The Preliminary Study Of Basic Theory Of The Trace Transform And Its Application In Seismic Exploration

Seismic records contain the underground structure and lithology, but these information are superimposed in the background interference, so using seismic data to explain the geological is difficulty. Hence the field of seismic data needs digital processing for geological interpretation of seismic data more reliable, more accurate.According to the interference of characteristic in the seismic record, the noise of seismic exploration can be divided into the coherent noise and random noise. Coherent noise has certain frequency noise and visual speed. Yet, coherent noise has appeared on the laws in time, and has obviously the cinematic characteristics。Coherent noise and the effective wave have difference in frequency and visual speed. So it can be eliminated by filter and the characteristic of direction. The commonly used method to eliminate coherent noise has F - kfilter, t - kfilter, f - xfilter,Ï„-ptransform and so on. The random noise is no fixed random noise in the frequency and the transmit direction. It random emergence in the seismic record and it has a wide frequency. It has not yet a certain visual speed. So it would be difficult to eliminate by the difference between the effectively wave and it in the frequency or the transmit direction. At this time, we need to transform denoiseing ideas; we do not deal with noise, but according to the relevance of effective signal through multi-channel fitting to eliminate noise. Commonly used methods to eliminate random noise have f ? xdomain prediction filtering, polynomial fitting, K ? Ltransform, singular value decomposition (SVD) etc.Surface wave is a common coherent noise in seismic exploration. Its time-distance curve is a straight line. Radon transform is very effective in the elimination of surface wave and it has become an important technology to eliminate surface wave in oil and gas exploration。Radon transform not only in the elimination of surface wave is a very good application, but also it have good application in the elimination of other linear interference, wave field separation, velocity analysis, spatial interpolation, and other aspects. In recent years, the trace transform was advanced; it is the general form of Radon transform. Radon transform has been widely applied in seismic exploration. So the Trace transformation should be able to apply in the seismic exploration, in particular in the area to eliminate surface wave. This paper seeks to the Trace transform into seismic exploration, and from both theory and simulation analysis.1.Theoretical analysisThe Trace transform calculates a functionalT , over parameter t along line (ρ,p). Thus, one computes a number for each line defined by parameters(ρ,p). Plotting these numbers in a Cartesian coordinate system (ρ,p) constitutes the trace transform of the image. The Trace transform is only similar to the Radon transform in the sense that it also calculates functional of the image function along lines criss-crossing its domain. The Radon transform calculates a specific functional, namely, the integral of the image function. The Trace transform is not necessarily the integral of the image function.The functional of Trace transform choices to meet the nature of invariant functional and sensitive functional. Table 1 lists a number of the invariant functional and the nature of their meeting. Table 2 is the structure principles of new functional and their nature. Table 3 lists a number of sensitive functional and their nature. IF1 of Table 1 is the Radon transform that we are familiar. From Table 1 choice IF₂ as the objective formula of this analysis. In order to reflect completely the wavelet's nature, our remove the absolute value of and record as IF₂′. It has been proved that meet the principle of the invariant functional in Trace transform, namely, IF₂′is the Trace transform. From IF₂′starting, our compute the inverse transform formula of IF₂′. Combining t - x domain to theÏ„?pdomain of the coordinate transformation: t =Ï„+px, our compute the inverse transform formula of IF₂′and proving IF₂′that use the coordinate conversion relationship is still Trace Transform. At the same time, our compute the Trace transform and inverse Trace transform in frequency domain. This paper points out the relationship among the Trace transformation, the Radon transformation and theÏ„-p transform. Because using the t - xdomain to the domain of coordinate conversion, then the line in the t - xdomain become a point in theÏ„-p domain, and the hyperbolic in the t - xdomain become parabola in theÏ„-p domain. This is similar to theÏ„-p transformation.2.Simulation AnalysisFirstly, the paper makes a level of seismic event model with 80 traces, and doing the Trace transform and inverse transform to this model. From the theory records and the record-transform choose the 1,20,40,60,80 trace, and then contrast the waveform and amplitude spectrum. From the results discover the amplitude spectrum basic agreement and the waveform basic resumption. The "energy points" in the Trace transform filling zero, and then go back to the theory records. This time, the seismic event disappears. Choosing the 1,20,60,80 traces make contrast to the waveform and amplitude spectra from the theory records and the records of inverse transform that the"energy points"in Trace transform is filled zero. Comparative results show that the waveform is a line in the anti-transformation records and the amplitude spectrum has not change. For the seismic event of single level, this paper analysis the control relationship of the shape of"energy point"in Trace transform to the theory waveform. The left trough of the"energy point"controls the left trough of wavelet. Wave peak of the"energy point"controls the wavelet's peak. The right trough of"energy point"controls the wavelet's right trough.Then this paper makes the single tilt seismic event and the hyperbolic seismic event of 80 traces, and then does trace transform and inverse transform to these two models. By comparing the waveform to the amplitude spectrum, we found that the amplitude spectrum of theory record and anti-transform record are almost the same and the waveform was recovered basically. So the effect is very good. At the same time, this paper analysis the inverse transform which the"energy point"is filled zero in Trace transform. As a result, to the tilt and hyperbolic cases, the waveform has no amplitude and the amplitude spectrum is unchanged.As the time-distance curve of the surface wave is a line in seismic exploration. So theory and simulation analysis can offer application base for eliminate surface wave using trace transform in seismic exploration. Theory and simulation analysis shows that it is possible to use the trace transform in seismic exploration.