1 Direct Estimation of Porosity from Seismic Data using Rock and Wave Physics Informed Neural Networks RW -PINN

2025-04-28 0 0 1.47MB 20 页 10玖币

侵权投诉

Direct Estimation of Porosity from Seismic Data using Rock and Wave Physics Informed

Neural Networks (RW-PINN)

Divakar Vashisth*¹ and Tapan Mukerji2

1Department of Energy Science and Engineering, Stanford University, USA, 2Department of Energy

Science and Engineering, Stanford University, USA; Department of Geological Sciences, Stanford

University, USA; and Department of Geophysics, Stanford University, USA.

email: 1divakar.vashisth98@gmail.com, 2mukerji@stanford.edu

Abstract

Petrophysical inversion is an important aspect of reservoir modeling. However due to the lack of a unique

and straightforward relationship between seismic traces and rock properties, predicting petrophysical

properties directly from seismic data is a complex task. Many studies have attempted to identify the direct

end-to-end link using supervised machine learning techniques, but face different challenges such as a lack

of large petrophysical training dataset or estimates that may not conform with physics or depositional

history of the rocks. We present a rock and wave physics informed neural network (RW-PINN) model

that can estimate porosity directly from seismic image traces with no or limited number of wells, with

predictions that are consistent with rock physics and geologic knowledge of deposition. As an example,

we use the uncemented sand rock physics model and normal-incidence wave physics to guide the learning

of RW-PINN to eventually get good estimates of porosities from normal-incidence seismic traces and

limited well data. Training RW-PINN with few wells (weakly supervised) helps in tackling the problem

of non-uniqueness as different porosity logs can give similar seismic traces. We use weighted normalized

root mean square error loss function to train the weakly supervised network and demonstrate the impact

of different weights on porosity predictions. The RW-PINN estimated porosities and seismic traces are

compared to predictions from a completely supervised model, which gives slightly better porosity

estimates but poorly matches the seismic traces, in addition to requiring a large amount of labeled training

data. In this paper, we demonstrate the complete workflow for executing petrophysical inversion of

seismic data using self-supervised or weakly supervised rock physics informed neural networks.

2 
 
Introduction 
Seismic data is widely used in exploration and exploitation industry to infer subsurface geophysical and 
geological  properties  to  eventually  delineate  an  underlying  reservoir.  The  conventional  approach  for 
reservoir characterization involves geophysical inversion of seismic data to obtain elastic properties like 
seismic velocities and densities (Tarantola, 2005; Sen, 2006; Sen and Stoffa, 2013; Biswas et al., 2019; 
Das et al., 2019) followed by petrophysical inversion with the help of rock physics models obtained from 
core and well log data to retrieve petrophysical properties like porosities and water saturation (Avseth et 
al., 2005; Bachrach, 2006; Mavko et al., 2009, Aleardi, 2018; Grana et al., 2021). Several researchers 
have attempted petrophysical inversion of seismic data using deterministic methods (Angeleri and Carpi, 
1982; Dolberg et al., 2000; Bosch, 2004), stochastic methods (Ma, 2002; Eidsvik et al., 2004; Saltzer et 
al.,  2005;  Bachrach,  2006)  and  geostatistical  methods  (Gonzalez  et  al.,  2008; Bosch  et  al., 
2009a, 2009b; Azevedo  and  Soares,  2017;  Grana  et  al.,  2021).  Avseth  et  al.  (2005)  and  Grana  et  al. 
(2021) have provided a detailed review on different methods and workflows to perform seismic inversion 
for reservoir characterization. 
There is no direct relationship between seismic data and petrophysical properties hence many studies have 
made  use  of  machine  learning  methods  to  approximate  the  complex  nonlinear  functional  mapping 
between  input  (seismic  trace)  and  output  (petrophysical  properties)  without  specifying  any  explicit 
physical relationships. Some examples include the use of support vector regressor and artificial neural 
networks  (Wong  et  al.,  2002; Gholami  and  Ansari,  2017; Chaki  et  al.,  2018;  Singh  et  al., 
2021).  However, these studies  are based on supervised learning that requires  a large labeled training 
dataset that is geologically consistent with the target reservoir, which can hinder the use of supervised 
methods. Das and Mukerji (2020) used convolutional neural networks (CNN) to estimate petrophysical 
properties directly from seismic data  and used  very few  wells to  augment the  training data.  Jo  et al. 
(2021) used ResUNet++ to estimate porosity from spectral decomposed seismic data. 
Another shortcoming of solving the inverse problem using purely supervised learning techniques is that 
the  estimates  are  not  guaranteed  to  be  physically  or  geologically  consistent,  honoring  the  different 

