Wavelet estimation for a multidimensional acoustic or elastic earth

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 902-913 ◽  
Author(s):  
Arthur B. Weglein ◽  
Bruce G. Secrest
Keyword(s):  
Estimation Method ◽  
Normal Derivative ◽  
Source Spectrum ◽  
Earth Model ◽  
Far Field ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Array Pattern ◽  
The Earth ◽  
Source Array

A new and general wave theoretical wavelet estimation method is derived. Knowing the seismic wavelet is important both for processing seismic data and for modeling the seismic response. To obtain the wavelet, both statistical (e.g., Wiener‐Levinson) and deterministic (matching surface seismic to well‐log data) methods are generally used. In the marine case, a far‐field signature is often obtained with a deep‐towed hydrophone. The statistical methods do not allow obtaining the phase of the wavelet, whereas the deterministic method obviously requires data from a well. The deep‐towed hydrophone requires that the water be deep enough for the hydrophone to be in the far field and in addition that the reflections from the water bottom and structure do not corrupt the measured wavelet. None of the methods address the source array pattern, which is important for amplitude‐versus‐offset (AVO) studies. This paper presents a method of calculating the total wavelet, including the phase and source‐array pattern. When the source locations are specified, the method predicts the source spectrum. When the source is completely unknown (discrete and/or continuously distributed) the method predicts the wavefield due to this source. The method is in principle exact and yet no information about the properties of the earth is required. In addition, the theory allows either an acoustic wavelet (marine) or an elastic wavelet (land), so the wavelet is consistent with the earth model to be used in processing the data. To accomplish this, the method requires a new data collection procedure. It requires that the field and its normal derivative be measured on a surface. The procedure allows the multidimensional earth properties to be arbitrary and acts like a filter to eliminate the scattered energy from the wavelet calculation. The elastic wavelet estimation theory applied in this method may allow a true land wavelet to be obtained. Along with the derivation of the procedure, we present analytic and synthetic examples.

Inversion of controlled source audio‐frequency magnetotellurics data for a horizontally layered earth

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1689-1697 ◽  
Author(s):  
Partha S. Routh ◽  
Douglas W. Oldenburg
Keyword(s):  
Field Data ◽  
Near Field ◽  
Dipole Source ◽  
Earth Model ◽  
Far Field ◽  
Audio Frequency ◽  
Controlled Source ◽  
The Earth ◽  
Data Points ◽  
Corrected Data

We present a technique for inverting controlled source audio‐frequency magnetotelluric (CSAMT) data to recover a 1-D conductivity structure. The earth is modeled as a set of horizontal layers with constant conductivity, and the data are apparent resistivities and phases computed from orthogonal electric and magnetic fields due to a finite dipole source. The earth model has many layers compared to the number of data points, and therefore the solution is nonunique. Among the possible solutions, we seek a model with desired character by minimizing a particular model objective function. Traditionally, CSAMT data are inverted either by using the far‐field data where magnetotelluric (MT) equations are valid or by correcting the near‐field data to an equivalent plane‐wave approximation. Here, we invert both apparent resistivity and phase data from the near‐field transition zone and the far‐field regions in the full CSAMT inversion without any correction. Our inversion is compared with that obtained by inverting near‐field corrected data using an MT algorithm. Both synthetic and field data examples indicate that a full CSAMT inversion provides improved information about subsurface conductivity.

Estimation of the depth-domain seismic wavelet based on velocity substitution and a generalized seismic wavelet model

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
Jie Zhang ◽  
Xuehua Chen ◽  
Wei Jiang ◽  
Yunfei Liu ◽  
He Xu
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Regularization Parameter ◽  
Estimation Method ◽  
Model Parameters ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Hydrocarbon Reservoir ◽  
Convolution Model

Depth-domain seismic wavelet estimation is the essential foundation for depth-imaged data inversion, which is increasingly used for hydrocarbon reservoir characterization in geophysical prospecting. The seismic wavelet in the depth domain stretches with the medium velocity increase and compresses with the medium velocity decrease. The commonly used convolution model cannot be directly used to estimate depth-domain seismic wavelets due to velocity-dependent wavelet variations. We develop a separate parameter estimation method for estimating depth-domain seismic wavelets from poststack depth-domain seismic and well log data. This method is based on the velocity substitution and depth-domain generalized seismic wavelet model defined by the fractional derivative and reference wavenumber. Velocity substitution allows wavelet estimation with the convolution model in the constant-velocity depth domain. The depth-domain generalized seismic wavelet model allows for a simple workflow that estimates the depth-domain wavelet by estimating two wavelet model parameters. Additionally, this simple workflow does not need to perform searches for the optimal regularization parameter and wavelet length, which are time-consuming in least-squares-based methods. The limited numerical search ranges of the two wavelet model parameters can easily be calculated using the constant phase and peak wavenumber of the depth-domain seismic data. Our method is verified using synthetic and real seismic data and further compared with least-squares-based methods. The results indicate that the proposed method is effective and stable even for data with a low S/N.

