Migration and inversion of seismic data

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2458-2472 ◽  
Author(s):  
R. H. Stolt ◽  
A. B. Weglein
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Principal Part ◽  
Nonlinear Inversion ◽  
Inversion Algorithm ◽  
Elastic Parameters ◽  
Seismic Migration ◽  
Prestack Migration ◽  
And Inversion ◽  
Physical Principles

Seismic migration and inversion describe a class of closely related processes sharing common objectives and underlying physical principles. These processes range in complexity from the simple NMO‐stack to the complex, iterative, multidimensional, prestack, nonlinear inversion used in the elastic seismic case. By making use of amplitudes versus offset, it is, in principle, possible to determine the three elastic parameters from compressional data. NMO‐stack can be modified to solve for these parameters, as can prestack migration. Linearized, wave‐equation inversion does not inordinately increase the complexity of data processing. The principal part of a migration‐inversion algorithm is the migration. Practical difficulties are considerable, including both correctable and intrinsic limitations in data quality, limitations in current algorithms (which we hope are correctable), and correctable (or perhaps intrinsic) limitations in computer power.

AVO detectability against tuning and stretching artifacts

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 494-503 ◽  
Author(s):  
Wenjie Dong
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Seismic Exploration ◽  
Inversion Algorithm ◽  
Amplitude Variation With Offset ◽  
Logical Point ◽  
Anomalous Reflection ◽  
Ricker Wavelet ◽  
And Migration ◽  
And Inversion

The [Formula: see text] of hydrocarbon‐bearing sediments normally deviates from the [Formula: see text] trend of the background rocks. This causes anomalous reflection amplitude variation with offset (AVO) in the seismic data. The estimation of these AVOs is inevitably affected by wave propagation effects and inversion algorithm limitations, such as thin‐bed tuning and migration stretch. A logical point is to determine the minimum [Formula: see text] change required for an anomalous AVO to be detectable beyond the background tuning and stretching effects. Assuming Ricker wavelet for the seismic data, this study addresses this point by quantifying the errors in the intercept/slope estimate. Using these results, two detectability conditions are derived. Denoting the background [Formula: see text] by γ and its variation by δγ, the thin‐bed parameter (thickness/wavelength) by ξ, the maximum background intercept closest to the AVO by |A|max, and the thin‐bed intercept value by |A|thin the two conditions are [Formula: see text] [Formula: see text] for detectability against stretching and tuning plus stretching, respectively. Tests on synthetic data confirm their validity and accuracy. These conditions provide a quantitative guideline for evaluating AVO applicability and effectiveness in seismic exploration. They can eliminate some of the subjectivity when interpreting AVO results in different attribute spaces. To improve AVO detectability, a procedure is suggested for removing the tuning and stretching effects.

Principle of prestack migration based on the full elastic two‐way wave equation

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 151-173 ◽  
Author(s):  
C. P. A. Wapenaar ◽  
N. A. Kinneging ◽  
A. J. Berkhout
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Wave Field ◽  
Particle Velocity ◽  
Synthetic Data ◽  
Matrix Operator ◽  
Shear Stresses ◽  
Elastic Wave Equation ◽  
Seismic Migration ◽  
Prestack Migration

The acoustic approximation in seismic migration is not allowed when the effects of wave conversion cannot be neglected, as is often the case in data with large offsets. Hence, seismic migration should ideally be founded on the full elastic wave equation, which describes compressional as well as shear waves in solid media (such as rock layers, in which shear stresses may play an important role). In order to cope with conversions between those wave types, the full elastic wave equation should be expressed in terms of the particle velocity and the traction, because these field quantities are continuous across layer boundaries where the main interaction takes place. Therefore, the full elastic wave equation should be expressed as a matrix differential equation, in which a matrix operator acts on a full wave vector which contains both the particle velocity and the traction. The solution of this equation yields another matrix operator. This full elastic two‐way wave field extrapolation operator describes the relation between the total (two‐way) wave fields (in terms of the particle velocity and the traction) at two different depth levels. Therefore it can be used in prestack migration to perform recursive downward extrapolation of the surface data into the subsurface (at a “traction‐free” surface, the total wave field can be described in terms of the detected particle velocity and the source traction). Results from synthetic data for a simplified subsurface configuration show that a multiple‐free image of the subsurface can be obtained, from which the angle‐dependent P-P and P-SV reflection functions can be recovered independently. For more complicated subsurface configurations, full elastic migration is possible in principle, but it becomes computationally complex. Nevertheless, particularly for the 3-D case, our proposal has improved the feasibility of full elastic migration significantly compared with other proposed full elastic migration or inversion schemes, because our method is carried out per shot record and per frequency component.

