REDUCING NUMERICAL DISPERSION AND DETERMINING MICROSEISMIC EVENT LOCATION USING HIGH ORDER FINITE DIFFERENCE - Syamsurizal
The finite difference method was a wave modeling technique in seismic migration. However, in the application of high-frequency modeling, numerical dispersion appears. This numerical dispersion will reduce the quality of the resulting microseismic source. One way to reduce the numerical dispersion in synthetic seismograms in forward modeling is to use a high-order finite difference method to obtain a more accurate modeling solution. In this study, acoustic and elastic wave modeling was carried out with the assumption that there is no attenuation in each layer. Acoustic wave modeling uses the pressure wave equation while elastic wave modeling uses the stress-strain equation. To reduce numerical dispersion in the seismograms resulting from acoustic wave modeling, the wave equation is discretized using a regular grid model by adding higher orders to the spatial side. Next, forward modeling with a wave source originating from a certain depth and propagating in all directions through an isotropic homogeneous and heterogeneous medium and recorded by a receiver on the surface. We propose a new source function to increase the wave energy and use a proportional grid to reduce computational time and suppress numerical dispersion. The study results show that low-order spatial discretization produces numerical dispersion in the seismogram. By using the proposed method there is an increase in wave energy but numerical dispersion still appears in low order modeling. This numerical dispersion effect will decrease as the accuracy of the modeling solution increases using higher order discretization in spatial side of acoustic wave equation. In modeling using elastic waves, there are 2 types of body waves, namely P waves and S waves, both of which have amplitudes of different orders, where the S wave has a greater amplitude than the P wave so that at relatively low dominant frequencies, numerical dispersion appears in the S wave. Forward modeling is carried out using Ricker wavelet where the wave source is at a certain depth and propagates in all directions by passing through an isotropic and anisotropic medium in the heterogeneous velocity model. The study results show that there is a large numerical dispersion at low orders. At dominant frequencies greater than 10 Hz, dispersion in the S wave has already appeared and becomes larger at higher dominant frequencies, whereas at the frequency the P wave does not yet show any numerical dispersion. Numerical dispersion in P and S waves generally arises because the waves pass through the layer at low velocity. The lower the medium speed, the greater the numerical dispersion and the contribution of high vdocity to the numerical dispersion is very small. To reduce the numerical dispersion in these waves, we apply high-order finite differences using the Staggered Grid (SG) discretization model. Determining location of microseismic events is carried out using the wave back propagation method in isotropic and anisotropic media. In isotropic media which is modeled using 2D acoustic waves and anisotropic media which is modeled using 2D stress strain equations. The most important parameter in this study is the recorded seismogram on the surface which will be used as a source to propagate waves from the receiver to the meeting point of all wavefields. Based on this study, it can be seen that the wave source can be associated with the maximum amplitude due to the maximum interference of all wavefields originating from the receiver. In both isotropic and anisotropic media, the maximum amplitude from the receiver (adjoint source) occurs at origin time. However, in anisotropic media, the maximum amplitude at origin time will not occur if the medium has a very high level of anisotropy. The amount of energy collected depends on the number of recording stations. The greater the number of stations, the greater the energy collected at origin time and the better the quality of the detected microseismic source.