Study Of Wave-equation Pre-stack Migration And Waveform Inversion

We discussed two hot topics in seismic exploration:wave-equation pre-stack migration and waveform inversion. The key point of depth migration is the wave field extrapolation operator. Several of them have been performed by computer program, they are PS,PSPI,SSF,FFD and GS. Numerical examples indicate that each operator has its advantage and limitation,we must consider imaging accuracy and time consumption according to the feature of the media before migration is performed. The common-shot pre-stack migration is visual,easy to be operated,and high precision, but its calculated amount is huge. In recent years,people have developed several migration techniques which don't use common-shot records in order to improve computational efficiency for pre-stack migration. Based on survey-sinking concept, double square root equation migration downward continues source and record at the same time,so it is quite efficient. While in plane wave migration,we first perform plane wave decomposition on source and record,then migrate each plane wave data. Obviously, the redundancy of multifold seismic record has decreased. Both of the two methods could export common-image gathers for velocity analysis or other use. In order to provide input for pre-stack migration,we generated common-shot record based on Huygens's principle. Compared with other modeling strategy,our method is more efficient,the types of wave are more complete and clear,and the signal-to-noise ratio is higher. It enable us to choose wave field extrapolation operator freely. Furthermore,the method is available when the recording geometry is complicated such as rugged earth surface. The processing of relief surface is a key factor for imaging in complex area.We follow the concept of Reshef's "step-to-step-accumulation" for wave field extrapolation,filling constant velocity over rugged surface,so the surface turns into flat one and general way for modeling and migration could be adopted. The computing result shows that it's an effective approach handling complex surface. Migration is the basic strategy for structure imaging,however,along with the progress of oil/gas exploration,people eagerly hope to get more information about rock's physical property from seismic data ,meanwhile, velocity field of high accuracy is also necessary as input for migration.Hence,different seismic inversion methods have been developed rapidly. Wave equation waveform inversion adopts differential equation model directly, it could take full advantage of seismic information,get more accurate and reliable inversion result,so it has become hot point.However,traditional gradient method suffers from disadvantage of poor convergence rate and difficulty to reconstruct the low wave number component of the velocity field,while the calculated amount of Gauss-Newton method is large .We calculated Jacobian matrix by the way combining virtual source method and reciprocity principle which is proposed by foreign scholars in recent years ,and accomplished Gauss-Newton waveform inversion. We compared it with gradient method,achieving much understanding about the feature of wave field inversion . Numerical example indicates that the calculated amout decreases remarkably when Jacobian matrix is obtained in this way. And the inversion converges fast , the high wave number component of the velocity field is much easier to be reconstructed. We believe,along with the development of high performance computer,waveform inversion based on wave equation will become an available approach for more accurate imaging of rock's physical property.