Stable estimation of the interval anelliptical parameter for P‐wave pre‐stack imaging

Geophysical Prospecting

2015

A B S T R A C TWe suggest a new method to determine the piecewise-continuous vertical distribution of instantaneous velocities within sediment layers, using different order time-domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root-mean-square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix-type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non-uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth-order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth-order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time-to-depth conversion. about different time-domain effective velocities at interface points. In the context of this paper, interface points refer mainly to sparse vertical points picked through the velocity analysis process (e.g., at maximum vertical semblance profiles). The vertical intervals between these points are considered specific local units (or layers) characterized by their geological nature: water column, sediment rocks with 517 C 2015 European Association of Geoscientists & Engineers 518 Z. Koren and I. Ravve monotonously increasing velocities, or hard rocks with constant vel...

Section: Discussion: Constrained Velocity Inversionmentioning

confidence: 99%

Piecewise‐continuous velocity inversion

Geophysical Prospecting

2015

“…Several regularization approaches were proposed to overcome the ill-posed problem, and implicit methods have been developed, so that a single erroneous value of effective velocity does not easily corrupt the entire inversion. These methods are generally called constrained velocity inversion (Oldenburg et al, 1984;DuBose, 1988;Harlan, 1999;Zhang and Wang, 2003;Ren et al, 2004;Valenciano et al, 2004;Cameron et al, 2007). In case of the generalized Dix inversion, we obtain three local parameters: the fast and slow local NMO velocities and the azimuth of the slow velocity.…”

Section: Limitation Of the Methodsmentioning

confidence: 99%

Azimuthally dependent anisotropic velocity model update

2014

GEOPHYSICS

Constrained Dix inversion

2006

GEOPHYSICS

We propose a stable inversion method to create geologically constrained instantaneous velocities from a set of sparse, irregularly picked stacking- or rms-velocity functions in vertical time. The method is primarily designed for building initial velocity models for curved-ray time migration and initial macromodels for depth migration and tomography. It is mainly applicable in regions containing compacted sediments, in which the velocity gradually increases with depth and can be laterally varying. Inversion is done in four stages: establishing a global initial background-velocity trend, applying an explicit unconstrained inversion, performing a constrained least-squares inversion, and finally, fine gridding. The method can be applied to create a new velocity field (create mode) or to update an existing one (update mode). In the create mode, initially, the velocity trend is assumed an exponential, asymptotically bounded function, defined locally by three parameters at each lateral node and calculated from a reference datum surface. Velocity picks related to nonsediment rocks, such as salt flanks or basalt boundaries, require different trend functions and therefore are treated differently. In the update mode, the velocity trend is a background-velocity field, normally used for time or depth imaging. The unconstrained inversion results in a piecewise-constant, residual instantaneous velocity with respect to the velocity trend and is mainly used for regularizing the input data. The constrained inversion is performed individually for each rms-velocity function in vertical time, and the lateral and vertical continuities are controlled by the global velocity-trend function. A special damping technique suppresses vertical oscillations of the results. Finally, smoothing and gridding (interpolation) are done for the resulting instantaneous velocity to generate a regular, fine grid in space and time. This method leads to a stable and geologically plausible velocity model, even in cases of noisy input rms-velocity or residual rms-velocity data.