Elastic pre-stack seismic inversion through Discrete Cosine Transform reparameterization and Convolutional Neural Networks

Geophysics ◽  
2020 ◽  
pp. 1-70
Author(s):  
Mattia ALEARDI ◽  
Alessandro Salusti
Keyword(s):  
Discrete Cosine Transform ◽  
Elastic Properties ◽  
Seismic Data ◽  
Orthogonal Transformation ◽  
Seismic Inversion ◽  
Joint Probability Distribution ◽  
Elastic Model ◽  
Inversion Algorithm ◽  
Elastic Parameters ◽  
Cosine Transform

We develop a pre-stack inversion algorithm that combines a Discrete Cosine Transform (DCT) reparameterization of data and model spaces with a Convolutional Neural Network (CNN). The CNN is trained to predict the mapping between the DCT-transformed seismic data and the DCT-transformed 2-D elastic model. A convolutional forward modeling based on the full Zoeppritz equations constitutes the link between the elastic properties and the seismic data. The direct sequential co-simulation algorithm with joint probability distribution is used to generate the training and validation datasets under the assumption of a stationary non-parametric prior and a Gaussian variogram model for the elastic properties. The DCT is an orthogonal transformation that is here used as an additional feature extraction technique that reduces the number of unknown parameters in the inversion and the dimensionality of the input and output of the network. The DCT reparameterization also acts as a regularization operator in the model space and allows for the preservation of the lateral and vertical continuity of the elastic properties in the recovered solution. We also implement a Monte Carlo simulation strategy that propagates onto the estimated elastic model the uncertainties related to both noise contamination and network approximation. We focus on synthetic inversions on a realistic subsurface model that mimics a real gas-saturated reservoir hosted in a turbiditic sequence. We compare the outcomes of the implemented algorithm with those provided by a popular linear inversion approach and we also assess the robustness of the CNN inversion to errors in the estimated source wavelet and to erroneous assumptions about the noise statistic. Our tests confirm the applicability of the proposed approach, opening the possibility of estimating the subsurface elastic parameters and the associated uncertainties in near real-time while satisfactorily preserving the assumed spatial variability and the statistical properties of the elastic parameters.

Porosity estimation based on rock skeleton general formula and comprehensive pore structure parameter – An application to a tight-sand reservoir

2021 ◽  
pp. 1-59
Author(s):  
Kai Lin ◽  
Xilei He ◽  
Bo Zhang ◽  
Xiaotao Wen ◽  
Zhenhua He ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Pore Structure ◽  
Seismic Data ◽  
Rock Physics ◽  
Structure Parameters ◽  
Pore Structure Parameter ◽  
Elastic Parameters ◽  
Physics Model ◽  
Rock Physics Model ◽  
Porosity Estimation

Most of current 3D reservoir’s porosity estimation methods are based on analyzing the elastic parameters inverted from seismic data. It is well-known that elastic parameters vary with pore structure parameters such as pore aspect ratio, consolidate coefficient, critical porosity, etc. Thus, we may obtain inaccurate 3D porosity estimation if the chosen rock physics model fails properly address the effects of pore structure parameters on the elastic parameters. However, most of current rock physics models only consider one pore structure parameter such as pore aspect ratio or consolidation coefficient. To consider the effect of multiple pore structure parameters on the elastic parameters, we propose a comprehensive pore structure (CPS) parameter set that is generalized from the current popular rock physics models. The new CPS set is based on the first order approximation of current rock physics models that consider the effect of pore aspect ratio on elastic parameters. The new CPS set can accurately simulate the behavior of current rock physics models that consider the effect of pore structure parameters on elastic parameters. To demonstrate the effectiveness of proposed parameters in porosity estimation, we use a theoretical model to demonstrate that the proposed CPS parameter set properly addresses the effect of pore aspect ratio on elastic parameters such as velocity and porosity. Then, we obtain a 3D porosity estimation for a tight sand reservoir by applying it seismic data. We also predict the porosity of the tight sand reservoir by using neural network algorithm and a rock physics model that is commonly used in porosity estimation. The comparison demonstrates that predicted porosity has higher correlation with the porosity logs at the blind well locations.

