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70  2 Exploration Methods
                                 The travel time T between shot point S and geophone G is given by the length of
                               the ray path L and the seismic velocity v within the subsurface layer, such that
                                        L
                                    T =                                                   (2.12)
                                        v
                                 From Figure 2.12, we see that
                                        2
                                      L      2    
 2
                                                 x
                                          = D +                                           (2.13)
                                      2          2
                                                      2 1/2
                                                  2
                                 Such that T = 1/v(4D + x )
                                 This equation contains D and v as unknowns, which can be constrained if
                               measurements of T are available for many geophones and shot points. Depending
                               on the shot point layout and the spacing of geophones, there is usually considerable
                               overlap of measurements over a common point on the reflector, which is referred
                               to as fold. Assuming a horizontal layer as the reflector, the travel times for
                               reflection events from a common point vary with offset (x in Figure 2.12). This
                               variation in travel time depends only on the velocity of the subsurface layer, thus
                               the subsurface velocity can be derived, assuming this velocity does not change
                               horizontally.
                                 Incidence elastic waves reflected at a single reflector and then detected at the
                               surface are called primary reflections. However, in reality, many waves are reflected at
                               multiple interfaces before they are detected and are therefore referred to as multiple
                               reflections or multiples. Multiples generally have lower amplitudes than primary
                               reflections as energies are split at every reflection. The correct identification of
                               multiples is a crucial step in the interpretation of seismic traces. Travel times
                               of multiples can be calculated from the corresponding primary reflections and
                               can be identified and filtered by appropriate processing techniques. As signal
                               strength decreases significantly with depth, processing will always need to involve
                               improvement of the signal-to-noise ratio.
                                 Each shot from the source generates not only multiple reflections but also
                               several different primary reflections from different boundaries at various depths.
                               The arrival times of the reflected waves vary with the depth of the reflector and
                               with the velocities of the different layers crossed by the wave. The seismic trace
                               resulting from a single shot at one receiver is thus composed of a series of
                               arrivals. These ‘‘spikes’’ will vary considerably in amplitude depending on the
                               attenuation within the subsurface. Generally, amplitude decreases rapidly with
                               depth. In addition to the reflections generated at different depths and the arrival of
                               multiples, seismic traces contain a lot of seismic noise and signals from surface
                               waves and air waves. All these signals result in a rather complex diagram, which
                               requires extensive processing before reflections can be recognized and interpreted.
                               The traces recorded by all receivers resulting from an individual shot are assembled
                               in shot gathers. Usually the traces are plotted side by side, allowing an alignment
                               of reflection events and their correlation from trace to trace.
                                 Reflection profiles are taken with shot points and geophones aligned and
                               moved along lines, resulting in a 2D seismic survey. Such surveys are very
                               common, also for geothermal exploration. They supply sufficient information of
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