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ABSTRACT An amplitude variation with angle (AVA) inversion method is presented for estimating density and velocities of a stratified elastic medium from reflection seismograms in the intercept time-horizontal slowness domain. The elastic medium parameters are assumed to vary continuously with depth. The seismograms are Green’s function precritical incidence primary P-wave reflections of time length , assumed to obey differential equations of a model for elastic primary P-wave backscattering, similar to seismograms representing the first term in the well-known Bremmer series/Wentzel–Kramers–Brillouin–Jeffreys iterative solution model. A relation is found between the plane-wave Green’s function seismograms at each horizontal slowness and the medium properties in time. The Green’s function seismograms after normal-moveout correction are directly inverted for the medium parameters as a function of zero-offset traveltime. It is documented theoretically and verified numerically that the signal at the fundamental frequency must be present in the seismograms for the AVA method to provide the parameter trends of the elastic medium, implying that ultralow frequencies <1 Hz for s must be generated and recorded. Noise in the seismograms at ultralow frequencies is not considered because the theoretical AVA model does not handle microseisms that would be measured in real data. The main mathematical findings are illustrated by using simple model seismograms.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
- Geophysics > Seismic Surveying > Seismic Interpretation > Seismic Reservoir Characterization > Amplitude vs Offset (AVO) (1.00)
- Geophysics > Seismic Surveying > Seismic Interpretation > Seismic Reservoir Characterization > Amplitude vs Angle (AVA) (1.00)
ABSTRACT Many modeling techniques have been developed to find the acoustic and elastic responses of a stack of plane layers to a plane spectral wave. For an elastic medium bounded above by an acoustic half-space, the acoustic wave propagator matrix modeling method can be modified to model pseudoelastic PP arrivals and PSSP arrivals. PP arrivals propagate as pure longitudinal (P) waves in the layers, whereas PSSP arrivals propagate as shear (S) waves in the elastic part of the model. A simple modification of the pseudoelastic PP response modeling scheme allows modeling of primary P reflections. A primary reflection event involves just one reflection in the plane stratified model and thus excludes internal multiples. The propagator modeling scheme is formulated in the frequency-horizontal slowness domain. By applying inverse Fourier transforms over the frequency and horizontal wavenumbers, where the wavenumber is the horizontal slowness divided by the frequency, modeled seismograms are computed and displayed in the time-space domain. By applying an inverse Fourier transform over the frequency for selected horizontal slowness components, the computed seismograms can be shown in the intercept time-horizontal slowness () domain. When the source wavelet is unity for frequencies of interest, the domain seismograms become plane-wave Green’s function seismograms. The -traces of the Green’s function primary P-wave seismograms accumulate with increasing time band-limited step functions weighted by reflection strengths.
ABSTRACT A theory is presented for estimating the background velocity and density of an acoustic stratified medium by iterative least-squares waveform inversion in the frequency-horizontal slowness domain of low-frequency precritical reflection incidence seismograms of time length . The initial model is constant. The prerequisites for the method are that the reflection seismograms should be Green’s function seismograms and that the fundamental frequency component is present. Then, the gradients of the objective function provide the low-wavenumber trend of the medium. A matrix formulation for the model update is expressed mathematically by the classic seismogram residual, Jacobian, gradient, and Hessian in the Levenberg-Marquardt approximation. The first iteration, which is equal to a constant-parameter migration inversion (CPMI), is thoroughly analyzed, and expressions for band-limited gradients and block Hessians are found. For primary precritical reflection incidence seismograms of infinite bandwidth, it is shown theoretically that the partial gradients in the CPMI model become a reflection strength-weighted sum of shifted discrete sign functions, typical of step or staircase functions, which provide interface locations in Born depth and amplitudes that can be mapped to velocity and density information. For frequency-band-limited primary reflection seismograms, the partial gradients become a reflection strength-weighted sum of wavenumber-band-limited discrete sign functions. When the fundamental frequency component in the seismograms is present, the band-limited discrete sign functions are oscillatory but keep the information of the step function characteristic of the partial gradient. When the fundamental frequency component in the seismograms is absent, the band-limited discrete sign functions keep information of where the steps are located but lose the information of the amplitudes of the steps. The Hessian elements are nonstandard with the Hessian modeled over a broader frequency range than the frequencies of the observed low-frequency seismogram to avoid it becoming close to singular. The main mathematical findings are illustrated by a simple model and seismograms, for which the background models are found after two iterations. For the sake of completeness, the background models are classically used as initial models in a Levenberg-Marquardt least-squares inversion scheme to estimate the layer velocities and densities from broadband seismograms.
