A new paper is added to the collection of reproducible documents: Fast streaming local time-frequency transform for nonstationary seismic data processing 

Schematic illustration of the proposed SLTFT

The CPU time comparison among the time-frequency analysis methods. Orange line: STFT; blue dash line: SLTFT; red dot line: streaming attributes; green dash-dot line: LTF decomposition. The convergence speed affects the CPU time of the LTF decomposition, resulting in a non-smooth curve

Time-frequency analysis serves as a useful approach to solve different complex problems in seismic data processing. From a practical standpoint, the majority of time-frequency transform techniques frequently grapple with the trade-off between time and frequency localization adaptability, flexibility in sampling time and frequency, and the pursuit of computational efficiency. To address this, we tailor the streaming computation to implement a fast time-frequency transform, namely the streaming local time-frequency transform (SLTFT), which can significantly decrease the computational cost of adaptive time-frequency analysis. We add a localization scalar to the proceeding streaming algorithm to circumvent the need for taper functions, which provides rapid forward and inverse transforms and applicability in various scenarios. We demonstrate the adaptive time-frequency characteristics of the proposed method, which offers a nonstationary time-frequency representation with variable time-frequency localization. Numerical tests indicate that the proposed SLTFT is a more balanced method compared to previous time-frequency adaptive transforms. It proves suitable for a range of practical applications in nonstationary seismic data processing, including ground-roll attenuation, inverse-Q filtering, and multicomponent data registration.

An old paper is added to the collection of reproducible documents: Effects of lateral heterogeneity on time-domain processing parameters

Time-domain processing of seismic reflection data has always been an important engine that is routinely utilized to produce seismic images and to expeditiously construct subsurface models. The conventional procedure involves analysing parameters related to the derivatives of reflection traveltime with respect to offset including normal moveout (NMO) velocities (second-order derivatives) and quartic coefficients (fourth-order derivatives). In this study, we propose to go beyond the typical assumption of 1-D laterally homogeneous medium when relating those ‘processing’ parameters to the subsurface medium parameters and take into account the additional influences from lateral heterogeneity including curved interfaces and smoothly variable velocities. We fill in the theoretical gap from previous studies and develop a general framework for such connection in layered anisotropic media. We show that in general, the influences of lateral heterogeneity get accumulated from all layers via a recursive relationship according to the Fermat’s principle and can be approximately quantified in terms of the lateral derivatives of the layer interface surfaces and velocities. Based on the same general principle, we show that our approach can also be used to study the lateral heterogeneity effects on diffraction traveltime and its second-order derivative related to time-migration velocity. In this paper, we explicitly specify expressions for NMO and time-migration velocities with the influences from both types of heterogeneity suitable for 2-D data sets and also discuss possible extensions of the proposed theory to 3-D data sets and to parameters related to higher-order traveltime derivatives. Using numerical examples, we demonstrate that the proposed theory can lead to more accurate reflection and diffraction traveltime predictions in comparison with those obtained based on the 1-D assumption. Both the proposed theoretical framework and its numerical testing for forward traveltime computation presented in this study aid in understanding the effects from lateral heterogeneity on time-processing parameters and also serve as an important basis for designing an efficient technique to separate those influences in important processes such as Dix inversion for a more accurate subsurface model in the future.

An old paper is added to the collection of reproducible documents: Well log interpolation guided by geologic distance

Seismic reflection images can be used to interpolate rock properties between well logs. However, geologic faults may introduce discontinuities that interfere with the interpolation. We propose a modification of an image guided well log interpolation method that incorporates geologic structures including faults and unconformities. We first use predictive painting to spread the lithological information along seismic images from well locations. Then we measure the geologic distance following seismic horizons, and modify the distance across faults during interpolation based on fault attribute measurements. After that, painting interpolation not only honors the seismic horizon structures, but also gets constrained at faults while still remaining effective within the range of conforming regions. Both synthetic and field data examples show a significant improvement in robustness of predictive painting interpolation in complex subsurface structure around fault location.

