Divergence Effects in a Layered Earth

Abstract

Of the various factors which influence reflection amplitudes in a seismic recording, divergence effects are possibly of least direct interest to the interpreter. Nevertheless, proper compensation for these effects is mandatory if reflection amplitudes are to be of diagnostic value. For an earth model consisting of horizontal, isotropic layers, and assuming a point source, we apply ray theory to determine an expression for amplitude correction factors in terms of initial incidence, source‐receiver offset, and reflector depth. The special case of zero offset yields an expression in terms of two‐way traveltime, velocity in the initial layer, and the time‐weighted rms velocity which characterizes reflections. For this model it follows that information which is needed for divergence compensation in the region of normal incidence is available from the customary analysis of normal moveout (NMO). It is hardly surprising that NMO and divergence effects are intimately related when one considers the expanding wavefront situation which is responsible for both phenomena. However, it is evident that an amplitude correction which is appropriate for the primary reflection sequence cannot in general be appropriate for the multiples. At short offset distances the disparity in displayed amplitude varies as the square of the ratio of primary to multiple rms velocities, and favors the multiples. These observations are relevant to a number of concepts which are founded upon plane‐wave theory, notably multiple attenuation processes and record synthesis inclusive of multiples.

Simple Processing Sequence to VSP-Seismic data matching in Sindbad oil field, south of Iraq

“…Therefore the signal decays both as a function of recording depth down the borehole and with time along any trace [8], as in the Figure (7). A further complication concerning the signal amplitude is the variability in coupling between tool and formation.…”

Effect of flood basalt stratigraphy on the phase of seismic waveforms recorded offshore Faroe Islands

“…Different VSP runs were merged after quality control of the downhole and hydrophone recordings. Newman's (1973) geometric spreading compensation was then applied to the wavefield before the up and downgoing wavefields were separated by a median filter using 5-9 traces. A low-or bandpass filter usually follows the subtraction process of the median filter to remove high-frequency artifacts that are caused by imperfect source repeatability.…”

Comparison of amplitude decay rates in reflection, refraction, and local earthquake records

“…The amplitude decay of both earthquake and reflection seismograms has been extensively studied over the last two decades (e.g., O'DOHERTY and ANSTEY, 1971;NEWMAN, 1973;AKI and CHOUET, 1975;and AKI, 1980a,b, among many others). Without undertaking a comprehensive review, we should note a few important points: First, the amplitude decay of a seismogram is controlled by the geometric spreading of the source wavefield and relative strengths of intrinsic attenuation and seismic wave scattering (AKI, 1982).…”