No abstract

We considered the importance of low frequencies in seismic reflection data for enhanced resolution, better penetration, and waveform and impedance inversion. We reviewed various theoretical arguments underlining why adding low frequencies may be beneficial and provided experimental evidence for the improvements by several case studies with recently acquired broadband data. We discussed where research and development efforts in the industry with respect to low frequencies should be focusing.

Velocity model building and impedance inversion generally suffer from a lack of intermediate wavenumber content in seismic data. Intermediate wavenumbers may be retrieved directly from seismic data sets if enough low frequencies are recorded. Over the past years, improvements in acquisition have allowed us to obtain seismic data with a broader frequency spectrum. To illustrate the benefits of broadband acquisition, notably the recording of low frequencies, we discuss the inversion of land seismic data acquired in Inner Mongolia, China. This data set contains frequencies from 1.5–80 Hz. We show that the velocity estimate based on an acoustic full‐waveform inversion approach is superior to one obtained from reflection traveltime inversion because after full‐waveform inversion the background velocity conforms to geology. We also illustrate the added value of low frequencies in an impedance estimate.

A B S T R A C TDense, wide-aperture and broad frequency band acquisition improves seismic imaging and potentially allows the use of full waveform inversion for velocity model building. The cost of dense acquisitions however limits its applicability. Blended or simultaneous shooting could lead to a good compromise between cost and dense acquisition, although the cross-talk between simultaneous sweeps may reduce imaging capabilities. Onshore, a compromise is achieved with distance separated simultaneous sweeping acquisition, because the shots are easily separated when the processing focuses on pre-critical reflected events. Full waveform inversion for velocity model building however relies on post-critical reflected, refracted and diving events. These events can interfere in a distance separated simultaneous sweeping acquisition. By using a single vibrator, single receiver data set recorded in Inner Mongolia, China, a distance separated simultaneous sweeping data set is created to study the robustness of full waveform inversion in this acquisition context. This data set is well suited for full waveform inversion since it contains frequencies down to 1.5 Hz and offsets up to 25 km. Full waveform inversion after a crude deblending of the distance separated simultaneous sweeping data set leads to a result very similar to the one obtained from the single vibrator, single receiver data set. The inversion of the blended data set gives a slightly less good result because of the cross-talk but it is still quite satisfactory.

Closed forms are given for a large number of quantities occurring in the theory of potential scattering in an arbitrary partial-wave state l for the cases (i) the 5-shell potential V(r) = -A,R 25(r -R), and (ii) the 5-shell plus Coulomb potential. Furthermore, the trajectories of the poles of the total T operator in the complex k plane, with varying complex A, , are investigated in detail for zero, repulsive, and attractive Coulomb force, respectively, Expressions are given for the effective-range parameters, and the Coulomb-modified effective-range parameters, for all I, with application to the NN system, and the Nu system, respectively. The connection between Coulomb-level shifts and effective-range parameters is considered. Improvements on the standard small-shift approximation, which is relatively poor, are suggested. NUCLEAR REACTIONS Charged-particle scattering. 5-shell plus Coulomb potential. Effective-range parameters for all l. Application to NN and Na. Coulomb-level shifts.