Peter Traynin

Underground imaging by frequency-domain electromagnetic migration

A new method of the resistivity imaging based on frequency-domain electromagnetic migration is developed. Electromagnetic (EM) migration involves downward diffusion of observed EM fields whose time flow has been reversed. Unlike downward analytical continuation, migration is a stable procedure that accurately restores the phase of the upgoing field inside the Earth. This method is indented for the processing and interpretation of EM data collected for both TE and TM modes of plane-wave excitation. Until recently, the method could be applied only for determining the position of anomalous structures and for finding interfaces between layers of different conductivity. There were no well developed approaches to the resistivity imaging, which is the key problem in the inversion of EM data. We provide a novel approach to determining not only the position of anomalous structures but their resistivity as well. The main difficulty in the practical realization of this approach is determining the background resistivity distribution for migration. We discuss the method of the solution of this problem based on differential transformation of apparent resistivity curves. The final goal of migration is to provide a first order interpretation using a computational effort equivalent to a forward modeling calculation.

Magnetic modeling for highly permeable bodies with remanent magnetization

A numerical method is given for the solution of the 3D magnetostatic problem for a rb i t ra r i ly shaped bodies wi th h igh s u s c e p t i b i l i t y , including remanent magnet iza t ion . The in tegra l equa t ion i s so lved us ing the method of f in i te e lements and a modified version of Pohankas (1988) a lgor i thm for the magne tos ta t i c case . Some theore t i ca l examples a re cons ide red and demagnetization factors are shown. These methods p romise to be essen t ia l in in te rp re t ing the magne t ic f i e ld over a reas conta in ing h igh ly magnet ic ob jec t s , such as l a n d f i l l s w i t h b u r i a l s i n s t e e l d r u m s .

Interactive Modeling of Potential Fields in Three Dimensions

The goal of the research is to develop a full space, real time and interactive modeling technique for potential fields in three dimensions. The modeling of potential fields in three dimensions includes three aspects: gravity field computation, physical properties, and geometry model construction. This paper focuses on analysis of the field computation algorithm and geometric model construction.

Incorporating non‐seismic information for improved positioning with anisotropic PSDM

Theoretical and numerical studies have shown that surface seismic data alone do not adequately constrain VTI anisotropy parameter estimation (Tsvankin and Thomsen, 1995). The integration of sonic log, vertical checkshot, offset checkshot (OCS), and horizon-based constraints into our migration velocity analysis procedure allows us to develop models for the VTI parameters V0, e, and δ (Thompson, 1985) that are consistent with geology, measured traveltimes, and moveout of the seismic data. We show anisotropic PSDM (APSDM) examples from three marine areas, each of which exhibits marked P-wave anisotropy. Our velocity analysis procedure leads to models that are physically reasonable, and in each case we observe improved positioning accuracy compared to isotropic PSDM.

Migration and analytic continuation in geoelectric imaging

Geoelectric imaging can be accomplished by using downward continuation or migration of the observed electromagnetic (EM) field in the lower halfspace. The method assumes a known background resistivity distribution. It is based on a finite-difference analytical continuation and migration of the EM field in the frequency domain. Vertical maps of the downward extrapolated or migrated fields (amplitudes and phases) produce useful images of the geoelectrical cross-section. We demonstrate also a simple technique of transforming the migrated field into resistivity images which correspond rat her well to the actual resistivity cross-sections. The method can be applied to surface (profile) magnetotelluric or controled source EM data and to borehole EM data as well.

Inversion versus migration in two‐dimensional geoelectrical problems

One of the most challenging problems in electromagnetic (EM) geophysical methods is developing fast and stable methods of imaging inhomogeneous underground structures using EM data. In our previous publications we developed a novel approach to this problem, using EM migration. In this paper we demonstrate that there is a very close connection between the method of EM migration and the solution of the conventional EM inverse problem. Actually, we show that migration is an approximate inversion. It realizes the first iteration in the inversion algorithm, based on the minimization of the residual field energy flow through the profile of observations. This new theoretical result opens a way for formulating a new electromagnetic imaging condition.