The Green's function of the Poisson equation, and its spatial derivatives, lead to a family of wavelets specifically tailored to potential fields. Upward continuation of the field is seen to be identical to these wavelets' scale change operation. The maxima at all heights of the field's horizontal gradients are termed the field's multiscale edges. A multiscale edge's field strength variation an...

One way of developing a wave-equation approach to seismic imaging is based on the concept of downward continuation of the surface reflection data. Seismic imaging is typically based on the single scattering approximation, and assumes the knowledge of a, smooth, background model in which the mentioned downward continuation is carried out. The downward continued data are subjected, at each depth,...

an_eul is a new automatic method for simultaneous approximation of location, depth, and structural index (geometry) of magnetic sources. in the 2d case analytic signal is defined as a conjugate function whose imaginary part is the hilbert transform of its real part. since the first vertical derivative of the magnetic field is the hilbert transform of its horizontal derivative, vertical and hori...

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the disturbing gravity observations are only available on the earth’s surface. downward contin...

Data mapping is a procedure for transforming seismic or acoustic data collected with one set of source/receiver locations and wavespeed model, to data equivalent to that collected in a diierent source/receiver connguration and wavespeed model. A major application of this general process is downward continuation of the waveeeld, or wave-equation datuming. Unlike many previous implementations of ...