We demonstrate for the first time that seismic resonant multiples, usually considered as noise, can be used for super-resolution imaging in the far-field region of sources and receivers. Tests with both synthetic data and field data show that resonant multiples can image reflector boundaries with resolutions more than twice the classical resolution limit. Resolution increases with the order of ...

Water-bottom multiples from a dipping interface have the same kinematics in a Common Midpoint (CMP) gather as a primary from a reflector with twice the dip at twice the perpendicular depth at the CMP location. When migrated with the velocity of the primaries, these multiples are overmigrated just as primaries migrated with higher velocity, and their moveout is thus predictable in image space. D...

There has been a significant increase in the number of twins and higher multiples so that one child in 33 is now a multiple. It is therefore not unusual for schools to have several sets of twins, as well as triplets and even higher multiples. By being the same age and in the same school year if not class, twins and higher multiples are not like brothers and sisters born closely together. Teache...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

A shot-profile migration algorithm is modified to image multiple reflections at their correct location in the subsurface. This method replaces the impulsive source with an areal source made of recorded primaries and multiples. In addition, the extrapolated wavefield at the receivers consists of recorded multiples only which have been previously separated from the primaries. Migration results wi...

Marchenko imaging can produce seismic reflection images in which artifacts related to multiples are suppressed. However, in state-of-the-art implementations, multiples do not contribute to the imaged reflectors. With an “event-byevent” deconvolution imaging approach, it is possible to use multiples in Marchenko imaging. We illustrate this for a 1D reflection response in which the primary reflec...

Proof. First, we’ll give an intuitive proof. Let b > 0 be given. Mark off multiples of b on the number line. The integer a will fall between two different multiples. qb is the smaller multiple, and r is the distance from qb to a. Clearly the choices of q and r are unique. Why we need the well-ordering principle: it’s not clear that a will fall between two different multiples of b if the numbers...

This study presents and tests an approach for estimating the potential price of equity investments, which are not (yet) traded in a market. In practice, multiples derived from comparable companies that are traded and priced in the market are frequently used as a point of reference. The accuracy of those multiples can be empirically assessed by comparing the pricing result for a company with an ...