighteddata.In practice,we can see this method is well compensated by the strata absorption, thereflection waveform of the superficial, mid-deep and Deep layer are basically the same, theresolution of mid-deep significantly is improved, high frequency is enhanced and frequencyband is broaden.This "anisotropy" base can make Curvelet transform near-optimal representation for thesmooth singularity curve of objective function; Application Curvelet Transform directivitycan directional Narrow processing the signal without affecting other signal processing specificto a particular angle position, This provides a new method for high-precision seismic dataprocessing; The effective signal and the random noise in Curvelet domain storedseparately,we can only extract the effective signal processing without correspondingenhancement of the energy of the noise and random interference; The most typicalcharacteristics of absorption compensation based on Curvelet transform is only compensateeffective signal without corresponding enhance noise and random interference.