Research On Gaussian-beam Linear Waveform Inversion

With the increasing difficulty of the oil and gas exploration,conventional migration methods have couldn't meet the requirement of the oil and gas exploration at present.As is known to all,seismic image should achieve three goals: imaging subsurface geological formations in shape,true amplitude imaging and estimating subsurface lithological parameters.Whereas,there exist some phenomena that seismic acquisition data are sampled irregularly and seismic traces are missed in the complex geological cases.These problems could result in migration artifacts in the next imaging process.In addition,there are kinematic features reflecting subsurface structural shapes and dynamic features(e.g.amplitude and frequency)reflecting lithology in seismic records.So it has become a development trend of seismic exploration that amplitude information in migrated images is applied to AVA/AVO inversion.The major factors affecting amplitude-preserved imaging are sparse receiver sampling,narrow source-receiver apertures,and limited signal bandwidth et al.Worse still,migration methods couldn't reach the high-resolution imaging goal in the rapid development of seismic exploration,especially for the deep carbonate reservoirs in western China.Migration in fact,as an adjoint operator of the linear forward modeling but not an inverse operator,produces a blurred subsurface image.In actual production,the efficiency problem of seismic migration should be also solved in consideration of huge amounts of data.Gaussian-beam propagator,which is widely used in seismic forward modeling and migration methods,has very high application prospect and research value,because it combines the advantages of the high computational efficiency of ray-based propagator with the high accuracy of wave-equation propagator.In this dissertation,we apply Gaussian-beam propagator to the framework of linear waveform inversion so as to obtain seismic images with fewer artifacts,higher fidelity and better resolution.And my major work includes the following several aspects:(1)Based on wave equation,I derive the formulas of both Gaussian beam and Green's function in terms of Gaussian beams,and introduce the kinematic and dynamic ray tracing equations.(2)Based on Born approximation,I derive the primary reflected wavefiled propagation formula.The simulation of primary reflected waves is called Gaussian-beam linear forward modeling,which is adjoint operator of Gaussian beam migration.Gaussian-beam linear forward modeling not only accurately produces recorded data without multiple and direct waves,but also achieve target-oriented modeling.(3)Linear waveform inversion can be carried out in either data space or model space.On the one hand,the data-space inversion can deblur the migrated image by implicitly computing the Hessian matrix.This iterative scheme produces an optimal estimate of the reflectivity,which is consistent with the recorded data.On the other hand,in the assumptions of both high-frequency approximation and infinite acquisition aperture,the model-space inversion computes the diagonal Hessian explicitly,and then applies its inverse to the migrated image.The final chapter draws conclusions about Gaussian-beam linear waveform inversion(GBLWI).We also give future plan on GBLWI in last chapter.