Introduction

The goal of exploration seismology is to find oil and gas reservoirs by seismically imaging the earth's reflectivity distribution. Towards this goal, exploration geophysicists perform seismic experiments ideally equivalent to that shown in Figure 1. Here, the source excites seismic waves, and the resulting primary reflections are recorded by a geophone located at the source position. If we assume only primary reflections then this defines the ideal zero-offset (ZO) experiment. For now we assume a magic filter (to be described later as data processing) that eliminates all events but primary reflections.

A seismic source is usually some mechanical device or explosive that thumps the earth, and a geophone records the time history of the earth's vertical particle velocity, denoted as a seismic trace d(x,z=0,t). Larger amplitudes on the Figure 1 traces correspond to faster ground motion and the up-going (down-going) motion is denoted here by the blackened (unblackened) lobes. The strength of these amplitudes is roughly proportional to the reflectivity strength m(x,z) of the corresponding reflector. Assuming a constant density and a 1-D medium , the reflectivity m(x,z) is roughly defined as as

$$\cong \frac{v(z+dz) - v(z)}{v(z+dz) + v(z)},$$ m(x,z) (1.1)

where v(z) is the propagation velocity at depth z.

After recording at one location, the source and receiver are moved a bit over and the idealized ZO seismic experiment is iteratively repeated for different ground positions. All recorded traces are lined up next to one another and the resulting section is defined as a ZO or poststack seismic section, as shown on the RHS of Figures 1 and 2. Note that the depth d of the first reflector can be calculated by multiplying the 2-way reflection time t by half the velocity v of the first layer, i.e. d = tv/2.

The reflection section in Figure 1 roughly resembles the actual geology, where one side of the signal is colored black to help enhance visual detection of the interface. Unfortunately, this experiment and the ZO seismic section are ideal because they assume no coherent noises such as multiples, out-of-the-plane scattering, surface waves, converted waves and so on. In practice, a real ZO experiment cannot generate the ideal seismic section because the source also generates strong coherent noise and near-source scattering energy. To solve this problem, explorationists perform non-zero offset experiments (where one shot shots into many far-offset geophones), filter coherent noise from these data and make time-shift corrections to the traces so that they are roughly equivalent to the ideal ZO traces. The steps for processing these data are described in a later section.

  

Figure 1.1: Figure 1. Earth model on left and idealized zero-offset (ZO) seismic section on right, where each trace was recorded by an experiment where the source has zero offset from the geophone. The above ZO seismic section represented by d(x,z=0,t) roughly resembles the earth's reflectivity model m(x,z) because we unrealistically assume it contains only the primary reflections.