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (0.67)
An amplitude versus angle (AVA) method is presented for estimating density and velocities of a stratified elastic medium. The seismograms are multiple-free, intercept time-horizontal slowness domain Green’s functions of time length T assumed to obey the first order WKBJ model for elastic single P-wave scattering. The WKBJ method is known to apply when the wave appears to be propagating in a medium which is changing slowly relative to the vertical wavelength of the wave. The signal at the fundamental frequency f=1/T where T is record length must be present in the seismograms, implying that ultra-low frequencies <1 Hz for T>1 s must be generated and recorded. A relation is found between planewave Green’s functions at each horizontal slowness and the medium properties in time. The main mathematical findings are illustrated by using simple model seismograms.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.95)
- Geophysics > Seismic Surveying > Seismic Interpretation > Seismic Reservoir Characterization > Amplitude vs Offset (AVO) (0.94)
- Geophysics > Seismic Surveying > Seismic Interpretation > Seismic Reservoir Characterization > Amplitude vs Angle (AVA) (0.65)
ABSTRACT Least-squares full-waveform inversion (FWI) is considered in the frequency domain for a set of noise-free observations of time length at the surface obeying the 1D wave equation, with a known source. The initial model is of constant velocity. The first iteration, which equals the constant-velocity migration inversion (CVMI), is thoroughly analyzed. In CVMI, for the unit source power spectrum, it is within reach to analytically derive and interpret the mathematical formulas of the first-order partial derivatives of the modeled observations (Jacobian), and the gradient and Gauss-Newton Hessian of the objective function, and learn what information the calculation requires to obtain a successful physical result (i.e., velocity update). We recognize the gradient elements, except the last one, to be sums of reflection-amplitude weighted band-limited sign functions and the Hessian elements, except along the last column and row, to be band-limited, diagonal-centered triangle functions, which for infinite bandwidth reduces to the Kronecker delta function. When the fundamental frequency is lacking in the observations, the gradient loses information of the low-wavenumber trend of the velocity update. The Hessian becomes close to singular, and any stabilized inverse has no chance to repair the deficiencies of the gradient caused by any missing low frequency in the observations. FWI is started by applying CVMI. First, Jacobians are modeled by classic reflectivity modeling. Second, the diagonal Hessians can be used for estimating discrete velocity updates. Third, the Jacobian can be modeled in the first-order Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation and by neglecting transmission effects. Finally, single-frequency and low-frequency seismograms can be inverted by using broadband Hessians. The main mathematical findings are developed by simple numerical models and data.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
We review the up-down (U/D) deconvolution and the more general multidimensional deconvolution (MDD) methods for source designature and attenuation of free-surface multiples recorded in ocean-bottom node seismic surveys. In spite of the theoretical limitation of stratified Earth, U/D deconvolution is known to perform well even for complex geology beneath a ‘flattish’ seabed. Examples are shown. MDD is analyzed to explain the good properties of U/D deconvolution. Presentation Date: Tuesday, October 13, 2020 Session Start Time: 1:50 PM Presentation Time: 1:50 PM Location: 362D Presentation Type: Oral
- Europe > Norway > North Sea > Northern North Sea > East Shetland Basin > Block 33/9 > Statfjord Field > Statfjord Group (0.99)
- Europe > Norway > North Sea > Northern North Sea > East Shetland Basin > Block 33/9 > Statfjord Field > Cook Formation (0.99)
- Europe > Norway > North Sea > Northern North Sea > East Shetland Basin > Block 33/9 > Statfjord Field > Brent Group (0.99)
- (10 more...)
