Correlation of borehole
results with MCS reflection data requires relating lithostratigraphy and
physical properties of sediments and hard rocks to seismic reflections. To do
so, we use one-dimensional synthetic seismograms created from density and
velocity logs, MST data, and downhole wireline logs. We treat the relatively
noisy core and MST data with a robust-mode filter employing a 5-m window, using
GMT software (Wessel and Smith, 1995). This filter is a maximum likelihood
probability estimator that calculates the mode (i.e., the most frequently
occurring data value) within the given data window. In addition, the median of
the filtered data is computed during filtering, and outliers with values 2.5
times greater than the L1 scale are replaced with the median ("robust"
filter option). The L1 scale is defined as 1.4826 times the median absolute
deviation (MAD), because, in a Gaussian distribution, the expected value for the
MAD is the standard deviation 
/1.4826.
Filtering noisy index properties data with various filters with and without the
"robust" option shows that a robust-mode filter is the most efficient
way to smooth the data and remove outlying data points. In most cases, a filter
width of 3.5-5 m yields the best results.
If no check shots with the WST are available to determine transit time directly, we sum log transit times to create a record of two-way traveltime (TWT) vs. depth. The TWT log is linearly resampled using a sampling interval of 0.1-0.5 ms, depending on the sampling of the raw data. Downhole logs typically sample every 15 cm, whereas the sampling interval of physical properties measurements varies highly, depending on recovery. To avoid aliasing, linear resampling in TWT oversamples the data; other resampling methods (e.g., splines and near-neighbor) cause artifacts at data gaps. We then resample velocities and densities, using the TWT array, and multiply to obtain impedance.
We then calculate reflection coefficients from impedance contrasts. We compute a second time series of reflection coefficients including interbed multiples and transmission losses based on a Fourier domain method from Lavergne (1989), implemented using MATLAB. Both reflection coefficient time series are convolved with a Ricker wavelet with a peak frequency of 40 or 30 Hz, depending on the frequency content of the MCS data. We chose this wavelength by trial and error, as we found that wavelets with higher or lower peak frequencies do not match the MCS data as well.