An old paper is added to the collection of reproducible documents: Estimation of timeshifts in time-lapse seismic images using spectral decomposition

Time-lapse timeshifts are difficult to measure from seismic data in the presense of low frequencies or thin beds causing tuning effects. We propose to decompose time-lapse seismic images into discrete frequency components using the local time-frequency transform before estimating timeshifts. Use of high frequency components mitigate problems associated with sidelobe interference. We use amplitude-adjusted plane-wave destruction (APWD) filters to invert for both timeshifts and amplitude changes between the time-lapse seismic images at each frequency. Plane-wave destruction can efficiently measure small shifts between seismic traces, making this algorithm particularly effective. The effectiveness of the proposed workflow is confirmed using a 1D synthetic example and a field data example from the Cranfield CO sequestration project.

An old paper is added to the collection of reproducible documents: Least-squares non-stationary triangle smoothing

We propose a fast and accurate method to estimate the radius of non-stationary triangle smoothing for matching two seismic datasets. The smoothing radius is estimated by non-linear least-squares inversion using an iterative Gauss-Newton approach. We derive and implement the derivative of the smoothing operator to compute the gradient for inversion. The proposed method is useful for implementing non-stationary triangle smoothing as a low-cost edge-preserving filter. The efficiency of the proposed method is also confirmed in several field data examples of seismic data matching applications in non-stationary local signal and noise orthogonalization, non-stationary local slope estimation, and matching low-resolution and high resolution seismic images from the same exploration area.

An old paper is added to the collection of reproducible documents: Investigating the possibility of locating microseismic sources using distributed sensor networks

Distributed sensor networks are designed to provide computation in-situ and in real-time. The conventional time-reversal imaging approach for microseismic event location may not be optimal for such an environment. To address this challenge, we develop a methodology of locating multiple microseismic events with unknown start times based on the cross-correlation imaging condition borrowed from active-source seismic imaging. The imaging principle states that a true microseismic source must correspond to the location where all the backward-propagated events coincide in both space and time. Instead of simply stacking the backward-propagated seismic wavefields, as suggested by time-reversal imaging, we perform multiplication reduction to compute a high-resolution microseismicity map. The map has an extra dimension of time, indicating the start times of different events. Combined with a distributed sensor network, our method is designed for monitoring microseismic activities and mapping fracture development during hydraulic fracturing in-situ and in real-time. We use numerical examples to test the ability of the proposed technique to produce high-resolution images of microseismic locations.

An old paper is added to the collection of reproducible documents: Using well-seismic mistie to update the velocity model

We propose a method to aid in velocity model building based on misties between modeled synthetic seismograms from well log data and the seismic image. The method is based on the fact that when the migration velocity is inconsistent with the true migration velocity, there is a mistie between a modeled synthetic seismogram from well log data and the seismic image. The proposed approach uses local similarity to estimate the mistie at every sample along the synthetic seismogram and uses the result to update the migration velocity at the well location. The updated velocity information is interpolated along seismic structure using predictive painting to generate a new geologically consistent velocity model. We iteratively update the migration velocity model using only the seismic-well tie mistie. The results of our experiments with a simple layered model and an isotropic synthetic model indicate that the proposed workflow provides an effective method for integrating well log data in conventional velocity model building workflows.

An old paper is added to the collection of reproducible documents: Full waveform inversion of passive seismic data for sources and velocities

From the seismic imaging point of view, the difficulty in locating passive seismic sources lies in their unknown start times. In other words, the source model has an additional dimension of time, which leads to an extended model space. Without proper preconditioning, the computational cost of directly inverting for the source functions can be intractable. Using the recently proposed cross-correlation time-reversal imaging condition, we formulate the imaging task as an inverse problem, and use a sparse weighting function calculated from the cross-correlation of back-propagated events to constrain the model space. We demonstrate that the proposed approach can effectively reduce the number of model parameters, leading to a rapid convergence rate using preconditioned conjugate-gradient iterations. The least-squares imaging of passive seismic sources can be further incorporated into full waveform inversion for Earth properties using the variable projection method. Synthetic examples verify the proposed method.

An old paper is added to the collection of reproducible documents: Microseismic source localization using time-domain path-integral migration

Localization of passive seismic sources is crucial for real-time monitoring of hydraulic fracturing. Using the similarity of diffraction imaging and passive seismic imaging, we propose a method that uses path-integral formulation to apply diffraction-type migration on time-shifted microseismic records and to focus seismic energy focuses at correct onsets and accurate locations in time coordinates. An efficient workflow is applied to do path-integral migration based on analytical integration. Passive seismic sources can be additionally highlighted by envelope stacking. Numerical experiments with synthetic data verify the effectiveness of the proposed method.