The reflectivity method that is used to calculate synthetic seismograms (Kennett, 1983) includes most aspects of the wavefield expected for a given one-dimensional (1-D) velocity structure, including interbed multiples and frequency-dependent interaction in the presence of thin layering. These effects are not accounted for when generating synthetics by simple zero-offset convolution. Given the presence of thin beds at Site 1276, these effects are potentially important. Reflectivities and transmissivities are calculated in the tau-p domain for a series of layers with different velocities, densities, and attenuations using Kennett's algorithm as implemented by the commercial software package Nucleus (see Kennett, 1983, for a full description). The tau-p synthetic is transformed to the x-t domain using an inverse Radon transformation, yielding an x-t synthetic seismogram that consists of a prestack CMP gather. For comparison with the coincident MCS data, the synthetic CMP gather is corrected for normal moveout and stacked. The input for this method is the earth model described above and an estimate of the source wavelet, which is described below.
Two separate approaches were used to estimate the source wavelet: (1) deconvolution of the first seafloor multiple with the seafloor reflection and (2) source modeling of the gun array used during the acquisition of the reflection data. The first approach follows the method employed by Korenaga et al. (1997). The first seafloor multiple is deconvolved with the primary seafloor reflection after applying a spherical divergence correction for geometrical spreading. The second approach models the source signature (near- and far-field) using the size and arrangement of the air gun source. These methods produce estimates of the source wavelet that are similar to one another and to reflections from the seafloor, which is typically a simple, sharp interface and whose seismic response should approximate the source wavelet (Fig. F7). This consistency gives us confidence that our estimate of the source wavelet is accurate. We used the source wavelet estimated from the second method because the software used for that method is the same as used for the remainder of our calculations.
A direct link between TWT and depth is typically obtained during logging operations by firing an air gun at the surface and recording the one-way traveltime to a geophone positioned within the borehole (i.e., a checkshot survey). Because the upper 800 m at Site 1276 were not cored or logged, this critical piece of information is missing from our analysis, and a tie between depth and the traveltime of some reflection must be established by other means. As described in the Leg 210 Initial Reports volume, the reflection with a positive peak at 6.982 s originally appeared to be the best candidate to make this link (Shipboard Scientific Party, 2004). Discontinuous, low-amplitude reflections lie above this horizon and continuous, high-amplitude reflections are found below (Fig. F2). The depth to this horizon estimated from velocities obtained from semblance plots of MCS reflection data prior to drilling (~900 mbsf) was within 4% of the depth (864.7 mbsf) below which the lithology changed from mostly hemipelagic claystone (lithologic Unit 1) to consistently alternating layers of carbonate-cemented grainstone and mudstone (lithologic Unit 2). Some of the carbonate-cemented sandstones and claystones in Unit 2 have high velocities (up to 5.8 km/s) compared to the overlying hemipelagic claystones (~2–2.5 km/s) and thus were expected to produce high-amplitude reflections (Fig. F3). Because of these features, we chose this lithologic change to tie TWT to depth in the shipboard analysis (Shipboard Scientific Party, 2004). Below this horizon, the time-depth relationship was determined from laboratory measurements of P-wave velocity.
We have subsequently tested this tie between TWT and depth by creating a new velocity model from the MCS reflection data (red line, Fig. F8). Picks of horizons from eight adjacent CMP gathers near Site 1276 served as input into forward modeling using RAYINVR (Zelt and Smith, 1992). Nine horizons were interpreted and assigned picking errors of 8 ms; these included the prominent AU1 and U reflections. Iterative forward modeling and inversion of the 3796 data points provided a 1-D model with a chi-squared of 0.404 and a root-mean-square traveltime residual of 5 ms. The upper 500 m is characterized by low velocities (1.5–1.84 km/s) and a low-velocity gradient, and from 500 to ~820 mbsf the velocity increases to ~2.2 km/s with a slightly steeper gradient. This section is underlain by a rapid increase in velocity, reaching a maximum velocity of 2.55 km/s at 901 mbsf or 5.46 km below sea level. These high velocities correspond to the bright horizontal reflections at ~7 s TWT (Fig. F8). Beneath this section, velocities decrease again to 2.40 km/s, and then increase gradually to 2.65 km/s through the comparatively transparent section of sediments between 7.15 and 7.5 s. Below this section lies the bright U reflection. The section beneath U is marked by a rapid increase in velocities (modeled as 2.85–4.25 km/s from the MCS data).
To create synthetic seismograms, we used the velocities determined by the above analysis for the section above the shallowest core sample. Below the shallowest sample, we used laboratory measurements of velocity. From this model, we estimate that the shallowest in-place sample (800 mbsf, Core 210-1276A-2R) has an associated TWT of 6.954 s. (We exclude the wash Core 210-1276A-1W, which includes materials from unknown depths between 753 and 800 mbsf). In the following sections, we compare the waveforms of synthetic seismic reflection data to those of coincident seismic reflection data in order to further refine this depth-time tie.