Enabling isotropic reflectivity modeling and inversion in anisotropic media

2021 ◽  
Vol 40 (4) ◽  
pp. 267-276
Author(s):  
Peter Mesdag ◽  
Leonardo Quevedo ◽  
Cătălin Tănase
Keyword(s):  
Synthetic Data ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Seismic Inversion ◽  
Stratified Medium ◽  
Effective Parameters ◽  
Elastic Parameters ◽  
Pp Wave ◽  
Anisotropic Elastic ◽  
And Inversion

Exploration and development of unconventional reservoirs, where fractures and in-situ stresses play a key role, call for improved characterization workflows. Here, we expand on a previously proposed method that makes use of standard isotropic modeling and inversion techniques in anisotropic media. Based on approximations for PP-wave reflection coefficients in orthorhombic media, we build a set of transforms that map the isotropic elastic parameters used in prestack inversion into effective anisotropic elastic parameters. When used in isotropic forward modeling and inversion, these effective parameters accurately mimic the anisotropic reflectivity behavior of the seismic data, thus closing the loop between well-log data and seismic inversion results in the anisotropic case. We show that modeling and inversion of orthorhombic anisotropic media can be achieved by superimposing effective elastic parameters describing the behavior of a horizontally stratified medium and a set of parallel vertical fractures. The process of sequential forward modeling and postinversion analysis is exemplified using synthetic data.

Prestack Kirchhoff depth migration of shallow seismic data

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1241-1247 ◽  
Author(s):  
Linus Pasasa ◽  
Friedemann Wenzel ◽  
Ping Zhao
Keyword(s):  
Waste Disposal ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Disposal Site ◽  
Model Estimation ◽  
Waste Disposal Site ◽  
Depth Migration ◽  
Prestack Migration ◽  
Shallow Seismic ◽  
Kirchhoff Depth Migration

Prestack Kirchhoff depth migration is applied successfully to shallow seismic data from a waste disposal site near Arnstadt in Thuringia, Germany. The motivation behind this study was to locate an underground building buried in a waste disposal. The processing sequence of the prestack migration is simplified significantly as compared to standard common (CMP) data processing. It includes only two parts: (1) velocity‐depth‐model estimation and (2) prestack depth migration. In contrast to conventional CMP stacking, prestack migration does not require a separation of reflections and refractions in the shot data. It still provides an appropriate image. Our data example shows that a superior image can be achieved that would contain not just subtle improvements but a qualitative step forward in resolution and signal‐to‐noise ratio.

scholarly journals Wave Equation Datuming Applied to Seismic Data in Shallow Water Environment and Post-Critical Water Bottom Reflection

Energies ◽  
2017 ◽  
Vol 10 (9) ◽  
pp. 1414 ◽  
Author(s):  
Umberta Tinivella ◽  
Michela Giustiniani ◽  
Ivan Vargas-Cordero
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Seismic Data ◽  
Water Environment ◽  
Shallow Water Environment ◽  
Water Bottom

scholarly journals Musification of Seismic Data

2016 ◽  
Author(s):  
Ryan McGee ◽  
David Rogers
Keyword(s):  
Wave Equation ◽  
New Media ◽  
Seismic Data ◽  
Seismic Events ◽  
Digital Audio ◽  
The Public ◽  
General Wave ◽  
Musical Compositions ◽  
The Creation ◽  
Earth's Crust

Seismic events are physical vibrations induced in the earth’s crust which follow the general wave equation, making seismic data naturally conducive to audification. Simply increasing the playback rates of seismic recordings and rescaling the amplitude values to match those of digital audio samples (straight audification) can produce eerily realistic door slamming and explosion sounds. While others have produced a plethora of sucha udifications for international seismic events (i.e. earthquakes), the resulting sounds, while distinct to the trained auditory scientist, often lack enough variety to produce multiple instrumental timbres for the creation of engaging music for the public. This paper discusses approaches of sonification processing towards eventual musification of seismic data, beginning with straight audification and resulting in several musical compositions and new-media installations containing a variety of seismically derived timbres.

Traveltime information-based wave-equation inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC27-WCC36 ◽  
Author(s):  
Yu Zhang ◽  
Daoliu Wang
Keyword(s):  
Wave Equation ◽  
Conventional Method ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Velocity Model ◽  
Data Fitting ◽  
Inversion Method ◽  
New Wave ◽  
Seismic Record

We propose a new wave-equation inversion method that mainly depends on the traveltime information of the recorded seismic data. Unlike the conventional method, we first apply a [Formula: see text] transform to the seismic data to form the delayed-shot seismic record, back propagate the transformed data, and then invert the velocity model by maximizing the wavefield energy around the shooting time at the source locations. Data fitting is not enforced during the inversion, so the optimized velocity model is obtained by best focusing the source energy after a back propagation. Therefore, inversion accuracy depends only on the traveltime information embedded in the seismic data. This method may overcome some practical issues of waveform inversion; in particular, it relaxes the dependency of the seismic data amplitudes and the source wavelet.

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