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## Symmetric data acquisition

The premise of reciprocal acquisition geometry is intimately related to symmetric data acquisition. The idea of symmetric wave field sampling was described by Ongkiehong 1988 and Vermeer . Their recommendation is to record seismic data as generally as possible and perform data reduction later, in the processing step. Array forming is thus done not in the field but on the computer. This method, of course, requires sufficient dynamic range of recording equipment, but does not discriminate against propagation effects. Data are most unbiased if they are collected symmetrically, that is, for each (vector) source throughout the survey we must have a (vector) receiver at the same location. Ongkiehong and Vermeer show asymmetric sampling examples and their effects on stack arrays. The effect can be seen on the changes in amplitude changes with offset during migration and inversion. The acquisition geometry issue is independent of the type of experiment carried out and applies to scalar, as well as vector field, experiments. Symmetric sampling is a general notion and offers general guidelines for processing. Their conclusion is that symmetric acquisition geometry offers the best unbiased acquisition and allows the most flexibility in later preprocessing. I'd like to extend their observation and claim that reciprocal acquisition geometry offers the best unbiased acquisition and allows new directions in processing that data.

Figure and are examples of nearly reciprocal data acquisition. Figure plots the source and receiver positions of a prestack multi-component data set. Besides one source gap, the acquisition geometry is regular. Each source is located between a receiver position. Figure and represent the symmetric and antisymmetric components of a time slice through the prestack data set. Source and geophone positions were interpolated by nearest neighbours before determining the amount of symmetry and deviation. The surprising result is that the symmetric part and the symmetric part are about the same magnitude. One would not expect this, if one thought that equation (2) holds for this data set. The lack of symmetry (or reciprocity) demands some explanation. I chose to explain it by differences in source behavior, assuming that differences in receiver behavior are small compared to the potentially nonlinear behavior of seismic sources. The lack of symmetry can be employed to set up a minimization problem, where the objective function maximizes symmetry in a source-location and source-component consistent way.

sgplot
Figure 2
Pembrook 9-c data acquisition geometry is shown in source and receiver coordinates. This space is identical for all components. The recording is very regular, and nearly reciprocal. The source coordinates are between receiver coordinates.

slicexx1
Figure 3
Time slices of the part of the data for which reciprocal data exist for 50 source points (Xx-component). To go through time slices, press the button.

slicexx2
Figure 4
Reciprocal time slices of the part of the data for which reciprocal data exist for 50 source points (Xx component). To go through time slices, press the button.

symslicexx
Figure 5
Symmetric part of the data (Xx-component). To go through time slices press the button.

devslicexx
Figure 6
Antisymmetric part of the data (Xx-component). To go through time slices, press the button.

Next: THE OPTIMIZATION PROBLEM Up: SYMMETRIZING THE WAVE FIELD Previous: Wave field types
Stanford Exploration Project
11/18/1997