Guided waves in marine CSEM

Recently, marine controlled source electromagnetics (CSEM) has shown great potential in hydrocarbon exploration, where the goal is to detect thin resistive layers at depth below the seafloor. The experiment comprises a horizontal electric dipole transmitter towed over an array of receivers at the seafloor. The transmitter emits a low-frequency signal (< 1 Hz) and measurements of the electric field are made. The depth of the target layer requires transmitter-receiver separations of several kilometres. As a function of separation r, the electromagnetic signal consists of a short-ranging contribution with an exponential decay resulting from the transmission through ocean and sediment (including the reflection at all interfaces) and a long-ranging contribution with a dominant 1/r(3) -decay associated with the airwave guided at the air-ocean interface. Of particular interest among the exponentially decaying waves is the wave guided in the resistive target layer with a well-defined long decay length. In a shallow sea, this 'resistive-layer mode' is partly masked by the airwave. The topics of this study are the airwave and the resistive-layer mode. For a general 1-D conductivity distribution we derive the simple expression of the leading term of the airwave for arbitrary transmitter and receiver position and define a 'pure' complete airwave, which for all separations is close to the asymptotic expansion of the airwave in powers of 1/r. Whereas the treatment of the airwave can be done in terms of Bessel function integrals with real wavenumbers, the resistive-layer mode requires the complex wavenumber plane, where it is defined as the residual at the TM-mode pole with the smallest imaginary part. For sufficiently high integrated resistivity of the layer, we give a simple method to determine the position of this pole. In the complex wavenumber plane, the pure complete airwave is presented by a branch-cut integral. For a typical model, this study concludes with the remarkable result that the superposition of airwave and resistive-layer mode provides an excellent description of the electric field over a wide range of separations.