Semblance Features and Deep Learning: A Comprehensive Tutorial on Velocity Model Building

Velocity model building is a cornerstone of seismic data processing, influencing the accuracy of subsurface imaging and subsequent geological interpretations. This article explores the integration of semblance features with deep learning (DL) techniques for enhanced velocity model estimation. It provides a detailed tutorial on leveraging multi-information fusion networks (MIFN) and addresses the challenges and opportunities associated with using both field and synthetic data in DL-driven velocity inversion.

Introduction

Accurate velocity models are crucial for various applications, including:

Geophysical exploration
Monitoring of geologically stored CO2
Improving the quality of seismic images
Enhancing geological interpretation

Traditional velocity model-building methods, such as normal moveout (NMO) correction, tomographic inversion, and full waveform inversion, have been widely used. However, these methods often rely on linearized inversion and simplifying assumptions, which can lead to inadequate representation of subsurface complexities, especially in areas with complex geological features.

Deep learning (DL) offers a promising alternative by using multi-layered neural networks to learn and model complex, nonlinear relationships between input data and target outputs. This article delves into how DL can be effectively used for velocity model building, focusing on the use of semblance features and the development of a multi-information fusion network (MIFN).

Velocity Analysis Fundamentals

Velocity analysis encompasses several key areas:

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Prestack time migration velocity estimation
Stack velocity estimation
Velocity inversion

Prestack time migration velocity uses root mean square (RMS) velocity to optimize the prestack time migration impact. NMO velocity, also known as stack velocity, optimizes the poststack gather. Velocity inversion, the most challenging problem, aims to reconstruct a velocity model that approximates the true subsurface properties.

Traditional methods for stack velocity picking based on prestack common midpoint (CMP) gathers include:

Estimating the best stacking velocity from a range of constant velocities based on the images of the t2−x2 plane or the NMO correction results of the CMP gather.
Semblance analysis, which computes the velocity spectrum and identifies points with the local maximum coherence value as the velocity picking.

These traditional methods are often semi-automatic, requiring significant human participation.

Deep Learning for Velocity Picking

The rapid development of deep learning (DL) has accelerated its application in stack velocity picking. Recent approaches include:

Regression Models: Convolutional neural networks (CNNs) map the NMO-corrected seismic gather to the NMO velocity deviation to obtain the NMO velocity (stack velocity).
Recurrent Neural Networks (RNNs): RNNs recognize NMO velocity directly from CMP gather fragment images.
Object Detection Algorithms: Algorithms like You Only Look Once (YOLO) detect energy blobs on the velocity spectrum, often optimized with long short-term memory (LSTM) networks.
Image Classification Methods: These methods regress each segment split by the time domain to a velocity encode.
CNN-based Feature Extraction: CNNs encode the CMP gather to a mid-level feature like the velocity spectrum, with recursive CNNs and LSTM networks used to estimate principal reflection time, RMS velocity, and interval velocity.
Iterative Estimation Methods: These methods perform NMO correction on prestack CMP gathers using a set of NMO velocities estimated on the velocity spectrum for initialization, followed by NMO CMP gather detection using a deep CNN.

Multi-Information Fusion Network (MIFN)

This article proposes an automatic velocity picking method using a multi-information fusion network (MIFN) based on U-Net. U-Net has been widely used in seismic data processing for tasks such as velocity auto-picking, seismic data reconstruction, seismic data interpolation, and first break picking.

The MIFN approach enhances the U-Net architecture by adding the stacked gather slice (SGS) to the input of the segmentation network. This helps achieve spectrum pickup with low signal-to-noise ratio (SNR). The SGS contains adjacent sample information and velocity prior information, improving the picking accuracy of low SNR velocity spectra and the robustness of picking results. Compared to iterative methods, MIFN requires only one prediction, significantly reducing computational costs.

MIFN Architecture and Components

The proposed velocity automatic picking method consists of four main steps:

Feature Map Computation: Input the velocity spectrum and the SGS to compute feature maps separately.
Multi-Information Fusion: Concatenate the feature maps from the first step to fuse the multi-information.
Semantic Segmentation: Employ U-Net to complete the semantic segmentation task.

Semblance Calculation

Seismic velocity spectrum is calculated from CMP gathers using a coherence measure, i.e., stacked amplitude, normalized stacked amplitude, semblance, etc. In this paper, we use the semblance.

Velocity Spectrum Enhancement

To address the instability of local estimation and balance the capacity to recognize energy clusters with different sizes, a velocity spectrum enhancement method is proposed. This method obtains multi-observation spectra, simulating how people observe the spectrum with different distances and focus.

The spectrum enhancement method involves several steps:

Local Smoothing: Balances the column signals of the velocity spectrum and enhances local weak signals.
Exponential Inflation: Enhances the strong signals.
Layer-wise Normalization: Balances the signals of deep and shallow layers, strengthening weak signals in the deep layers.
Amplitude Limitation: Removes global weak signals and suppresses excessively strong signals.

