scholarly journals Traveltime calculations from frequency‐domain downward‐continuation algorithms

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1380-1388 ◽  
Author(s):  
Changsoo Shin ◽  
Seungwon Ko ◽  
Wonsik Kim ◽  
Dong‐Joo Min ◽  
Dongwoo Yang ◽  
...  
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Downward Continuation ◽  
Calculation Algorithm ◽  
Near Surface ◽  
Absolute Value ◽  
Head Waves ◽  
First Arrival ◽  
The One ◽  
Derivatives Of

We present a new, fast 3D traveltime calculation algorithm that employs existing frequency‐domain wave‐equation downward‐continuation software. By modifying such software to solve for a few complex (rather than real) frequencies, we are able to calculate not only the first arrival and the approximately most energetic traveltimes at each depth point but also their corresponding amplitudes. We compute traveltimes by either taking the logarithm of displacements obtained by the one‐way wave equation at a frequency or calculating derivatives of displacements numerically. Amplitudes are estimated from absolute value of the displacement at a frequency. By using the one‐way downgoing wave equation, we also circumvent generating traveltimes corresponding to near‐surface upcoming head waves not often needed in migration. We compare the traveltimes computed by our algorithm with those obtained by picking the most energetic arrivals from finite‐difference solutions of the one‐way wave equation, and show that our traveltime calculation method yields traveltimes comparable to solutions of the one‐way wave equation. We illustrate the accuracy of our traveltime algorithm by migrating the 2D IFP Marmousi and the 3D SEG/EAGE salt models.

scholarly journals Refraction traveltime tomography using damped monochromatic wavefield

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. U1-U7 ◽  
Author(s):  
Sukjoon Pyun ◽  
Changsoo Shin ◽  
Dong-Joo Min ◽  
Taeyoung Ha
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Computational Effort ◽  
Fréchet Derivative ◽  
Reciprocity Theorem ◽  
Damped Wave Equation ◽  
Traveltime Tomography ◽  
Frechet Derivatives ◽  
First Arrival ◽  
Fréchet Derivatives

For complicated earth models, wave-equation–based refraction-traveltime tomography is more accurate than ray-based tomography but requires more computational effort. Most of the computational effort in traveltime tomography comes from computing traveltimes and their Fréchet derivatives, which for ray-based methods can be computed directly. However, in most wave-equation traveltime-tomography algorithms, the steepest descent direction of the objective function is computed by the backprojection algorithm, without computing a Fréchet derivative directly. We propose a new wave-based refraction-traveltime–tomography procedure that computes Fréchet derivatives directly and efficiently. Our method involves solving a damped-wave equation using a frequency-domain, finite-element modeling algorithm at a single frequency and invoking the reciprocity theorem. A damping factor, which is commonly used to suppress wraparound effects in frequency-domain modeling, plays the role of suppressing multievent wavefields. By limiting the wavefield to a single first arrival, we are able to extract the first-arrival traveltime from the phase term without applying a time window. Computing the partial derivative of the damped wave-equation solution using the reciprocity theorem enables us to compute the Fréchet derivative of amplitude, as well as that of traveltime, with respect to subsurface parameters. Using the Marmousi-2 model, we demonstrate numerically that refraction traveltime tomography with large-offset data can be used to provide the smooth initial velocity model necessary for prestack depth migration.

First-Arrival Traveltime and Amplitude Calculation From Monochromatic Two-Way Wave Equation in Frequency Domain

2005 ◽  
Vol 48 (2) ◽  
pp. 467-473 ◽  
Author(s):  
Yi-Long QIN ◽  
Zhong-Jie ZHANG ◽  
Changsoo Shin ◽  
Ko Seungwon ◽  
Yun CHEN ◽  
...  
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
First Arrival

scholarly journals Hybrid Kinematic-Dynamic Approach to Seismic Wave-Equation Modeling, Imaging, and Tomography