velocity-porosity relations in different depositional environments. To overcome these limitations, we

propose a rock and wave physics informed machine learning model inspired by the autoencoder

architecture (Goodfellow et al., 2016). This machine learning model learns on its own by maximizing the

match between the input and the output. Calderon-Macias et al. (1998) used wave physics informed fully

connected neural network for automatic normal moveout correction and velocity estimation. Biswas et al.

(2019) used wave physics guided CNN for seismic impedance inversion while Dhara and Sen (2022) used

physics guided autoencoder to perform full waveform inversion. Feng et al. (2020) used unsupervised

CNN to estimate porosity from poststack seismic data but required a low-frequency prior porosity along

with the source wavelet to correctly predict the absolute value of porosity.

In this paper, we estimate porosity directly from normal-incidence seismic image trace using rock and

wave physics informed neural network (RW-PINN). We begin with a brief description of our RW-PINN

architecture for both self-supervised and weakly supervised cases. Then, in order to demonstrate the

efficacy of our proposed architecture, we provide insights into the synthetic data we generated using

uncemented sand rock physics model and normal-incidence wave physics model. This is followed by a

comparison between results from completely self-supervised and weakly supervised RW-PINN model

trained using a few wells with a discussion on the impact of number of wells and weights on normalized

root mean square error loss function. Finally, we compare the RW-PINN results with a completely

supervised model and discuss the pros and cons of the different approaches.

Rock and Wave Physics Informed Neural Network (RW-PINN)

The RW-PINN architecture can be sub-divided into two parts: an encoder and a decoder (Figure 1). The

encoder is a deep CNN that takes the seismic trace as input and gives a latent vector as output. Then, this

output vector acts as input for the decoder where it passes through the rock physics block encapsulating

the porosity to velocity relationship, followed by the wave physics block to give normal-incidence

reflectivities that are convolved with the source wavelet to output a predicted seismic trace from the

decoder. The network learns on its own by minimizing the misfit between the input seismic trace and

predicted seismic trace. Once the training is complete, the encoder output vector gets a meaning in the

form of petrophysical porosity and the encoder is separated and used to predict porosity directly from the

seismic trace. For the completely self-supervised case, root mean square (RMS) misfit is minimized

between the input seismic trace and the predicted seismic trace from the decoder.

Figure 1. Self-supervised RW-PINN architecture, where NT is number of time samples and ND is

number of depth samples. Encoder is a deep CNN that is trained to output porosity from a given input

seismic trace while decoder has all the physics required to guide the learning of the encoder.

We use He initialization method (He et al., 2015) for weights while bias terms of all the convolution

layers are initialized to 0 in the encoder. We use dropout regularization (randomly sets 30% of the input

units of a layer to zero at each epoch) only in the last convolution layer to avoid overfitting during

training (Srivastava et al., 2014). Rectified linear units (ReLU) activation function (Nair and Hinton,

2010) is used to introduce non-linearity in the CNN network while hyperbolic tangent (tanh) activation

function is applied to the CNN output vector to scale the output between -1 to 1 before passing it as input

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

1DirectEstimationofPorosityfromSeismicDatausingRockandWavePhysicsInformedNeuralNetworks(RW-PINN)DivakarVashisth*¹andTapanMukerji21DepartmentofEnergyScienceandEngineering,StanfordUniversity,USA,2DepartmentofEnergyScienceandEngineering,StanfordUniversity,USA;DepartmentofGeologicalSciences,StanfordUniv...

展开>> 收起<<

1 Direct Estimation of Porosity from Seismic Data using Rock and Wave Physics Informed Neural Networks RW -PINN.pdf

共20页,预览4页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

1 Direct Estimation of Porosity from Seismic Data using Rock and Wave Physics Informed Neural Networks RW -PINN

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: