Common Offset Research Articles

Common‐reflection‐surface (CRS) stack for common offset

We provide a data‐driven macro‐model‐independent stacking technique that migrates 2D prestack multicoverage data into a common‐offset (CO) section. We call this new process the CO common‐reflection‐surface (CRS) stack. It can be viewed as the generalization of the zero‐offset (ZO) CRS stack, by which 2D multicoverage data are stacked into a well‐simulated ZO section. The CO CRS stack formula can be tailored to stack P‐P, S‐S reflections as well as P‐S or S‐P converted reflections. We point out some potential applications of the five kinematic data‐derived attributes obtained by the CO CRS stack for each stack value. These include (i) the determination of the geometrical spreading factor for reflections, which plays an important role in the construction of the true‐amplitude CO section, and (ii) the separation of the diffractions from reflection events. As a by‐product of formulating the CO CRS stack formula, we have also derived a formula to perform a data‐driven prestack time migration.

Influence of Data Irregularities on 3d Common Offset Migration

In 3D seismics offset is a vector characterized by the source-receiver distance and azimuth. Due to irregularities in the acquisition (for instance streamer feathering in marine acquisition) common offset data are not available and, in turn, 3D common offset migration does not make sense any longer. We then introduce the concept of migration by offset class: it is a straightforward extension of common offset migration in which we migrate all traces that belong to a given offset class, namely all traces with offset close to a given one. The result of such a migration depends of course on how the offset class is constructed or, in other words, on what is meant with close . The aim of this paper is to investigate by means of a 3D numerical study how to design offset classes so as to obtain migrated images that can be interpreted without trouble (such an interpretation is a key element for a successful migration velocity analysis). We have to find a trade-off between two extremes:- a too loose offset class that would mix heterogeneous offsets (in particular mixing substantially different azimuths can be dangerous); - a too narrow offset class that would result in sparse seismic traces with, in turn, an inadequate coverage of the reflector. The regularity, within an offset class, of the offset variation as well as the one of the distribution of midpoints are parameters that can have a drastic influence on the quality of the migrated image. It is shown that migration by offset class appears as a robust procedure all the more than the offset varies slowly with the midpoint coordinate within an offset class. Besides, the smaller the mean offset norm, the lower is the contamination of the image due to the mixing of azimuths within an offset class.

2-D and 3-D processing and interpretation of multi-fold ground penetrating radar data: a case history from an archaeological site

A 2.5-D and 3-D multi-fold GPR survey was carried out in the Archaeological Park of Aquileia (northern Italy). The primary objective of the study was the identification of targets of potential archaeological interest in an area designated by local archaeological authorities. The second geophysical objective was to test 2-D and 3-D multi-fold methods and to study localised targets of unknown shape and dimensions in hostile soil conditions. Several portions of the acquisition grid were processed in common offset (CO), common shot (CSG) and common mid point (CMP) geometry. An 8×8 m area was studied with orthogonal CMPs thus achieving a 3-D subsurface coverage with azimuthal range limited to two normal components. Coherent noise components were identified in the pre-stack domain and removed by means of FK filtering of CMP records. Stack velocities were obtained from conventional velocity analysis and azimuthal velocity analysis of 3-D pre-stack gathers. Two major discontinuities were identified in the area of study. The deeper one most probably coincides with the paleosol at the base of the layer associated with activities of man in the area in the last 2500 years. This interpretation is in agreement with the results obtained from nearby cores and excavations. The shallow discontinuity is observed in a part of the investigated area and it shows local interruptions with a linear distribution on the grid. Such interruptions may correspond to buried targets of archaeological interest. The prominent enhancement of the subsurface images obtained by means of multi-fold techniques, compared with the relatively poor quality of the conventional single-fold georadar sections, indicates that multi-fold methods are well suited for the application to high resolution studies in archaeology.

Common-reflection-point stacking in laterally inhomogeneous media

An important seismic reflection-imaging process which is widely applied in practice in an approximate form is the simulation of a zero-offset (ZO) section from a set of common-offset (CO) sections. Rather than using the familiar common-midpoint (CMP) stack (which suffers from reflection-point dispersal when the reflectors are dipping), the aim now increasingly is to perform an accurate common-reflection-point (CRP) stack. In the latter case, all primary CO reflections used for the simulation of a particular ZO reflection are expected to have a common reflection point. A CRP stack can be performed with a macro-velocity model or with the near-surface velocity only. The fundamental CRP reflection and stacking trajectories involved in both of these CRP stacking techniques are inherently related. The aims of this paper are (a) to give some simple analytic formulae for these trajectories for the constant-velocity case and (b) to describe two CRP stacking methods for 21) laterally inhomogeneous media that make use of the formulae.

AVO analysis by offset-limited prestack migrations of crustal seismic data

The physical causes of reflections from the crystalline crust are still a matter of debate. The polarity of the wavelet and the amplitude-versus-offset (AVO) dependence of seismic reflection data can help to reveal the nature of a reflector. In contrast to seismic data from sedimentary environments, however, it is very difficult to get polarity and AVO information from crystalline basement data. Reflections in prestack data are typically weak, incoherent and often obscured by numerous diffractions. There is, however, a better chance of obtaining reliable AVO information from prestack-migrated data after true-amplitude processing, as the migration process unravels the jumble of reflections and diffractions and improves the signal/noise ratio. Important steps in this processing sequence are careful editing followed by surface-consistent amplitude corrections for source and receiver coupling to the ground. Migration-velocity models can be obtained from refraction seismics and/or from migration-velocity analyses. The migration itself is of Kirchhoff-type and applied to COF gathers (COF = Common OFfset) to get one migrated section for each COF. These COF-migrated images can then be used to get AVO functions for specific reflections. Examples from the DEKORP near-vertical reflection line KTB8502 show some strong reflections, from beneath a granite body, at about 9 to 11 km depth. Both the positive and negative reflection coefficients of the reflectors are consistent with an interval velocity model obtained from migration-velocity analyses. AVO functions from these reflections include offsets from zero to 12 km and reflection angles from zero to about 30°. Absolute reflection coefficients are surprisingly small with maximum values of 0.015. Two-layer modelling has been done to match the AVO dependence of these reflections.

Migrating around on hyperbolas and parabolas

The term “migration” in seismic reflection imaging is traditionally used to describe a strategy by which one can transfer primary time‐domain reflections (e.g., as observed in a common‐shot or common‐offset section) into their correct spatial positions on the searched‐for subsurface reflector. It is also employed to describe a strategy to transfer primary reflections into their time‐migrated positions directly in the time domain. More recently, the term migration has also been used to describe the process by which primary reflections, as observed in a common‐offset (CO) section, are transferred to the positions where they would be observed in the zero‐offset (ZO) section. The latter procedure is referred to as migration‐to‐zero offset (MZO). It is the subject to which we want to contribute.

Migrating around in circles: Part II

This paper proposes (1) simulating a zero‐offset (ZO) section from common‐offset (CO) sections of different offsets and (2) a possibility to find the best velocity to do this simulation. More precisely, the paper discusses the kinematic aspects of a common‐reflection‐point (CRP) stack for an unknown velocity model.

Method and apparatus employing audio frequency offset extraction and floating-point conversion for digitally encoding and decoding high-fidelity audio signals

An audio signal is initially represented by a series of high-resolution pulse code modulated (PCM) data. A lower rate series of representative values are extracted from the initial series of PCM data. Half of the lower rate is at an intermediate audio frequency so that the lower rate series encodes low frequency components of the audio signal. The PCM data are adjusted by offsetting in accordance with corresponding representative values and are then converted to a floating-point representation by extracting scale factor or exponents. The combination of the series of representative values and the floating-point data provides a rate-compressed representation of the audio signal which is capable of being decoded after transmission or storage to reproduce the audio signal without substantial noise, distortion or loss of dynamic range. The splitting of the audio information between the lower rate series and the adjusted floating-point PCM limits the normally destructive effect that low frequency components of high amplitude have upon high frequency components of relatively low amplitude. In a preferred embodiment, a common offset is determined for each block by computing the arithmetic mean of the maximum and minimum PCM data values for the block and truncating the result, the PCM data are adjusted by subtracting their corresponding common offsets, and a common exponent is determined for the block of adjusted PCM data. For encoding high-fidelity audio, preferably the audio signal is initially represented by a series of 16-bit PCM samples at a rate of at least 36 kilohertz, the block size is chosen to be 16 audio samples, and the encoded and compressed data for each block includes a 160 bit frame consisting of an 8-bit block offset, a 3-bit block exponent, a 5-bit error correction code, and sixteen floating-point values each including eight data bits and one parity bit. This format permits 9 stereo audio channels and frame synchronization to be readily transmitted over a conventional video channel.