Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
details [2013/01/03 13:13] espen |
details [2013/01/04 13:36] (current) barn |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| //This page is under development// | //This page is under development// | ||
| - | Our main research areas are seismic modeling, wave equation migration velocity analysis (WEMVA) and full waveform inversion (FWI). | + | Our main research areas are seismic modeling, wave equation migration velocity analysis (WEMVA) and full waveform inversion (FWI). |
| - | ==== Seismic Modeling ==== | + | |
| - | The purpose of a seismic modeling (or seismic stimulation) is a process where computers are used to simulate how seismic waves propagate through the Earth. The results from the simulations are used to understand how seismic waves in a real experience behave | + | |
| + | ==== Seismic Modelling ==== | ||
| + | Seismic modeling is the process of modeling (simulating) how seismic waves propagate through the earth | ||
| + | using a computer. | ||
| + | The results from the simulations are used to understand how seismic waves behave and propagate and a typical practical application is designing and optimising new seismic surveys. Also seismic modelling is an integral part of seismic software used to obtain images and mechanical parameters of the subsurface. In order to actually perform seismic modelling, software based on a modeling algorithm is needed in addition to computer hardware. | ||
| + | The starting point for a modeling algorithm is mathematical equations which describe seismic waves. Two standard equations are the acoustic wave equation (AWE) and the elastic wave equation (EWE). The major difference between these two equations is that the latter includes [[http:// | ||
| + | |||
| + | The mathematical equation must be translated into a " | ||
| + | mechanical parameters. These parameters are used as input data to the modelling software. | ||
| + | |||
| + | It is impossible to simulate wave propagation phenomena which are completely identical to the real ones observed in nature. This fact is due to the principle that when performing modelling several // | ||
| + | |||
| + | === Example === | ||
| + | Consider a two-dimensional medium with a box which is placed in the middle of the model, see the image below. The density, P- and S-wave velocities are used as physical model in the simulation. Below is an image of the P-wave velocities. The topology of the density and S-wave velocity are the same as the P-wave velocity. | ||
| + | {{ :vp.png?300 |The P-wave velocities used in the modeling}} | ||
| + | |||
| + | Now, a seismic wave is starting to propagate from the left in the model. The wave propagation at different times after the start are given in the images below. | ||
| + | |||
| + | {{: | ||
| ==== Wave Equation Migration Velocity Analysis (WEMVA) ==== | ==== Wave Equation Migration Velocity Analysis (WEMVA) ==== | ||
| + | The ultimate objective of seismic surveys is to compute mechanical parameters like bulk modulus, shear modulus and density of the subsurface using seismic data observed at the surface. If we imagine that the subsurface is divided into small regular cells of size, say, 10 meters in all three directions, the seismic //inverse problem// then consists of estimating an average mechanical quantity for each cell. Usually seismic surveys covers an area of several thousand square kilometers to a depth of about 5-10 kilometer, implying that a very large number of unknown parameters need to be estimated. | ||
| + | |||
| + | Wave equation migration velocity analysis is one of the approaches used to estimate primarily the bulk modulus, or equivalently the wave velocity for pressure-waves. The main idea for performing this is to | ||
| + | create an image of the subsurface by focusing the reflected seismic waves. The focusing is entirely artificial and performed by software on a computer system. It turns out that the sharpness of the image depends on the wave velocity. By systematically changing the wave velocity until a sharp image is found, one obtains an estimate of the correct wave velocity. Focusing is mainly sensitive to the average of the seismic velocities over many cells, which implies that the estimated velocities are a smoothed version of the true velocity as can be seen on the example below. | ||
| + | |||
| ==== Full Waveform Inversion (FWI) ==== | ==== Full Waveform Inversion (FWI) ==== | ||
| === Example === | === Example === | ||
| Line 19: | Line 40: | ||
| {{ : | {{ : | ||
| - | |||
| ~~DISCUSSION: | ~~DISCUSSION: | ||