A novel seismic wavelet estimation method

2013 ◽  
Vol 90 ◽  
pp. 92-95 ◽  
Author(s):  
Jing Zheng ◽  
Su-ping Peng ◽  
Ming-chu Liu ◽  
Zhe Liang
Keyword(s):  
Estimation Method ◽  
Wavelet Estimation ◽  
Seismic Wavelet

Wavelet estimation from marine pressure measurements

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2108-2119 ◽  
Author(s):  
Are Osen ◽  
Bruce G. Secrest ◽  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Pressure Field ◽  
Estimation Method ◽  
Seismic Source ◽  
Time Function ◽  
Pressure Measurements ◽  
Source Time Function ◽  
Wavelet Estimation ◽  
The Earth ◽  
Scattered Energy ◽  
Direct Pressure

A new and alternative procedure for the deterministic estimation of the seismic source time function (wavelet) is proposed. This paper follows a series of reports on source signature estimation, requiring neither statistical assumptions on the signature nor any knowledge about the earth below the receivers. The proposed estimation method, which in principle is exact, uses conventional recordings of the pressure on a surface below the source and recordings of the pressure at one or more locations above the receiver surface. The derivation of the method is based on the Kirchhoff‐Helmholtz integral equation. The formulation ensures that the scattered energy is filtered from the wavelet estimation, enabling the wavelet to be detected from the direct pressure field. Along with the derivation, we present a numerical example.

2.1.3.2 The earth model

2005 ◽  
pp. 85-96
Author(s):  
A. M. Dziewonski ◽  
D. L. Anderson
Keyword(s):  
Earth Model ◽  
The Earth

scholarly journals Rigid-Earth Nutation Models

2000 ◽  
Vol 180 ◽  
pp. 190-195
Author(s):  
J. Souchay
Keyword(s):  
Transfer Function ◽  
Rigid Body ◽  
Earth Model ◽  
High Quality ◽  
Frequency Dependent ◽  
Relative Improvement ◽  
The Earth ◽  
Rigid Earth

AbstractDespite the fact that the main causes of the differences between the observed Earth nutation and that derived from analytical calculations come from geophysical effects associated with nonrigidity (core flattening, core-mantle interactions, oceans, etc…), efforts have been made recently to compute the nutation of the Earth when it is considered to be a rigid body, giving birth to several “rigid Earth nutation models.” The reason for these efforts is that any coefficient of nutation for a realistic Earth (including effects due to nonrigidity) is calculated starting from a coefficient for a rigid-Earth model, using a frequency-dependent transfer function. Therefore it is important to achieve high quality in the determination of rigid-Earth nutation coefficients, in order to isolate the nonrigid effects still not well-modeled.After reviewing various rigid-Earth nutation models which have been established recently and their relative improvement with respect to older ones, we discuss their specifics and their degree of agreement.

Validity of Resolving the 785 km Discontinuity in the Lower Mantle with P′P′ Precursors?

2020 ◽  
Vol 91 (6) ◽  
pp. 3278-3285
Author(s):  
Baolong Zhang ◽  
Xiangfang Zeng ◽  
Jun Xie ◽  
Vernon F. Cormier
Keyword(s):  
Lower Mantle ◽  
Forward Modeling ◽  
Earth Model ◽  
Frequency Content ◽  
Waveform Data ◽  
Mantle Discontinuities ◽  
The Earth ◽  
Earth Models ◽  
Beamforming Technique ◽  
Ray Paths

Abstract P ′ P ′ precursors have been used to detect discontinuities in the lower mantle of the Earth, but some seismic phases propagating along asymmetric ray paths or scattered waves could be misinterpreted as reflections from mantle discontinuities. By forward modeling in standard 1D Earth models, we demonstrate that the frequency content, slowness, and decay with distance of precursors about 180 s before P′P′ arrival are consistent with those of the PKPPdiff phase (or PdiffPKP) at epicentral distances around 78° rather than a reflection from a lower mantle interface. Furthermore, a beamforming technique applied to waveform data recorded at the USArray demonstrates that PKPPdiff can be commonly observed from numerous earthquakes. Hence, a reference 1D Earth model without lower mantle discontinuities can explain many of the observed P′P′ precursors signals if they are interpreted as PKPPdiff, instead of P′785P′. However, this study does not exclude the possibility of 785 km interface beneath the Africa. If this interface indeed exists, P′P′ precursors at distances around 78° would better not be used for its detection to avoid interference from PKPPdiff. Indeed, it could be detected with P′P′ precursors at epicentral distances less than 76° or with other seismic phases such as backscattered PKP·PKP waves.

Robust wavelet estimation and blind deconvolution of noisy surface seismics

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. V37-V46 ◽  
Author(s):  
Mirko van der Baan ◽  
Dinh-Tuan Pham
Keyword(s):  
Blind Deconvolution ◽  
General Purpose ◽  
Sufficient Accuracy ◽  
Wiener Filtering ◽  
Challenging Problem ◽  
Limited Data ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Principal Frequency ◽  
Band Limited

Robust blind deconvolution is a challenging problem, particularly if the bandwidth of the seismic wavelet is narrow to very narrow; that is, if the wavelet bandwidth is similar to its principal frequency. The main problem is to estimate the phase of the wavelet with sufficient accuracy. The mutual information rate is a general-purpose criterion to measure whiteness using statistics of all orders. We modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise. No minimum phase assumptions were made. After wavelet estimation, we obtained an optimal deconvolution output using Wiener filtering. The new procedure performs well, even for very band-limited data; and it produces frequency-dependent phase estimates.

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