THE AIM OF THIS PROJECT IS TO DEVELOP AND TEST ALGORITHMS AND VECTOR COMPUTER PROGRAMS FOR THE MODELLING OF SEISMIC WAVE PROPAGATION IN 3D LATERALLY HETEROGENEOUS MEDIA IN AN ATTEMPT, AMONG OTHER THINGS, TO REDUCE COMPUTING COSTS.
The growing importance of 3-dimensional seismic surveys in hydrocarbon exploration requires the development of appropriate forward modelling techniques for quality control and interpretation of results. A wide band technique was considered appropriate, suitable for the simulation of the full wave response in 3-dimensional generally varying media and allowing the implementation of various rheologies.
Discrete representations of the relevant equations of motion in seismics were developed. The 3-dimensional acoustic elastic case and generalizations to viscoacoustic elastic and anisotropic media were considered, successively. The numerous numerical examples have shown that the Fourier pseudospectral approach represented an accurate way of 3-dimensional full wave seismic modelling of laterally inhomogeneous media. In fact this method can be considered as the only one which is really practicable today in view of computer storage limitations.
The 2 new time integration techniques which have been developed can be considered as major progress in numerical seismic modelling. They constitute an unconditionally stable method which avoids numerical dispersion and thus offers considerable advantages over conventional finite difference time stepping.
This is of particular importance in viscoacoustic elastic modelling where it is essential to distinguish the inherent physical dispersion from numerical artefacts.
The elimination of reflections from the model boundaries has been achieved by introducing a dissipative zone around the model. The simple method is quite successful but requires additional storage. One major difficulty, however, seems to be the modelling of the free surface situation by the Fourier method. The main reason for this lies in the inherent periodicity of this method. Future work should therefore be concentrated in the solution of this problem of great importance for seismic modelling.
Complementary to the Fourier method, an advanced hybrid modelli ng algorithm has been outlined for the 2-dimensional acoustic case. This technique is based on a combination of the boundary integral equation and the finite difference methods.
The numerical results on 2-dimensional seismic modelling and 3-dimensional seismic modelling by the Fourier method show that this method in conjunction with the new time integration techniques can be successfully applied to the study of wave propagation in isotropic acoustic, elastic, viscoelastic and also anisotropic media.
THE BASIC PHYSICAL PHENOMENA GOVERNING SEISMIC WAVE PROPAGATION WILL BE SEQUENTIALLY CONSIDERED. EACH INTERIM STAGE WILL INVOLVE THE DEVELOPMENT OF MODELLING ALGORITHMS, THE FORMULATION OF DIFFERENTIAL OPERATORS BY FOURIER, FINITE DIFFERENCE AND HYBRID METHODS, THE DEVELOPMENT OF NEW CONVOLUTIONAL ALGORITHMS.
PROGRAMMING AND TESTING ON VECTOR COMPUTER AND MODEL WORKSTATION WILL ALSO BE PERFORMED AND NUMERICAL CALCULATIONS WILL BE MADE. THEIR RESULTS WILL BE COMPARED WITH ANALYTICAL SOLUTIONS. THE MAIN FEATURES OF 3D MODELLING SCHEDULE WILL BE AS FOLLOWS:
- ACOUSTIC: CHECK OF A PROGRAMME PROTOTYPE (KOSLOFF; FOURIER METHOD) AGAINST ANALYTICAL SOLUTIONS: DETERMINE THE FREQUENCY BAND FOR WHICH NUMERICAL MODELLING CAN BE SAFELY USED.
- ELASTIC: DEVELOP AND TEST ALGORITHMS AND PROGRAMMES FOR 3D LATERALLY HETEROGENEOUS MEDIA: COMPARE MODELLING RESULTS WITH ANALYTICAL SOLUTIONS: INCORPORATE VARIOUS SOURCES.
AS TO THE ABSORBING BOUNDARY CONDITIONS, A CHOICE WILL BE MADE FROM THE CURRENT METHODS OR COMBINATIONS OF THEM. DIFFERENTIAL OPERATORS WILL BE SOUGHT, ALTERNATIVE TO THE CURRENTLY USED ONES, TO IMPROVE EFFICIENCY. HYBRID METHODS WILL BE INVESTIGATED FOR WAVE PROPAGATION THROUGH HOMOGENEOUS REGIONS.
AN ALGORITHM WILL BE DEVELOPED WHICH WILL INCLUDE MAPPING FROM A DEFORMED GRID TO A UNIFORM ONE: IF SUCCESSFUL, IT WILL BE APPLIED TO THE PROBLEM "DATUMING".
- VISCOELEASTIC: INCORPORATION OF STANDARD LINEAR RHEOLOGY CONCEPTS; IF SUCCESSFUL, APPLY TO P AND S WAVE ABSORPTION IN HIGHLY ATTENUATING LAYERS.
- ANISOTROPY: INCORPORATION OF A GENERAL ELASTICITY TENSOR: IF SUCCESSFUL, COMPARE WITH ANALYTICAL SOLUTIONS FOR THE HOMOGENEOUS CASE.
- POROUS MEDIUM: CONSIDER WAVE PROPAGATION IN A TWO-PHASE FLUID/POROUS SOLID: IF SUCCESSFUL, MODEL BRIGHT/FLAT SPOT PROBLEM. THE FOLLOWING PROBLEMS WILL ALSO BE INVESTIGATED AND THEIR MODELLING ATTEMPTED: VELOCITY GRADIENTS (VERTICAL AND HORIZONTAL), VELOCITY INCLUSIONS (HIGH AND LOW), PINCHOUTS, SALT DOMES, VSP-SIMULATIONS, LOG-MODELLING.