Synthetic seismograms are a computer-generated aid in the search for hydrocarbons. Heretofore the solution has been done by z-transforms. This thesis presents a solution based on the method of finite differences. The resulting algorithm is fast and compact. The method is applied to three variations of the problem, all three are reduced to the same approximating equation, which is shown to be optimal, in that grid refinement does not change it. Two types of algorithms are derived from the equation. The number of obvious multiplications, additions and subtractions of each is analyzed. Critical section of each requires one multiplication, two additions and two subtractions. Four sample synthetic seismograms are shown. Implementation of the new algorithm runs twice as fast as previous computer program.

This thesis integrated geology, geophysics, and petroleum engineering data to build a detailed reservoir characterization models for three gas pay sands in the Grand Isle 33 & 43 fields, offshore Louisiana. The reservoirs are Late Miocene in age and include the upper (PM), middle (QH), and lower (RD) sands. The reservoir models address the stratigraphy of the upper (PM) sand and help delineate the lower (RD) reservoir. In addition, this research addresses the partially depleted QH-2 reservoir compartment. The detailed models were constructed by integrating seismic, well log, and production data. These detailed models can help locate recoverable oil and gas that has been left behind. The upper PM model further delineated that the PM sand has several areas that are shaled-out effectively creating a flow barrier within reservoir compartments. Due to the barrier in the PM-1 reservoir compartment, an area of potentially recoverable hydrocarbons remains. In Grand Isle 33, the middle QH sand was partially depleted in the QH-2 reservoir compartment by a series of development wells. Bottom hole pressure data from wells in Grand Isle 32 & 33 reveal that the two QH fault compartments are in communication across a leaking fault. Production wells in the QH-1 compartment produced reserves from the QH-2 compartment. The lower RD sand model helped further delineate the reservoir in the RD-2 compartment and show that this compartment has been depleted. The RD model also shows the possible presence of remaining recoverable hydrocarbons in the RD-1 compartment. It is estimated that about 6.7 billion cubic feet of gas might remain within this reservoir waiting to be recovered. A seismic amplitude anomaly response from the QH and RD sands is interpreted to be a lithologic indicator rather than the presence of hydrocarbons. Amplitude response from the PM level appears to be below the resolution of the seismic data. A synthetic seismogram model was generated to represent the PM and surrounding sands. This model shows that by increasing the frequency of the seismic data from 20 Hz to a dominant frequency of 30 Hz that the PM and surrounding sands could be seismically resolvable. Also the PM-1 compartment has possible recoverable hydrocarbons of 1.5 billion cubic feet of gas remaining.

Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods o er a better control on the accuracy and more geometrical exibility than the Finite Di erence methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis are con rmed by numerical experiments performed using an implementation of these methods. The methods are tested using two benchmarks: Lamb's problems and the SEG/EAGE salt dome model. / text