This enhanced method equalizes the signal information of the velocity spectrum without changing the local extremum. Different combinations of parameters can simulate visual signals when the human eye observes the velocity spectrum at different distances with distinct focus. Nine groups of parameters are selected to generate nine enhanced feature maps as a part of the network input, denoted as multi-scale feature maps.

Stacked Gather Slice (SGS)

For velocity spectra with low SNR, the semantic information required for automatic velocity pickup is relatively sparse. Therefore, adding other information is necessary to enrich the semantic information of segmentation. In this work, the SGS, which contains the nearby gathers information, assists in guiding the semantic segmentation model.

SGS is a stacked amplitude gather scanned by a series of stacking velocity curves, calculated by multiplying the reference velocity by a series of percentages. These scanned gathers correspond to the velocity spectra of the current CMP and the adjacent CMPs. The reference velocity generally adopts the regional velocity or the velocity of the adjacent work area.

SGS Encoder

The SGS encoder consists of two encoding processes:

Velocity Curve (VC) Encoding: Velocity curve is encoded as a VC mask.
SGS Gather Encoding: SGS gather is encoded as a SGS vector.

Each row of the VC mask is multiplied by each element of the SGS vector to obtain the SGS feature map.

The SGS gather encoder has three basic modules:

Convolution-Batch Normalization-Leaky ReLU (CBL) Module: Consists of a convolutional layer, a batch-normalization layer, and a Leaky ReLU.
Spatial Pyramid Pooling (SPP) Module: Extracts multi-scale features using max pooling layers.
Bilinear Interpolation (BI) Module: Interpolates the map to a vector with the same length as the spectrum, providing flexibility to respond to dimensional changes.

MIFN Architecture Details

The proposed MIFN is divided into three parts:

Precoding Part: Extracts basic feature maps of the velocity spectrum and SGS based on geophysics knowledge, consisting of a spectrum feature extractor and SGS encoder.
Encoder: U-Net's down-sample block (DB) consisting of two CBR modules and a max pooling layer.
Decoder: U-Net's up-sample block (UB) with a 2D transposed convolution operator, ReLU activation layer, and CBR modules.

The precoding part completes the information encoding and feature fusion of the velocity spectrum and SGS. The precoded features are input to U-Net to implement semantic segmentation. To precode the information of the velocity spectrum, the spectrum enhance method is used as a spectrum feature extractor (SFE) to obtain the multi-scale observation spectrum, which is then concatenated with the original velocity spectrum.

Training the MIFN

For training the MIFN, the soft label and Binary cross entropy (BCE) loss function are adopted.

Field Data vs. Synthetic Data

DL models can be trained using either field data or synthetic data. Each approach has its advantages and disadvantages:

Field Data

Advantages: Models trained on field data produce superior results, more geologically plausible predictions, and sharper geophysical migration images.
Disadvantages: Labeled field data can be scarce, and the data may contain noise and artifacts that can affect the model's performance.

Synthetic Data

Advantages: Synthetic data can be generated in large quantities and with precise labels. It is especially useful when labeled field data are scarce.
Disadvantages: Models trained on synthetic data may not generalize well to field data due to the domain gap between the two.

The efficacy of synthetic data-driven models largely depends on bridging the domain gap between training and test data through the use of advanced wave equation solvers and geologic priors.

Bridging the Domain Gap

To effectively use synthetic data for training DL models, it is crucial to minimize the domain gap between synthetic and field data. This can be achieved by:

Using advanced wave equation solvers (acoustic or elastic) to accurately model seismic wave propagation.
Incorporating detailed geologic priors into the synthetic model.
Matching the acquisition parameters of the field shot gathers.
Employing data augmentation techniques to increase the variability of the training data.

Case Study: Gulf of Mexico

A study focused on a challenging region of the Gulf of Mexico demonstrates DL's capability to harness labeled seismograms for accurate velocity model recovery. The 3D seismic dataset includes a legacy seismic velocity model that only partially overlaps with the corresponding seismic data. The seismic data have been preprocessed following standard industry practices, including denoising, deghosting, direct arrival removal, and 5D interpolation.

Data Preparation

The legacy velocity model and seismic data are divided into training and testing folds. The training fold encompasses seismic data that overlap with complete portions of the velocity model, whereas the test fold includes seismic data covering incomplete sections of the legacy model.

The input data features are adjacent 2D seismic shot gathers, combined to form a 3D tensor. Output labels are 2D velocity models probed by their respective input data features.

Network Architecture

The DL architecture is a simple encoder-decoder design with convolutional layers, which are known for their ability to capture spatially correlated input features in seismic data.

Training Datasets

Several datasets are employed to train DL models, with each one’s performance evaluated on the test fold. The distinct input features define the differences between the training datasets, which are never mixed. These datasets include:

Field Data: Seismic data fully overlapping with complete portions of the legacy velocity model.
Synthetic Data (Acoustic Wave Equation): Labeled synthetic training data created using the acoustic wave equation.
Synthetic Data (Elastic Wave Equation): Labeled synthetic training data created using the elastic wave equation.

tags: #semblance #features #deep #learning #velocity #model