Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Conventionally, such a complex-valued eikonal is mainly computed either by tracing rays exactly in complex space or by tracing rays approximately in real space so that the resulting eikonal is distributed irregularly in real space. However, seismic data processing methods, such as prestack depth migration andmore »
Maximal immediate extensions of valued differential fields: MAXIMAL IMMEDIATE EXTENSIONS OF VALUED DIFFERENTIAL FIELDS
- Award ID(s):
- 1700439
- Publication Date:
- NSF-PAR ID:
- 10096376
- Journal Name:
- Proceedings of the London Mathematical Society
- Volume:
- 117
- Issue:
- 2
- Page Range or eLocation-ID:
- 376 to 406
- ISSN:
- 0024-6115
- Sponsoring Org:
- National Science Foundation
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