# Synthetic Seismograms for PS Seismic Data

Over the last few years, several articles on multicomponent seismic data have appeared in Geophysical Corner by Bob Hardage and his co-authors (January, February, April and August 2011, and February 2012), describing various aspects of processing and interpretation of such data.

In this article, we address an important question about correlation of synthetic seismograms with converted wave PS seismic data.

When a seismic wave (compressional or P-wave) impinges on a rock interface at oblique incidence, the contrast in the elastic parameters it encounters results in compressive and shear stresses. As a result, partitioning of energy takes place at the interface. This means that besides the reflection and refraction of the incident P-wave, there is P to S energy conversion. Thus an incoming P-wave gives rise to a reflected P-wave, a transmitted P-wave, a reflected S-wave and a transmitted S-wave as we show in figure 1.

The partitioning of energy of the incident wave that takes place at the interface into different components is dependent on the angle of incidence as well as the elastic parameters, which can all be derived from the P-velocity, S-velocity and density of the two media defining the interface. The angular relationships between the different wave components are governed by Snell’s law (which we all studied in high school) and the amplitude relationships between the incident wave and the reflected, transmitted and converted-wave components are described by Zoeppritz equations (which we have referred to in our earlier articles from October 2012 and June 2015).

## Synthetic Seismogram Generation

What we have stated above is that conversion of energy (P to S) takes place at oblique incidence of the incident waves. We may emphasize this aspect as normal for the incident wave – there will be no conversion of energy, and for angles of incidence less than 10 or 12 degrees, there is no detectable conversion. This PS data, when acquired and processed, may not show any visible amplitudes corresponding to such small angles of incidence. This is a consequence of the fact that PS waves follow asymmetric illumination ray paths at the reflecting surface, compared with the symmetric ray paths for the PP waves as seen in the conventional survey geometry (common mid-point reflection).

Synthetic seismograms are usually generated from well log data for identifying reflection events on stacked seismic data corresponding to different subsurface rock interfaces. The sonic and density log curves are used for generating an impedance log and the reflectivity derived therefrom is convolved with a wavelet to produce a synthetic trace at the location of the well. The wavelet used can be a mathematical wavelet of an appropriate frequency such as a Ricker wavelet, or it could be extracted from seismic data in the broad zone of interest using a statistical process, or it could be extracted by making use of well log data and seismic data.

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