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Alexandr S. Serdyukov ◽  
Anton A. Duchkov
Keyword(s):  
Mechanical Properties ◽  
Wave Equation ◽  
Efficient Implementation ◽  
Equation Modeling ◽  
Computationally Efficient ◽  
Time Step ◽  
Near Surface ◽  
Structure Response ◽  
Seismic Waveforms ◽  
First Arrival

Estimation of the structure response to seismic motion is an important part of structural analysis related to mitigation of seismic risk caused by earthquakes. Many methods of computing structure response require knowledge of mechanical properties of the ground which could be derived from near-surface seismic studies. In this paper we address computationally efficient implementation of the wave-equation tomography. This method allows inverting first-arrival seismic waveforms for updating seismic velocity model which can be further used for estimating mechanical properties. We present computationally efficient hybrid kinematic-dynamic method for finite-difference (FD) modeling of the first-arrival seismic waveforms. At every time step the FD computations are performed only in a moving narrowband following the first-arrival wavefront. In terms of computations we get two advantages from this approach: computation speedup and memory savings when storing computed first-arrival waveforms (it is not necessary to make calculations or store the complete numerical grid). Proposed approach appears to be specifically useful for constructing the so-called sensitivity kernels widely used for tomographic velocity update from seismic data. We then apply the proposed approach for efficient implementation of the wave-equation tomography of the first-arrival seismic waveforms.

Volumetric wavefield recording and wave equation inversion for near‐surface material properties

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1602-1611 ◽  
Author(s):  
Andrew Curtis ◽  
Johan O. A. Robertsson
Keyword(s):  
Wave Equation ◽  
Material Properties ◽  
Surface Condition ◽  
Elastic Wave Equation ◽  
Wave Type ◽  
Near Surface ◽  
The Earth ◽  
Spatial Derivatives ◽  
Seismic Wavefield ◽  
Derivatives Of

“Volumetric recording” of the seismic wavefield implies that the local receiver group or array approximately encloses a volume of the earth. We show how volumetric recording can be used to measure several spatial derivatives of the wavefield. By making use of the full elastic wave equation, the free surface condition on elastic wavefields, and derivative centering techniques analagous to Lax‐Wendroff corrections used in synthetic finite‐difference modeling, these derivative estimates can be inverted for P‐ and S‐velocities in the near surface directly beneath the receiver group. The quantities estimated are the effective velocities of the P‐ and S‐components experienced by the wavefield at any point in time. Hence, the velocity estimates may vary with both wave type and wavelength. The estimates may be useful to aid statics estimation and are exactly the effective velocities required for separation of the wavefield into P‐ and S‐, and up‐ and down‐going components.

Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China

2018 ◽  
Vol 6 (1) ◽  
pp. T1-T13
Author(s):  
Bin Lyu ◽  
Qin Su ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Data Quality ◽  
Model Building ◽  
Velocity Model ◽  
Lateral Velocity ◽  
Near Surface ◽  
Depth Migration ◽  
Time Migration ◽  
Head Waves ◽  
Velocity Variations

Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to-noise ratio that increases the difficulties in building an accurate velocity model for subsequent depth migration. We applied a multidomain cascaded noise attenuation workflow to suppress much of the linear noise. Strong lateral velocity variations occur not only at depth but near the surface as well, distorting the reflections and degrading all deeper images. Conventional elevation corrections followed by refraction statics methods fail in these areas due to poor data quality and the absence of a continuous refracting surface. Although a seismically derived tomographic solution provides an improved image, constraining the solution to the near-surface depth-domain interval velocities measured along the surface outcrop data provides further improvement. Although a one-way wave-equation migration algorithm accounts for the strong lateral velocity variations and complicated structures at depth, modifying the algorithm to account for lateral variation in illumination caused by the irregular topography significantly improves the image, preserving the subsurface amplitude variations. We believe that our step-by-step workflow of addressing the data quality, velocity model building, and seismic imaging developed for the Tuha Basin of China can be applied to other overthrust plays in other parts of the world.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave
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