Multisource encoding and decoding using the signal apparition technique
Amundsen, Lasse (Statoil Research Center, Norwegian Institute of Science and Technology) | Andersson, Fredrik (Seismic Apparition GmbH, Lund University) | van Manen, Dirk-Jan (Seismic Apparition GmbH, Institute of Geophysics) | Robertsson, Johan O. A. (Seismic Apparition GmbH, Institute of Geophysics) | Eggenberger, Kurt (Seismic Apparition GmbH)
ABSTRACT Signal apparition is a method for encoding sources in simultaneous multisource seismic acquisition and decoding the multisource response of the earth into its single-source responses. For sources, encoding is performed by applying periodic sequences of period to each of the sources along source lines. Decoding is achieved in the wavenumber domain for each frequency by solving an linear system of equations. The system’s matrix is the product of a Fourier matrix and an encoding matrix, the latter containing the information of the codes. The solution of the system is unique when the encoding matrix is invertible. When the encoding sequences consist of time delays applied to sources’ firing times, the determinant of the encoding matrix becomes a polynomial. A unique solution to decoding then exists if the roots of the polynomial avoid the unit circle. Periodic time-shift sequences for two, three, four, and six sources are discussed. A model example of simultaneous four-source data acquisition illustrates the performance of the encoding/decoding technique for the spatially nonaliased case.
- Europe > Norway (0.46)
- Europe > Switzerland (0.29)
- North America > United States (0.28)
- (2 more...)
Abramowitz, M., and I. A. Stegun, 1964, Handbook of Mathematical Almeida, L., 2004, Linear and nonlinear ICA based on mutual Functions, NBS Applied Mathematics Series 55, U.S. Government information - the MISEP method: Signal Processing, 84, no.
- Europe (1.00)
- North America > United States > Texas (0.67)
- North America > Canada > Alberta (0.67)
- Overview (1.00)
- Instructional Material > Course Syllabus & Notes (0.67)
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock (0.67)
- Energy > Oil & Gas > Upstream (1.00)
- Energy > Renewable > Geothermal > Geothermal Resource (0.45)
- Government > Regional Government > North America Government > United States Government (0.34)
- North America > United States > Texas > Permian Basin > Delaware Basin (0.99)
- North America > United States > Texas > East Texas Salt Basin > Alba Field (0.99)
- North America > United States > South Dakota > Williston Basin (0.99)
- (11 more...)
Productivity gains with signal-apparition enabled parallel multisource acquisition
Eggenberger, Kurt (Seismic Apparition GmbH) | Robertsson, Johan (Seismic Apparition GmbH) | Andersson, Fredrik (Seismic Apparition GmbH) | Van Manen, Dirk-Jan (Seismic Apparition GmbH) | Walker, Robin (No2ndPrize Ltd) | Amundsen, Lasse (Statoil ASA)
Similarly, for seabed seismic acquisition the receiver count Parallel multi-source acquisition is achieved by applying the is continuously growing to cover bigger swaths shot with novel method of signal apparition for decoding wavefields smaller shot grids (Lewis et al., 2016). Traditionally, most that were acquired simultaneously. The application of of the innovation took place on the recording hardware side periodically varying shot-to-shot modulation functions to with new cable-and node-based solutions emerging over the the firing times injects energy at predetermined positions years. Receiver handling is becoming increasingly along the wavenumber axes which enables a deterministic automated (Hovland, 2016) and new receiver deployment isolation of individual shots. We demonstrate the method for techniques are further fuelling productivity (Hovland, 2016; single vessel operations, first on a marine dual-source King et al., 2016; Walker et al., 2013). However, this configuration extracted from the SEG Advanced Modeling productivity gain is limited when receiver deployment Program (SEAM) Phase I dataset and then successfully and/or moving becomes unbalanced with source effort. On extend the methodology to an emulated real data marine the source side, productivity gains are achieved by triple-source example from the North Sea. The method is simultaneous multi-vessel acquisition with each vessel applicable both to marine as well as seabed seismic shooting sequential flip-flop but forfeiting the gains from acquisition and offers scope for significant productivity parallel source acquisition.
- Europe > United Kingdom > North Sea (0.37)
- Europe > Norway > North Sea (0.37)
- Europe > North Sea (0.25)
- (2 more...)
ABSTRACT Marine seismic data are distorted by ghosts as waves propagating upwards reflect downwards from the sea surface. Ghosts appear both on the source-side as well as on the receiver-side. However, whereas the receiver-side ghost problem has been studied in detail and many different solutions have been proposed and implemented commercially, the source-side ghost problem has remained largely "unsolved" with few satisfactory commercial solutions available. In this paper we propose a radically new and simple method to remove sea-surface ghosts that relies on using sources at different depths but not at the same lateral positions. The new method promises to be particularly suitable for 3D applications on sparse or incomplete acquisition geometries. Presentation Date: Tuesday, October 18, 2016 Start Time: 4:10:00 PM Location: 163/165 Presentation Type: ORAL