Interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing. A major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated. In this respect, a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events, nor estimation of these directions.The method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly, regardless of the original spatial interval, without any attempt to determine their true dips. The predictability of linear events in the f-x domain allows the missing traces to be expressed as the output of a linear system, the input of which consists of the recorded traces. The interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces.Synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations. Assessment of the method with a real data set shows that the interpolation yields an improved migrated section.

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[1] We present a sensitivity study applied to water front monitoring of an onshore oil reservoir, using a remote controlled source electromagnetic method (CSEM) with electric dipoles and a borehole-to-surface configuration. We have developed an optimized and parallelized code based on the method of moments, in order to study the influence of several static or time-varying background uncertainties on the time-lapse CSEM signal (also called 4-D CSEM). Analysis of the relative and absolute variations in phase or quadrature of the time-lapse signal induced by the fluid substitution process, inside the reservoir, has shown that the vertical electric dipole allows the shape of the water front to be monitored, while remaining less sensitive (compared to a horizontal electric source dipole) to the total volume of substituted fluid. We have examined the influence of missed anomalies (1-D/3-D), with more or less conductive properties, near to the ground surface or the reservoir, and with or without time-varying properties. In most cases, the 4-D signal behaves like a reliable filter, canceling almost all response anomalies. However, it can also lead to strong, local perturbations of the time-lapse signal. We have also shown that in the presence of steel cased boreholes at the source location, or with outlying steel cased boreholes, the recording of exploitable data does not present insurmountable difficulties at low frequencies (∼1 Hz), and for a dense array of surface receivers. These positive results with CSEM monitoring suggest that minimal, coarse-time 3-D explorations should be used to ensure reliable interpretation of the monitored data.Citation: Schamper, C., F. Rejiba, A. Tabbagh, and S. Spitz (2011), Theoretical analysis of long offset time-lapse frequency domain controlled source electromagnetic signals using the method of moments: Application to the monitoring of a land oil reservoir,